1,1,116,0,0.802603," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^9,x, algorithm=""maxima"")","-\frac{2520 \, a \log\left(\cos\left(d x + c\right)\right) - \frac{2520 \, a \cos\left(d x + c\right)^{8} - 5040 \, a \cos\left(d x + c\right)^{7} - 3360 \, a \cos\left(d x + c\right)^{6} + 3780 \, a \cos\left(d x + c\right)^{5} + 3024 \, a \cos\left(d x + c\right)^{4} - 1680 \, a \cos\left(d x + c\right)^{3} - 1440 \, a \cos\left(d x + c\right)^{2} + 315 \, a \cos\left(d x + c\right) + 280 \, a}{\cos\left(d x + c\right)^{9}}}{2520 \, d}"," ",0,"-1/2520*(2520*a*log(cos(d*x + c)) - (2520*a*cos(d*x + c)^8 - 5040*a*cos(d*x + c)^7 - 3360*a*cos(d*x + c)^6 + 3780*a*cos(d*x + c)^5 + 3024*a*cos(d*x + c)^4 - 1680*a*cos(d*x + c)^3 - 1440*a*cos(d*x + c)^2 + 315*a*cos(d*x + c) + 280*a)/cos(d*x + c)^9)/d","A",0
2,1,94,0,0.350111," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^7,x, algorithm=""maxima"")","\frac{420 \, a \log\left(\cos\left(d x + c\right)\right) - \frac{420 \, a \cos\left(d x + c\right)^{6} - 630 \, a \cos\left(d x + c\right)^{5} - 420 \, a \cos\left(d x + c\right)^{4} + 315 \, a \cos\left(d x + c\right)^{3} + 252 \, a \cos\left(d x + c\right)^{2} - 70 \, a \cos\left(d x + c\right) - 60 \, a}{\cos\left(d x + c\right)^{7}}}{420 \, d}"," ",0,"1/420*(420*a*log(cos(d*x + c)) - (420*a*cos(d*x + c)^6 - 630*a*cos(d*x + c)^5 - 420*a*cos(d*x + c)^4 + 315*a*cos(d*x + c)^3 + 252*a*cos(d*x + c)^2 - 70*a*cos(d*x + c) - 60*a)/cos(d*x + c)^7)/d","A",0
3,1,72,0,0.609151," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^5,x, algorithm=""maxima"")","-\frac{60 \, a \log\left(\cos\left(d x + c\right)\right) - \frac{60 \, a \cos\left(d x + c\right)^{4} - 60 \, a \cos\left(d x + c\right)^{3} - 40 \, a \cos\left(d x + c\right)^{2} + 15 \, a \cos\left(d x + c\right) + 12 \, a}{\cos\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*a*log(cos(d*x + c)) - (60*a*cos(d*x + c)^4 - 60*a*cos(d*x + c)^3 - 40*a*cos(d*x + c)^2 + 15*a*cos(d*x + c) + 12*a)/cos(d*x + c)^5)/d","A",0
4,1,50,0,0.482527," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{6 \, a \log\left(\cos\left(d x + c\right)\right) - \frac{6 \, a \cos\left(d x + c\right)^{2} - 3 \, a \cos\left(d x + c\right) - 2 \, a}{\cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*a*log(cos(d*x + c)) - (6*a*cos(d*x + c)^2 - 3*a*cos(d*x + c) - 2*a)/cos(d*x + c)^3)/d","A",0
5,1,26,0,0.789104," ","integrate((a+a*sec(d*x+c))*tan(d*x+c),x, algorithm=""maxima"")","-\frac{a \log\left(\cos\left(d x + c\right)\right) - \frac{a}{\cos\left(d x + c\right)}}{d}"," ",0,"-(a*log(cos(d*x + c)) - a/cos(d*x + c))/d","A",0
6,1,14,0,0.515011," ","integrate(cot(d*x+c)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\cos\left(d x + c\right) - 1\right)}{d}"," ",0,"a*log(cos(d*x + c) - 1)/d","A",0
7,1,42,0,0.718121," ","integrate(cot(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) - \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) - 2*a/(cos(d*x + c) - 1))/d","A",0
8,1,86,0,0.588456," ","integrate(cot(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) - \frac{2 \, {\left(5 \, a \cos\left(d x + c\right)^{2} + 3 \, 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) - 2*(5*a*cos(d*x + c)^2 + 3*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
9,1,126,0,0.569302," ","integrate(cot(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) - \frac{2 \, {\left(33 \, a \cos\left(d x + c\right)^{4} + 39 \, a \cos\left(d x + c\right)^{3} - 79 \, a \cos\left(d x + c\right)^{2} - 29 \, 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) - 2*(33*a*cos(d*x + c)^4 + 39*a*cos(d*x + c)^3 - 79*a*cos(d*x + c)^2 - 29*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
10,1,164,0,0.527312," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^8,x, algorithm=""maxima"")","\frac{256 \, {\left(15 \, \tan\left(d x + c\right)^{7} - 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 105 \, d x + 105 \, c - 105 \, \tan\left(d x + c\right)\right)} a + 35 \, a {\left(\frac{2 \, {\left(279 \, \sin\left(d x + c\right)^{7} - 511 \, \sin\left(d x + c\right)^{5} + 385 \, \sin\left(d x + c\right)^{3} - 105 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \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)\right)}}{26880 \, d}"," ",0,"1/26880*(256*(15*tan(d*x + c)^7 - 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 105*d*x + 105*c - 105*tan(d*x + c))*a + 35*a*(2*(279*sin(d*x + c)^7 - 511*sin(d*x + c)^5 + 385*sin(d*x + c)^3 - 105*sin(d*x + c))/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) + 105*log(sin(d*x + c) + 1) - 105*log(sin(d*x + c) - 1)))/d","A",0
11,1,134,0,0.817009," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^6,x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a - 5 \, a {\left(\frac{2 \, {\left(33 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \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)\right)}}{480 \, d}"," ",0,"1/480*(32*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a - 5*a*(2*(33*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 15*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) + 15*log(sin(d*x + c) + 1) - 15*log(sin(d*x + c) - 1)))/d","A",0
12,1,102,0,0.894069," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a + 3 \, a {\left(\frac{2 \, {\left(5 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \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)\right)}}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a + 3*a*(2*(5*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1)))/d","A",0
13,1,65,0,0.687454," ","integrate((a+a*sec(d*x+c))*tan(d*x+c)^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a + a {\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)}}{4 \, d}"," ",0,"-1/4*(4*(d*x + c - tan(d*x + c))*a + a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)))/d","A",0
14,1,31,0,1.222229," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a + \frac{a}{\sin\left(d x + c\right)}}{d}"," ",0,"-((d*x + c + 1/tan(d*x + c))*a + a/sin(d*x + c))/d","A",0
15,1,59,0,1.158750," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a + \frac{{\left(3 \, \sin\left(d x + c\right)^{2} - 1\right)} a}{\sin\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*((3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a + (3*sin(d*x + c)^2 - 1)*a/sin(d*x + c)^3)/d","A",0
16,1,79,0,0.620405," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a + \frac{{\left(15 \, \sin\left(d x + c\right)^{4} - 10 \, \sin\left(d x + c\right)^{2} + 3\right)} a}{\sin\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*((15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a + (15*sin(d*x + c)^4 - 10*sin(d*x + c)^2 + 3)*a/sin(d*x + c)^5)/d","A",0
17,1,100,0,1.029475," ","integrate(cot(d*x+c)^8*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(105 \, d x + 105 \, c + \frac{105 \, \tan\left(d x + c\right)^{6} - 35 \, \tan\left(d x + c\right)^{4} + 21 \, \tan\left(d x + c\right)^{2} - 15}{\tan\left(d x + c\right)^{7}}\right)} a + \frac{3 \, {\left(35 \, \sin\left(d x + c\right)^{6} - 35 \, \sin\left(d x + c\right)^{4} + 21 \, \sin\left(d x + c\right)^{2} - 5\right)} a}{\sin\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*((105*d*x + 105*c + (105*tan(d*x + c)^6 - 35*tan(d*x + c)^4 + 21*tan(d*x + c)^2 - 15)/tan(d*x + c)^7)*a + 3*(35*sin(d*x + c)^6 - 35*sin(d*x + c)^4 + 21*sin(d*x + c)^2 - 5)*a/sin(d*x + c)^7)/d","A",0
18,1,119,0,0.823137," ","integrate(cot(d*x+c)^10*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(315 \, d x + 315 \, c + \frac{315 \, \tan\left(d x + c\right)^{8} - 105 \, \tan\left(d x + c\right)^{6} + 63 \, \tan\left(d x + c\right)^{4} - 45 \, \tan\left(d x + c\right)^{2} + 35}{\tan\left(d x + c\right)^{9}}\right)} a + \frac{{\left(315 \, \sin\left(d x + c\right)^{8} - 420 \, \sin\left(d x + c\right)^{6} + 378 \, \sin\left(d x + c\right)^{4} - 180 \, \sin\left(d x + c\right)^{2} + 35\right)} a}{\sin\left(d x + c\right)^{9}}}{315 \, d}"," ",0,"-1/315*((315*d*x + 315*c + (315*tan(d*x + c)^8 - 105*tan(d*x + c)^6 + 63*tan(d*x + c)^4 - 45*tan(d*x + c)^2 + 35)/tan(d*x + c)^9)*a + (315*sin(d*x + c)^8 - 420*sin(d*x + c)^6 + 378*sin(d*x + c)^4 - 180*sin(d*x + c)^2 + 35)*a/sin(d*x + c)^9)/d","A",0
19,1,149,0,0.319646," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^9,x, algorithm=""maxima"")","-\frac{2520 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{5040 \, a^{2} \cos\left(d x + c\right)^{9} - 3780 \, a^{2} \cos\left(d x + c\right)^{8} - 6720 \, a^{2} \cos\left(d x + c\right)^{7} + 1260 \, a^{2} \cos\left(d x + c\right)^{6} + 6048 \, a^{2} \cos\left(d x + c\right)^{5} + 840 \, a^{2} \cos\left(d x + c\right)^{4} - 2880 \, a^{2} \cos\left(d x + c\right)^{3} - 945 \, a^{2} \cos\left(d x + c\right)^{2} + 560 \, a^{2} \cos\left(d x + c\right) + 252 \, a^{2}}{\cos\left(d x + c\right)^{10}}}{2520 \, d}"," ",0,"-1/2520*(2520*a^2*log(cos(d*x + c)) - (5040*a^2*cos(d*x + c)^9 - 3780*a^2*cos(d*x + c)^8 - 6720*a^2*cos(d*x + c)^7 + 1260*a^2*cos(d*x + c)^6 + 6048*a^2*cos(d*x + c)^5 + 840*a^2*cos(d*x + c)^4 - 2880*a^2*cos(d*x + c)^3 - 945*a^2*cos(d*x + c)^2 + 560*a^2*cos(d*x + c) + 252*a^2)/cos(d*x + c)^10)/d","A",0
20,1,110,0,0.427428," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^7,x, algorithm=""maxima"")","\frac{840 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{1680 \, a^{2} \cos\left(d x + c\right)^{7} - 840 \, a^{2} \cos\left(d x + c\right)^{6} - 1680 \, a^{2} \cos\left(d x + c\right)^{5} + 1008 \, a^{2} \cos\left(d x + c\right)^{3} + 280 \, a^{2} \cos\left(d x + c\right)^{2} - 240 \, a^{2} \cos\left(d x + c\right) - 105 \, a^{2}}{\cos\left(d x + c\right)^{8}}}{840 \, d}"," ",0,"1/840*(840*a^2*log(cos(d*x + c)) - (1680*a^2*cos(d*x + c)^7 - 840*a^2*cos(d*x + c)^6 - 1680*a^2*cos(d*x + c)^5 + 1008*a^2*cos(d*x + c)^3 + 280*a^2*cos(d*x + c)^2 - 240*a^2*cos(d*x + c) - 105*a^2)/cos(d*x + c)^8)/d","A",0
21,1,97,0,0.697478," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^5,x, algorithm=""maxima"")","-\frac{60 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{120 \, a^{2} \cos\left(d x + c\right)^{5} - 30 \, a^{2} \cos\left(d x + c\right)^{4} - 80 \, a^{2} \cos\left(d x + c\right)^{3} - 15 \, a^{2} \cos\left(d x + c\right)^{2} + 24 \, a^{2} \cos\left(d x + c\right) + 10 \, a^{2}}{\cos\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(60*a^2*log(cos(d*x + c)) - (120*a^2*cos(d*x + c)^5 - 30*a^2*cos(d*x + c)^4 - 80*a^2*cos(d*x + c)^3 - 15*a^2*cos(d*x + c)^2 + 24*a^2*cos(d*x + c) + 10*a^2)/cos(d*x + c)^6)/d","A",0
22,1,58,0,0.355197," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{12 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{24 \, a^{2} \cos\left(d x + c\right)^{3} - 8 \, a^{2} \cos\left(d x + c\right) - 3 \, a^{2}}{\cos\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*a^2*log(cos(d*x + c)) - (24*a^2*cos(d*x + c)^3 - 8*a^2*cos(d*x + c) - 3*a^2)/cos(d*x + c)^4)/d","A",0
23,1,43,0,0.317911," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c),x, algorithm=""maxima"")","-\frac{2 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{4 \, a^{2} \cos\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*a^2*log(cos(d*x + c)) - (4*a^2*cos(d*x + c) + a^2)/cos(d*x + c)^2)/d","A",0
24,1,31,0,0.392362," ","integrate(cot(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) - a^{2} \log\left(\cos\left(d x + c\right)\right)}{d}"," ",0,"(2*a^2*log(cos(d*x + c) - 1) - a^2*log(cos(d*x + c)))/d","A",0
25,1,34,0,0.528843," ","integrate(cot(d*x+c)^3*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{a^{2}}{\cos\left(d x + c\right) - 1}}{d}"," ",0,"-(a^2*log(cos(d*x + c) - 1) - a^2/(cos(d*x + c) - 1))/d","A",0
26,1,72,0,0.644010," ","integrate(cot(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) + 7 \, a^{2} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, {\left(5 \, a^{2} \cos\left(d x + c\right) - 4 \, a^{2}\right)}}{\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1}}{8 \, d}"," ",0,"1/8*(a^2*log(cos(d*x + c) + 1) + 7*a^2*log(cos(d*x + c) - 1) - 2*(5*a^2*cos(d*x + c) - 4*a^2)/(cos(d*x + c)^2 - 2*cos(d*x + c) + 1))/d","A",0
27,1,109,0,0.559604," ","integrate(cot(d*x+c)^7*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{9 \, a^{2} \log\left(\cos\left(d x + c\right) + 1\right) + 39 \, a^{2} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, {\left(33 \, a^{2} \cos\left(d x + c\right)^{3} - 18 \, a^{2} \cos\left(d x + c\right)^{2} - 37 \, a^{2} \cos\left(d x + c\right) + 26 \, a^{2}\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right) - 1}}{48 \, d}"," ",0,"-1/48*(9*a^2*log(cos(d*x + c) + 1) + 39*a^2*log(cos(d*x + c) - 1) - 2*(33*a^2*cos(d*x + c)^3 - 18*a^2*cos(d*x + c)^2 - 37*a^2*cos(d*x + c) + 26*a^2)/(cos(d*x + c)^4 - 2*cos(d*x + c)^3 + 2*cos(d*x + c) - 1))/d","A",0
28,1,165,0,0.454064," ","integrate(cot(d*x+c)^9*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{87 \, a^{2} \log\left(\cos\left(d x + c\right) + 1\right) + 297 \, a^{2} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, {\left(279 \, a^{2} \cos\left(d x + c\right)^{5} - 78 \, a^{2} \cos\left(d x + c\right)^{4} - 634 \, a^{2} \cos\left(d x + c\right)^{3} + 338 \, a^{2} \cos\left(d x + c\right)^{2} + 343 \, a^{2} \cos\left(d x + c\right) - 224 \, a^{2}\right)}}{\cos\left(d x + c\right)^{6} - 2 \, \cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1}}{384 \, d}"," ",0,"1/384*(87*a^2*log(cos(d*x + c) + 1) + 297*a^2*log(cos(d*x + c) - 1) - 2*(279*a^2*cos(d*x + c)^5 - 78*a^2*cos(d*x + c)^4 - 634*a^2*cos(d*x + c)^3 + 338*a^2*cos(d*x + c)^2 + 343*a^2*cos(d*x + c) - 224*a^2)/(cos(d*x + c)^6 - 2*cos(d*x + c)^5 - cos(d*x + c)^4 + 4*cos(d*x + c)^3 - cos(d*x + c)^2 - 2*cos(d*x + c) + 1))/d","A",0
29,1,151,0,0.666497," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^6,x, algorithm=""maxima"")","\frac{240 \, a^{2} \tan\left(d x + c\right)^{7} + 112 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a^{2} - 35 \, a^{2} {\left(\frac{2 \, {\left(33 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \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)\right)}}{1680 \, d}"," ",0,"1/1680*(240*a^2*tan(d*x + c)^7 + 112*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a^2 - 35*a^2*(2*(33*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 15*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) + 15*log(sin(d*x + c) + 1) - 15*log(sin(d*x + c) - 1)))/d","A",0
30,1,119,0,0.637004," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{24 \, a^{2} \tan\left(d x + c\right)^{5} + 40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{2} + 15 \, a^{2} {\left(\frac{2 \, {\left(5 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \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)\right)}}{120 \, d}"," ",0,"1/120*(24*a^2*tan(d*x + c)^5 + 40*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^2 + 15*a^2*(2*(5*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1)))/d","A",0
31,1,83,0,0.820124," ","integrate((a+a*sec(d*x+c))^2*tan(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, a^{2} \tan\left(d x + c\right)^{3} - 6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} - 3 \, a^{2} {\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 \, d}"," ",0,"1/6*(2*a^2*tan(d*x + c)^3 - 6*(d*x + c - tan(d*x + c))*a^2 - 3*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)))/d","A",0
32,1,48,0,0.575974," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{2} + \frac{2 \, a^{2}}{\sin\left(d x + c\right)} + \frac{a^{2}}{\tan\left(d x + c\right)}}{d}"," ",0,"-((d*x + c + 1/tan(d*x + c))*a^2 + 2*a^2/sin(d*x + c) + a^2/tan(d*x + c))/d","A",0
33,1,77,0,0.716900," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{2} + \frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 1\right)} a^{2}}{\sin\left(d x + c\right)^{3}} - \frac{a^{2}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*((3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^2 + 2*(3*sin(d*x + c)^2 - 1)*a^2/sin(d*x + c)^3 - a^2/tan(d*x + c)^3)/d","A",0
34,1,97,0,0.542805," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{2} + \frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} - 10 \, \sin\left(d x + c\right)^{2} + 3\right)} a^{2}}{\sin\left(d x + c\right)^{5}} + \frac{3 \, a^{2}}{\tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*((15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^2 + 2*(15*sin(d*x + c)^4 - 10*sin(d*x + c)^2 + 3)*a^2/sin(d*x + c)^5 + 3*a^2/tan(d*x + c)^5)/d","A",0
35,1,117,0,0.834142," ","integrate(cot(d*x+c)^8*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(105 \, d x + 105 \, c + \frac{105 \, \tan\left(d x + c\right)^{6} - 35 \, \tan\left(d x + c\right)^{4} + 21 \, \tan\left(d x + c\right)^{2} - 15}{\tan\left(d x + c\right)^{7}}\right)} a^{2} + \frac{6 \, {\left(35 \, \sin\left(d x + c\right)^{6} - 35 \, \sin\left(d x + c\right)^{4} + 21 \, \sin\left(d x + c\right)^{2} - 5\right)} a^{2}}{\sin\left(d x + c\right)^{7}} - \frac{15 \, a^{2}}{\tan\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*((105*d*x + 105*c + (105*tan(d*x + c)^6 - 35*tan(d*x + c)^4 + 21*tan(d*x + c)^2 - 15)/tan(d*x + c)^7)*a^2 + 6*(35*sin(d*x + c)^6 - 35*sin(d*x + c)^4 + 21*sin(d*x + c)^2 - 5)*a^2/sin(d*x + c)^7 - 15*a^2/tan(d*x + c)^7)/d","A",0
36,1,137,0,0.757378," ","integrate(cot(d*x+c)^10*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(315 \, d x + 315 \, c + \frac{315 \, \tan\left(d x + c\right)^{8} - 105 \, \tan\left(d x + c\right)^{6} + 63 \, \tan\left(d x + c\right)^{4} - 45 \, \tan\left(d x + c\right)^{2} + 35}{\tan\left(d x + c\right)^{9}}\right)} a^{2} + \frac{2 \, {\left(315 \, \sin\left(d x + c\right)^{8} - 420 \, \sin\left(d x + c\right)^{6} + 378 \, \sin\left(d x + c\right)^{4} - 180 \, \sin\left(d x + c\right)^{2} + 35\right)} a^{2}}{\sin\left(d x + c\right)^{9}} + \frac{35 \, a^{2}}{\tan\left(d x + c\right)^{9}}}{315 \, d}"," ",0,"-1/315*((315*d*x + 315*c + (315*tan(d*x + c)^8 - 105*tan(d*x + c)^6 + 63*tan(d*x + c)^4 - 45*tan(d*x + c)^2 + 35)/tan(d*x + c)^9)*a^2 + 2*(315*sin(d*x + c)^8 - 420*sin(d*x + c)^6 + 378*sin(d*x + c)^4 - 180*sin(d*x + c)^2 + 35)*a^2/sin(d*x + c)^9 + 35*a^2/tan(d*x + c)^9)/d","A",0
37,1,162,0,0.654982," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^9,x, algorithm=""maxima"")","-\frac{27720 \, a^{3} \log\left(\cos\left(d x + c\right)\right) - \frac{83160 \, a^{3} \cos\left(d x + c\right)^{10} - 13860 \, a^{3} \cos\left(d x + c\right)^{9} - 101640 \, a^{3} \cos\left(d x + c\right)^{8} - 41580 \, a^{3} \cos\left(d x + c\right)^{7} + 77616 \, a^{3} \cos\left(d x + c\right)^{6} + 64680 \, a^{3} \cos\left(d x + c\right)^{5} - 23760 \, a^{3} \cos\left(d x + c\right)^{4} - 38115 \, a^{3} \cos\left(d x + c\right)^{3} - 3080 \, a^{3} \cos\left(d x + c\right)^{2} + 8316 \, a^{3} \cos\left(d x + c\right) + 2520 \, a^{3}}{\cos\left(d x + c\right)^{11}}}{27720 \, d}"," ",0,"-1/27720*(27720*a^3*log(cos(d*x + c)) - (83160*a^3*cos(d*x + c)^10 - 13860*a^3*cos(d*x + c)^9 - 101640*a^3*cos(d*x + c)^8 - 41580*a^3*cos(d*x + c)^7 + 77616*a^3*cos(d*x + c)^6 + 64680*a^3*cos(d*x + c)^5 - 23760*a^3*cos(d*x + c)^4 - 38115*a^3*cos(d*x + c)^3 - 3080*a^3*cos(d*x + c)^2 + 8316*a^3*cos(d*x + c) + 2520*a^3)/cos(d*x + c)^11)/d","A",0
38,1,110,0,0.362520," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^7,x, algorithm=""maxima"")","\frac{360 \, a^{3} \log\left(\cos\left(d x + c\right)\right) - \frac{1080 \, a^{3} \cos\left(d x + c\right)^{8} - 960 \, a^{3} \cos\left(d x + c\right)^{6} - 540 \, a^{3} \cos\left(d x + c\right)^{5} + 432 \, a^{3} \cos\left(d x + c\right)^{4} + 480 \, a^{3} \cos\left(d x + c\right)^{3} - 135 \, a^{3} \cos\left(d x + c\right) - 40 \, a^{3}}{\cos\left(d x + c\right)^{9}}}{360 \, d}"," ",0,"1/360*(360*a^3*log(cos(d*x + c)) - (1080*a^3*cos(d*x + c)^8 - 960*a^3*cos(d*x + c)^6 - 540*a^3*cos(d*x + c)^5 + 432*a^3*cos(d*x + c)^4 + 480*a^3*cos(d*x + c)^3 - 135*a^3*cos(d*x + c) - 40*a^3)/cos(d*x + c)^9)/d","A",0
39,1,110,0,0.618561," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^5,x, algorithm=""maxima"")","-\frac{420 \, a^{3} \log\left(\cos\left(d x + c\right)\right) - \frac{1260 \, a^{3} \cos\left(d x + c\right)^{6} + 210 \, a^{3} \cos\left(d x + c\right)^{5} - 700 \, a^{3} \cos\left(d x + c\right)^{4} - 525 \, a^{3} \cos\left(d x + c\right)^{3} + 84 \, a^{3} \cos\left(d x + c\right)^{2} + 210 \, a^{3} \cos\left(d x + c\right) + 60 \, a^{3}}{\cos\left(d x + c\right)^{7}}}{420 \, d}"," ",0,"-1/420*(420*a^3*log(cos(d*x + c)) - (1260*a^3*cos(d*x + c)^6 + 210*a^3*cos(d*x + c)^5 - 700*a^3*cos(d*x + c)^4 - 525*a^3*cos(d*x + c)^3 + 84*a^3*cos(d*x + c)^2 + 210*a^3*cos(d*x + c) + 60*a^3)/cos(d*x + c)^7)/d","A",0
40,1,84,0,0.465712," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{60 \, a^{3} \log\left(\cos\left(d x + c\right)\right) - \frac{180 \, a^{3} \cos\left(d x + c\right)^{4} + 60 \, a^{3} \cos\left(d x + c\right)^{3} - 40 \, a^{3} \cos\left(d x + c\right)^{2} - 45 \, a^{3} \cos\left(d x + c\right) - 12 \, a^{3}}{\cos\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*a^3*log(cos(d*x + c)) - (180*a^3*cos(d*x + c)^4 + 60*a^3*cos(d*x + c)^3 - 40*a^3*cos(d*x + c)^2 - 45*a^3*cos(d*x + c) - 12*a^3)/cos(d*x + c)^5)/d","A",0
41,1,58,0,0.676088," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c),x, algorithm=""maxima"")","-\frac{6 \, a^{3} \log\left(\cos\left(d x + c\right)\right) - \frac{18 \, a^{3} \cos\left(d x + c\right)^{2} + 9 \, a^{3} \cos\left(d x + c\right) + 2 \, a^{3}}{\cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(6*a^3*log(cos(d*x + c)) - (18*a^3*cos(d*x + c)^2 + 9*a^3*cos(d*x + c) + 2*a^3)/cos(d*x + c)^3)/d","A",0
42,1,43,0,0.597732," ","integrate(cot(d*x+c)*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, a^{3} \log\left(\cos\left(d x + c\right) - 1\right) - 3 \, a^{3} \log\left(\cos\left(d x + c\right)\right) + \frac{a^{3}}{\cos\left(d x + c\right)}}{d}"," ",0,"(4*a^3*log(cos(d*x + c) - 1) - 3*a^3*log(cos(d*x + c)) + a^3/cos(d*x + c))/d","A",0
43,1,34,0,0.611695," ","integrate(cot(d*x+c)^3*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{a^{3} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, a^{3}}{\cos\left(d x + c\right) - 1}}{d}"," ",0,"-(a^3*log(cos(d*x + c) - 1) - 2*a^3/(cos(d*x + c) - 1))/d","A",0
44,1,59,0,0.408749," ","integrate(cot(d*x+c)^5*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, a^{3} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{4 \, a^{3} \cos\left(d x + c\right) - 3 \, a^{3}}{\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1}}{2 \, d}"," ",0,"1/2*(2*a^3*log(cos(d*x + c) - 1) - (4*a^3*cos(d*x + c) - 3*a^3)/(cos(d*x + c)^2 - 2*cos(d*x + c) + 1))/d","A",0
45,1,96,0,0.524215," ","integrate(cot(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) + 45 \, a^{3} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, {\left(51 \, a^{3} \cos\left(d x + c\right)^{2} - 81 \, a^{3} \cos\left(d x + c\right) + 34 \, a^{3}\right)}}{\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) - 1}}{48 \, d}"," ",0,"-1/48*(3*a^3*log(cos(d*x + c) + 1) + 45*a^3*log(cos(d*x + c) - 1) - 2*(51*a^3*cos(d*x + c)^2 - 81*a^3*cos(d*x + c) + 34*a^3)/(cos(d*x + c)^3 - 3*cos(d*x + c)^2 + 3*cos(d*x + c) - 1))/d","A",0
46,1,142,0,0.373244," ","integrate(cot(d*x+c)^9*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{21 \, a^{3} \log\left(\cos\left(d x + c\right) + 1\right) + 171 \, a^{3} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, {\left(213 \, a^{3} \cos\left(d x + c\right)^{4} - 303 \, a^{3} \cos\left(d x + c\right)^{3} - 95 \, a^{3} \cos\left(d x + c\right)^{2} + 333 \, a^{3} \cos\left(d x + c\right) - 136 \, a^{3}\right)}}{\cos\left(d x + c\right)^{5} - 3 \, \cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right) + 1}}{192 \, d}"," ",0,"1/192*(21*a^3*log(cos(d*x + c) + 1) + 171*a^3*log(cos(d*x + c) - 1) - 2*(213*a^3*cos(d*x + c)^4 - 303*a^3*cos(d*x + c)^3 - 95*a^3*cos(d*x + c)^2 + 333*a^3*cos(d*x + c) - 136*a^3)/(cos(d*x + c)^5 - 3*cos(d*x + c)^4 + 2*cos(d*x + c)^3 + 2*cos(d*x + c)^2 - 3*cos(d*x + c) + 1))/d","A",0
47,1,262,0,0.821587," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^6,x, algorithm=""maxima"")","\frac{11520 \, a^{3} \tan\left(d x + c\right)^{7} + 1792 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a^{3} + 35 \, a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{7} + 73 \, \sin\left(d x + c\right)^{5} - 55 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \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)\right)} - 840 \, a^{3} {\left(\frac{2 \, {\left(33 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \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)\right)}}{26880 \, d}"," ",0,"1/26880*(11520*a^3*tan(d*x + c)^7 + 1792*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a^3 + 35*a^3*(2*(15*sin(d*x + c)^7 + 73*sin(d*x + c)^5 - 55*sin(d*x + c)^3 + 15*sin(d*x + c))/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 840*a^3*(2*(33*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 15*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) + 15*log(sin(d*x + c) + 1) - 15*log(sin(d*x + c) - 1)))/d","A",0
48,1,210,0,0.455373," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{288 \, a^{3} \tan\left(d x + c\right)^{5} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{3} - 5 \, a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} + 8 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \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)\right)} + 90 \, a^{3} {\left(\frac{2 \, {\left(5 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \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)\right)}}{480 \, d}"," ",0,"1/480*(288*a^3*tan(d*x + c)^5 + 160*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^3 - 5*a^3*(2*(3*sin(d*x + c)^5 + 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 90*a^3*(2*(5*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1)))/d","A",0
49,1,147,0,0.451654," ","integrate((a+a*sec(d*x+c))^3*tan(d*x+c)^2,x, algorithm=""maxima"")","\frac{16 \, a^{3} \tan\left(d x + c\right)^{3} - 16 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} + a^{3} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \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)} - 12 \, 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)}}{16 \, d}"," ",0,"1/16*(16*a^3*tan(d*x + c)^3 - 16*(d*x + c - tan(d*x + c))*a^3 + a^3*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*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)))/d","A",0
50,1,85,0,0.433955," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{3} + 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)} + \frac{6 \, a^{3}}{\sin\left(d x + c\right)} + \frac{6 \, a^{3}}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c + 1/tan(d*x + c))*a^3 + a^3*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*a^3/sin(d*x + c) + 6*a^3/tan(d*x + c))/d","A",0
51,1,90,0,0.430720," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{3} + \frac{3 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 1\right)} a^{3}}{\sin\left(d x + c\right)^{3}} - \frac{a^{3}}{\sin\left(d x + c\right)^{3}} - \frac{3 \, a^{3}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*((3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^3 + 3*(3*sin(d*x + c)^2 - 1)*a^3/sin(d*x + c)^3 - a^3/sin(d*x + c)^3 - 3*a^3/tan(d*x + c)^3)/d","A",0
52,1,122,0,0.436921," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{3} + \frac{3 \, {\left(15 \, \sin\left(d x + c\right)^{4} - 10 \, \sin\left(d x + c\right)^{2} + 3\right)} a^{3}}{\sin\left(d x + c\right)^{5}} - \frac{{\left(5 \, \sin\left(d x + c\right)^{2} - 3\right)} a^{3}}{\sin\left(d x + c\right)^{5}} + \frac{9 \, a^{3}}{\tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*((15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^3 + 3*(15*sin(d*x + c)^4 - 10*sin(d*x + c)^2 + 3)*a^3/sin(d*x + c)^5 - (5*sin(d*x + c)^2 - 3)*a^3/sin(d*x + c)^5 + 9*a^3/tan(d*x + c)^5)/d","A",0
53,1,152,0,0.450137," ","integrate(cot(d*x+c)^8*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(105 \, d x + 105 \, c + \frac{105 \, \tan\left(d x + c\right)^{6} - 35 \, \tan\left(d x + c\right)^{4} + 21 \, \tan\left(d x + c\right)^{2} - 15}{\tan\left(d x + c\right)^{7}}\right)} a^{3} + \frac{9 \, {\left(35 \, \sin\left(d x + c\right)^{6} - 35 \, \sin\left(d x + c\right)^{4} + 21 \, \sin\left(d x + c\right)^{2} - 5\right)} a^{3}}{\sin\left(d x + c\right)^{7}} - \frac{{\left(35 \, \sin\left(d x + c\right)^{4} - 42 \, \sin\left(d x + c\right)^{2} + 15\right)} a^{3}}{\sin\left(d x + c\right)^{7}} - \frac{45 \, a^{3}}{\tan\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*((105*d*x + 105*c + (105*tan(d*x + c)^6 - 35*tan(d*x + c)^4 + 21*tan(d*x + c)^2 - 15)/tan(d*x + c)^7)*a^3 + 9*(35*sin(d*x + c)^6 - 35*sin(d*x + c)^4 + 21*sin(d*x + c)^2 - 5)*a^3/sin(d*x + c)^7 - (35*sin(d*x + c)^4 - 42*sin(d*x + c)^2 + 15)*a^3/sin(d*x + c)^7 - 45*a^3/tan(d*x + c)^7)/d","A",0
54,1,182,0,0.453660," ","integrate(cot(d*x+c)^10*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(315 \, d x + 315 \, c + \frac{315 \, \tan\left(d x + c\right)^{8} - 105 \, \tan\left(d x + c\right)^{6} + 63 \, \tan\left(d x + c\right)^{4} - 45 \, \tan\left(d x + c\right)^{2} + 35}{\tan\left(d x + c\right)^{9}}\right)} a^{3} + \frac{3 \, {\left(315 \, \sin\left(d x + c\right)^{8} - 420 \, \sin\left(d x + c\right)^{6} + 378 \, \sin\left(d x + c\right)^{4} - 180 \, \sin\left(d x + c\right)^{2} + 35\right)} a^{3}}{\sin\left(d x + c\right)^{9}} - \frac{{\left(105 \, \sin\left(d x + c\right)^{6} - 189 \, \sin\left(d x + c\right)^{4} + 135 \, \sin\left(d x + c\right)^{2} - 35\right)} a^{3}}{\sin\left(d x + c\right)^{9}} + \frac{105 \, a^{3}}{\tan\left(d x + c\right)^{9}}}{315 \, d}"," ",0,"-1/315*((315*d*x + 315*c + (315*tan(d*x + c)^8 - 105*tan(d*x + c)^6 + 63*tan(d*x + c)^4 - 45*tan(d*x + c)^2 + 35)/tan(d*x + c)^9)*a^3 + 3*(315*sin(d*x + c)^8 - 420*sin(d*x + c)^6 + 378*sin(d*x + c)^4 - 180*sin(d*x + c)^2 + 35)*a^3/sin(d*x + c)^9 - (105*sin(d*x + c)^6 - 189*sin(d*x + c)^4 + 135*sin(d*x + c)^2 - 35)*a^3/sin(d*x + c)^9 + 105*a^3/tan(d*x + c)^9)/d","A",0
55,1,212,0,0.442399," ","integrate(cot(d*x+c)^12*(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(3465 \, d x + 3465 \, c + \frac{3465 \, \tan\left(d x + c\right)^{10} - 1155 \, \tan\left(d x + c\right)^{8} + 693 \, \tan\left(d x + c\right)^{6} - 495 \, \tan\left(d x + c\right)^{4} + 385 \, \tan\left(d x + c\right)^{2} - 315}{\tan\left(d x + c\right)^{11}}\right)} a^{3} + \frac{15 \, {\left(693 \, \sin\left(d x + c\right)^{10} - 1155 \, \sin\left(d x + c\right)^{8} + 1386 \, \sin\left(d x + c\right)^{6} - 990 \, \sin\left(d x + c\right)^{4} + 385 \, \sin\left(d x + c\right)^{2} - 63\right)} a^{3}}{\sin\left(d x + c\right)^{11}} - \frac{{\left(1155 \, \sin\left(d x + c\right)^{8} - 2772 \, \sin\left(d x + c\right)^{6} + 2970 \, \sin\left(d x + c\right)^{4} - 1540 \, \sin\left(d x + c\right)^{2} + 315\right)} a^{3}}{\sin\left(d x + c\right)^{11}} - \frac{945 \, a^{3}}{\tan\left(d x + c\right)^{11}}}{3465 \, d}"," ",0,"1/3465*((3465*d*x + 3465*c + (3465*tan(d*x + c)^10 - 1155*tan(d*x + c)^8 + 693*tan(d*x + c)^6 - 495*tan(d*x + c)^4 + 385*tan(d*x + c)^2 - 315)/tan(d*x + c)^11)*a^3 + 15*(693*sin(d*x + c)^10 - 1155*sin(d*x + c)^8 + 1386*sin(d*x + c)^6 - 990*sin(d*x + c)^4 + 385*sin(d*x + c)^2 - 63)*a^3/sin(d*x + c)^11 - (1155*sin(d*x + c)^8 - 2772*sin(d*x + c)^6 + 2970*sin(d*x + c)^4 - 1540*sin(d*x + c)^2 + 315)*a^3/sin(d*x + c)^11 - 945*a^3/tan(d*x + c)^11)/d","A",0
56,1,90,0,0.319148," ","integrate(tan(d*x+c)^9/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{420 \, \log\left(\cos\left(d x + c\right)\right)}{a} + \frac{420 \, \cos\left(d x + c\right)^{6} + 630 \, \cos\left(d x + c\right)^{5} - 420 \, \cos\left(d x + c\right)^{4} - 315 \, \cos\left(d x + c\right)^{3} + 252 \, \cos\left(d x + c\right)^{2} + 70 \, \cos\left(d x + c\right) - 60}{a \cos\left(d x + c\right)^{7}}}{420 \, d}"," ",0,"-1/420*(420*log(cos(d*x + c))/a + (420*cos(d*x + c)^6 + 630*cos(d*x + c)^5 - 420*cos(d*x + c)^4 - 315*cos(d*x + c)^3 + 252*cos(d*x + c)^2 + 70*cos(d*x + c) - 60)/(a*cos(d*x + c)^7))/d","A",0
57,1,70,0,0.326014," ","integrate(tan(d*x+c)^7/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{60 \, \log\left(\cos\left(d x + c\right)\right)}{a} + \frac{60 \, \cos\left(d x + c\right)^{4} + 60 \, \cos\left(d x + c\right)^{3} - 40 \, \cos\left(d x + c\right)^{2} - 15 \, \cos\left(d x + c\right) + 12}{a \cos\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*log(cos(d*x + c))/a + (60*cos(d*x + c)^4 + 60*cos(d*x + c)^3 - 40*cos(d*x + c)^2 - 15*cos(d*x + c) + 12)/(a*cos(d*x + c)^5))/d","A",0
58,1,50,0,0.320443," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{6 \, \log\left(\cos\left(d x + c\right)\right)}{a} + \frac{6 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) - 2}{a \cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(6*log(cos(d*x + c))/a + (6*cos(d*x + c)^2 + 3*cos(d*x + c) - 2)/(a*cos(d*x + c)^3))/d","A",0
59,1,28,0,0.317422," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\cos\left(d x + c\right)\right)}{a} + \frac{1}{a \cos\left(d x + c\right)}}{d}"," ",0,"(log(cos(d*x + c))/a + 1/(a*cos(d*x + c)))/d","A",0
60,1,17,0,0.320541," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a d}"," ",0,"-log(cos(d*x + c) + 1)/(a*d)","A",0
61,1,47,0,0.324119," ","integrate(cot(d*x+c)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{3 \, \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*(3*log(cos(d*x + c) + 1)/a + log(cos(d*x + c) - 1)/a + 2/(a*cos(d*x + c) + a))/d","A",0
62,1,91,0,0.688831," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right) - 6\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{11 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a} + \frac{5 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a}}{16 \, d}"," ",0,"-1/16*(2*(5*cos(d*x + c)^2 - 3*cos(d*x + c) - 6)/(a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) - a) + 11*log(cos(d*x + c) + 1)/a + 5*log(cos(d*x + c) - 1)/a)/d","A",0
63,1,130,0,0.327567," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(33 \, \cos\left(d x + c\right)^{4} - 39 \, \cos\left(d x + c\right)^{3} - 79 \, \cos\left(d x + c\right)^{2} + 29 \, \cos\left(d x + c\right) + 44\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{63 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a} + \frac{33 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a}}{96 \, d}"," ",0,"1/96*(2*(33*cos(d*x + c)^4 - 39*cos(d*x + c)^3 - 79*cos(d*x + c)^2 + 29*cos(d*x + c) + 44)/(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) + 63*log(cos(d*x + c) + 1)/a + 33*log(cos(d*x + c) - 1)/a)/d","A",0
64,1,329,0,0.787385," ","integrate(tan(d*x+c)^8/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{165 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1095 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3138 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5118 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{1945 \, \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}}\right)}}{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{480 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{75 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{75 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a}}{240 \, d}"," ",0,"-1/240*(2*(165*sin(d*x + c)/(cos(d*x + c) + 1) - 1095*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3138*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5118*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 1945*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 315*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) - 480*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 75*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - 75*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a)/d","B",0
65,1,247,0,0.541064," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{71 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{137 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{33 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{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{48 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a}}{24 \, d}"," ",0,"1/24*(2*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 71*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 137*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 33*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) - 48*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 9*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - 9*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a)/d","B",0
66,1,163,0,0.779844," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\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}}\right)}}{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{4 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a}}{2 \, d}"," ",0,"-1/2*(2*(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) - 4*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a)/d","B",0
67,1,78,0,0.640911," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a}}{d}"," ",0,"-(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a)/d","B",0
68,1,93,0,0.603034," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{12 \, \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} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{3 \, {\left(\cos\left(d x + c\right) + 1\right)}}{a \sin\left(d x + c\right)}}{12 \, d}"," ",0,"1/12*((12*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 3*(cos(d*x + c) + 1)/(a*sin(d*x + c)))/d","A",0
69,1,137,0,0.965300," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(\frac{80 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a} - \frac{480 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{5 \, {\left(\frac{18 \, \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*(3*(80*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a - 480*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 5*(18*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
70,1,177,0,0.590424," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{6720 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1015 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{168 \, \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{13440 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{7 \, {\left(\frac{40 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{435 \, \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*((6720*sin(d*x + c)/(cos(d*x + c) + 1) - 1015*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 168*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a - 13440*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 7*(40*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 435*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","A",0
71,1,80,0,0.333033," ","integrate(tan(d*x+c)^9/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{60 \, \log\left(\cos\left(d x + c\right)\right)}{a^{2}} + \frac{120 \, \cos\left(d x + c\right)^{5} + 30 \, \cos\left(d x + c\right)^{4} - 80 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)^{2} + 24 \, \cos\left(d x + c\right) - 10}{a^{2} \cos\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(60*log(cos(d*x + c))/a^2 + (120*cos(d*x + c)^5 + 30*cos(d*x + c)^4 - 80*cos(d*x + c)^3 + 15*cos(d*x + c)^2 + 24*cos(d*x + c) - 10)/(a^2*cos(d*x + c)^6))/d","A",0
72,1,50,0,0.439099," ","integrate(tan(d*x+c)^7/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{12 \, \log\left(\cos\left(d x + c\right)\right)}{a^{2}} + \frac{24 \, \cos\left(d x + c\right)^{3} - 8 \, \cos\left(d x + c\right) + 3}{a^{2} \cos\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*log(cos(d*x + c))/a^2 + (24*cos(d*x + c)^3 - 8*cos(d*x + c) + 3)/(a^2*cos(d*x + c)^4))/d","A",0
73,1,40,0,0.872839," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, \log\left(\cos\left(d x + c\right)\right)}{a^{2}} + \frac{4 \, \cos\left(d x + c\right) - 1}{a^{2} \cos\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*log(cos(d*x + c))/a^2 + (4*cos(d*x + c) - 1)/(a^2*cos(d*x + c)^2))/d","A",0
74,1,31,0,0.326268," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}} - \frac{\log\left(\cos\left(d x + c\right)\right)}{a^{2}}}{d}"," ",0,"(2*log(cos(d*x + c) + 1)/a^2 - log(cos(d*x + c))/a^2)/d","A",0
75,1,35,0,0.410480," ","integrate(tan(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{\log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}}}{d}"," ",0,"-(1/(a^2*cos(d*x + c) + a^2) + log(cos(d*x + c) + 1)/a^2)/d","A",0
76,1,74,0,0.322275," ","integrate(cot(d*x+c)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(5 \, \cos\left(d x + c\right) + 4\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}} + \frac{7 \, \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*(5*cos(d*x + c) + 4)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2) + 7*log(cos(d*x + c) + 1)/a^2 + log(cos(d*x + c) - 1)/a^2)/d","A",0
77,1,110,0,0.325814," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(33 \, \cos\left(d x + c\right)^{3} + 18 \, \cos\left(d x + c\right)^{2} - 37 \, \cos\left(d x + c\right) - 26\right)}}{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}} + \frac{39 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}} + \frac{9 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{2}}}{48 \, d}"," ",0,"-1/48*(2*(33*cos(d*x + c)^3 + 18*cos(d*x + c)^2 - 37*cos(d*x + c) - 26)/(a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^3 - 2*a^2*cos(d*x + c) - a^2) + 39*log(cos(d*x + c) + 1)/a^2 + 9*log(cos(d*x + c) - 1)/a^2)/d","A",0
78,1,167,0,0.453880," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(279 \, \cos\left(d x + c\right)^{5} + 78 \, \cos\left(d x + c\right)^{4} - 634 \, \cos\left(d x + c\right)^{3} - 338 \, \cos\left(d x + c\right)^{2} + 343 \, \cos\left(d x + c\right) + 224\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{297 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2}} + \frac{87 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{2}}}{384 \, d}"," ",0,"1/384*(2*(279*cos(d*x + c)^5 + 78*cos(d*x + c)^4 - 634*cos(d*x + c)^3 - 338*cos(d*x + c)^2 + 343*cos(d*x + c) + 224)/(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) + 297*log(cos(d*x + c) + 1)/a^2 + 87*log(cos(d*x + c) - 1)/a^2)/d","A",0
79,1,301,0,0.606512," ","integrate(tan(d*x+c)^8/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{110 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{328 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{530 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{105 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)}}{a^{2} - \frac{5 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{10 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{45 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} - \frac{45 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}}{60 \, d}"," ",0,"-1/60*(2*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 110*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 328*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 530*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 105*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^2 - 5*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 10*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 45*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 - 45*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2)/d","B",0
80,1,196,0,0.821158," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(\frac{\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}}\right)}}{a^{2} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{6 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}}{3 \, d}"," ",0,"-1/3*(4*(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 - 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 6*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2)/d","B",0
81,1,123,0,0.513121," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{\sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"2*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)))/d","B",0
82,1,49,0,0.916449," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{\sin\left(d x + c\right)}{a^{2} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-2*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - sin(d*x + c)/(a^2*(cos(d*x + c) + 1)))/d","A",0
83,1,113,0,0.591043," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{165 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \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{240 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{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*((165*sin(d*x + c)/(cos(d*x + c) + 1) - 25*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 - 240*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 15*(cos(d*x + c) + 1)/(a^2*sin(d*x + c)))/d","A",0
84,1,157,0,0.603834," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{4410 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{770 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \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{6720 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{35 \, {\left(\frac{21 \, \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*((4410*sin(d*x + c)/(cos(d*x + c) + 1) - 770*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*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 - 6720*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 35*(21*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
85,1,197,0,0.885323," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{51345 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9765 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2331 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{405 \, \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{80640 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{63 \, {\left(\frac{15 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{185 \, \sin\left(d x + c\right)^{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*((51345*sin(d*x + c)/(cos(d*x + c) + 1) - 9765*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2331*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 405*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 - 80640*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 63*(15*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 185*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
86,1,90,0,0.417318," ","integrate(tan(d*x+c)^11/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{420 \, \log\left(\cos\left(d x + c\right)\right)}{a^{3}} + \frac{1260 \, \cos\left(d x + c\right)^{6} - 210 \, \cos\left(d x + c\right)^{5} - 700 \, \cos\left(d x + c\right)^{4} + 525 \, \cos\left(d x + c\right)^{3} + 84 \, \cos\left(d x + c\right)^{2} - 210 \, \cos\left(d x + c\right) + 60}{a^{3} \cos\left(d x + c\right)^{7}}}{420 \, d}"," ",0,"1/420*(420*log(cos(d*x + c))/a^3 + (1260*cos(d*x + c)^6 - 210*cos(d*x + c)^5 - 700*cos(d*x + c)^4 + 525*cos(d*x + c)^3 + 84*cos(d*x + c)^2 - 210*cos(d*x + c) + 60)/(a^3*cos(d*x + c)^7))/d","A",0
87,1,70,0,0.327409," ","integrate(tan(d*x+c)^9/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{60 \, \log\left(\cos\left(d x + c\right)\right)}{a^{3}} + \frac{180 \, \cos\left(d x + c\right)^{4} - 60 \, \cos\left(d x + c\right)^{3} - 40 \, \cos\left(d x + c\right)^{2} + 45 \, \cos\left(d x + c\right) - 12}{a^{3} \cos\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*log(cos(d*x + c))/a^3 + (180*cos(d*x + c)^4 - 60*cos(d*x + c)^3 - 40*cos(d*x + c)^2 + 45*cos(d*x + c) - 12)/(a^3*cos(d*x + c)^5))/d","A",0
88,1,50,0,0.314249," ","integrate(tan(d*x+c)^7/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{6 \, \log\left(\cos\left(d x + c\right)\right)}{a^{3}} + \frac{18 \, \cos\left(d x + c\right)^{2} - 9 \, \cos\left(d x + c\right) + 2}{a^{3} \cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*log(cos(d*x + c))/a^3 + (18*cos(d*x + c)^2 - 9*cos(d*x + c) + 2)/(a^3*cos(d*x + c)^3))/d","A",0
89,1,45,0,0.332287," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{4 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}} - \frac{3 \, \log\left(\cos\left(d x + c\right)\right)}{a^{3}} - \frac{1}{a^{3} \cos\left(d x + c\right)}}{d}"," ",0,"-(4*log(cos(d*x + c) + 1)/a^3 - 3*log(cos(d*x + c))/a^3 - 1/(a^3*cos(d*x + c)))/d","A",0
90,1,36,0,0.616207," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2}{a^{3} \cos\left(d x + c\right) + a^{3}} + \frac{\log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}}}{d}"," ",0,"(2/(a^3*cos(d*x + c) + a^3) + log(cos(d*x + c) + 1)/a^3)/d","A",0
91,1,60,0,0.497945," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{4 \, \cos\left(d x + c\right) + 3}{a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} \cos\left(d x + c\right) + a^{3}} + \frac{2 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}}}{2 \, d}"," ",0,"-1/2*((4*cos(d*x + c) + 3)/(a^3*cos(d*x + c)^2 + 2*a^3*cos(d*x + c) + a^3) + 2*log(cos(d*x + c) + 1)/a^3)/d","A",0
92,1,98,0,0.371963," ","integrate(cot(d*x+c)/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(51 \, \cos\left(d x + c\right)^{2} + 81 \, \cos\left(d x + c\right) + 34\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{45 \, \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*(51*cos(d*x + c)^2 + 81*cos(d*x + c) + 34)/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3) + 45*log(cos(d*x + c) + 1)/a^3 + 3*log(cos(d*x + c) - 1)/a^3)/d","A",0
93,1,146,0,0.439445," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(213 \, \cos\left(d x + c\right)^{4} + 303 \, \cos\left(d x + c\right)^{3} - 95 \, \cos\left(d x + c\right)^{2} - 333 \, \cos\left(d x + c\right) - 136\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{171 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}} + \frac{21 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{3}}}{192 \, d}"," ",0,"-1/192*(2*(213*cos(d*x + c)^4 + 303*cos(d*x + c)^3 - 95*cos(d*x + c)^2 - 333*cos(d*x + c) - 136)/(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) + 171*log(cos(d*x + c) + 1)/a^3 + 21*log(cos(d*x + c) - 1)/a^3)/d","A",0
94,1,188,0,1.396327," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(4395 \, \cos\left(d x + c\right)^{6} + 5505 \, \cos\left(d x + c\right)^{5} - 6940 \, \cos\left(d x + c\right)^{4} - 12780 \, \cos\left(d x + c\right)^{3} - 367 \, \cos\left(d x + c\right)^{2} + 6939 \, \cos\left(d x + c\right) + 2768\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{3285 \, \log\left(\cos\left(d x + c\right) + 1\right)}{a^{3}} + \frac{555 \, \log\left(\cos\left(d x + c\right) - 1\right)}{a^{3}}}{3840 \, d}"," ",0,"1/3840*(2*(4395*cos(d*x + c)^6 + 5505*cos(d*x + c)^5 - 6940*cos(d*x + c)^4 - 12780*cos(d*x + c)^3 - 367*cos(d*x + c)^2 + 6939*cos(d*x + c) + 2768)/(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) + 3285*log(cos(d*x + c) + 1)/a^3 + 555*log(cos(d*x + c) - 1)/a^3)/d","A",0
95,1,429,0,0.624449," ","integrate(tan(d*x+c)^12/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{11375 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{79723 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{269879 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{550089 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{749973 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{212625 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{26565 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}\right)}}{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{26880 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{13125 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} - \frac{13125 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{13440 \, d}"," ",0,"-1/13440*(2*(315*sin(d*x + c)/(cos(d*x + c) + 1) - 11375*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 79723*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 269879*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 550089*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 749973*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 212625*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 26565*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) - 26880*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + 13125*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 - 13125*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","A",0
96,1,343,0,0.702062," ","integrate(tan(d*x+c)^10/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{45 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{95 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{366 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1746 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3135 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{525 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)}}{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{480 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{285 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{285 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{240 \, d}"," ",0,"-1/240*(2*(45*sin(d*x + c)/(cos(d*x + c) + 1) - 95*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 366*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1746*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3135*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 525*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) + 480*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 285*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 285*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","B",0
97,1,257,0,0.521082," ","integrate(tan(d*x+c)^8/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{13 \, \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}} + \frac{21 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{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{16 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{13 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{13 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{8 \, d}"," ",0,"1/8*(2*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 13*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 21*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) + 16*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 13*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 13*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","B",0
98,1,171,0,0.446666," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\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{4 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{7 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{7 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{2 \, d}"," ",0,"-1/2*(2*(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) + 4*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 7*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 7*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","B",0
99,1,98,0,0.513920," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}} - \frac{4 \, \sin\left(d x + c\right)}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3 - 4*sin(d*x + c)/(a^3*(cos(d*x + c) + 1)))/d","B",0
100,1,72,0,0.447747," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{6 \, \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{6 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{3 \, d}"," ",0,"1/3*((6*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^3 - 6*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","A",0
101,1,133,0,0.434326," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{2730 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{560 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{126 \, \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^{3}} - \frac{3360 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{105 \, {\left(\cos\left(d x + c\right) + 1\right)}}{a^{3} \sin\left(d x + c\right)}}{1680 \, d}"," ",0,"1/1680*((2730*sin(d*x + c)/(cos(d*x + c) + 1) - 560*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 126*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^3 - 3360*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 105*(cos(d*x + c) + 1)/(a^3*sin(d*x + c)))/d","A",0
102,1,177,0,0.430138," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{31185 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6720 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1827 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{360 \, \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^{3}} - \frac{40320 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{105 \, {\left(\frac{24 \, \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^{3} \sin\left(d x + c\right)^{3}}}{20160 \, d}"," ",0,"-1/20160*((31185*sin(d*x + c)/(cos(d*x + c) + 1) - 6720*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1827*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 360*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 - 40320*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 105*(24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)^3/(a^3*sin(d*x + c)^3))/d","A",0
103,1,218,0,0.559109," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{5 \, {\left(\frac{264726 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{59136 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{18018 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{4554 \, \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{63 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)}}{a^{3}} - \frac{1774080 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{231 \, {\left(\frac{50 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{690 \, \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*(5*(264726*sin(d*x + c)/(cos(d*x + c) + 1) - 59136*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 18018*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 4554*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 770*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 63*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/a^3 - 1774080*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + 231*(50*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 690*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
104,1,177,0,0.462949," ","integrate((a+a*sec(d*x+c))*(e*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(3 \, e^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}}\right)} - 8 \, \left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}} e^{2}\right)} a}{12 \, d e}"," ",0,"-1/12*(3*e^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) + sqrt(2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e)) - 8*(e*tan(d*x + c))^(3/2)*e^2)*a/(d*e)","A",0
105,1,171,0,0.497339," ","integrate((a+a*sec(d*x+c))*(e*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(2 \, \sqrt{2} e^{\frac{5}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right) + 2 \, \sqrt{2} e^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right) + \sqrt{2} e^{\frac{5}{2}} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right) - \sqrt{2} e^{\frac{5}{2}} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right) - 8 \, \sqrt{e \tan\left(d x + c\right)} e^{2}\right)} a}{4 \, d e}"," ",0,"-1/4*(2*sqrt(2)*e^(5/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e)) + 2*sqrt(2)*e^(5/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e)) + sqrt(2)*e^(5/2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e) - sqrt(2)*e^(5/2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e) - 8*sqrt(e*tan(d*x + c))*e^2)*a/(d*e)","A",0
106,1,154,0,0.463842," ","integrate((a+a*sec(d*x+c))*(e*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{a e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}}\right)}}{4 \, d}"," ",0,"1/4*a*e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) + sqrt(2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e))/d","A",0
107,1,156,0,0.449714," ","integrate((a+a*sec(d*x+c))/(e*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 \, \sqrt{2} \sqrt{e} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right) + 2 \, \sqrt{2} \sqrt{e} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right) + \sqrt{2} \sqrt{e} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right) - \sqrt{2} \sqrt{e} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)\right)} a}{4 \, d e}"," ",0,"1/4*(2*sqrt(2)*sqrt(e)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e)) + 2*sqrt(2)*sqrt(e)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e)) + sqrt(2)*sqrt(e)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e) - sqrt(2)*sqrt(e)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e))*a/(d*e)","A",0
108,1,168,0,0.436596," ","integrate((a+a*sec(d*x+c))/(e*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} + \frac{8}{\sqrt{e \tan\left(d x + c\right)}}\right)}}{4 \, d e}"," ",0,"-1/4*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) + sqrt(2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) + 8/sqrt(e*tan(d*x + c)))/(d*e)","A",0
109,1,169,0,0.431611," ","integrate((a+a*sec(d*x+c))/(e*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{a {\left(\frac{6 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{6 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{3 \, \sqrt{2} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{e^{\frac{3}{2}}} - \frac{3 \, \sqrt{2} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{e^{\frac{3}{2}}} + \frac{8}{\left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}\right)}}{12 \, d e}"," ",0,"-1/12*a*(6*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/e^(3/2) + 6*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/e^(3/2) + 3*sqrt(2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/e^(3/2) - 3*sqrt(2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/e^(3/2) + 8/(e*tan(d*x + c))^(3/2))/(d*e)","A",0
110,1,196,0,0.430842," ","integrate((a+a*sec(d*x+c))/(e*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{a {\left(\frac{5 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}}\right)}}{e^{2}} + \frac{8 \, {\left(5 \, e^{2} \tan\left(d x + c\right)^{2} - e^{2}\right)}}{\left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}} e^{2}}\right)}}{20 \, d e}"," ",0,"1/20*a*(5*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) + sqrt(2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e))/e^2 + 8*(5*e^2*tan(d*x + c)^2 - e^2)/((e*tan(d*x + c))^(5/2)*e^2))/(d*e)","A",0
111,1,200,0,0.607825," ","integrate((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{24 \, \left(e \tan\left(d x + c\right)\right)^{\frac{7}{2}} a^{2}}{e} - \frac{7 \, {\left(3 \, e^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}}\right)} - 8 \, \left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}} e^{2}\right)} a^{2}}{e}}{84 \, d}"," ",0,"1/84*(24*(e*tan(d*x + c))^(7/2)*a^2/e - 7*(3*e^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) + sqrt(2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e)) - 8*(e*tan(d*x + c))^(3/2)*e^2)*a^2/e)/d","A",0
112,1,194,0,0.467569," ","integrate((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{8 \, \left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}} a^{2}}{e} - \frac{5 \, {\left(2 \, \sqrt{2} e^{\frac{5}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right) + 2 \, \sqrt{2} e^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right) + \sqrt{2} e^{\frac{5}{2}} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right) - \sqrt{2} e^{\frac{5}{2}} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right) - 8 \, \sqrt{e \tan\left(d x + c\right)} e^{2}\right)} a^{2}}{e}}{20 \, d}"," ",0,"1/20*(8*(e*tan(d*x + c))^(5/2)*a^2/e - 5*(2*sqrt(2)*e^(5/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e)) + 2*sqrt(2)*e^(5/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e)) + sqrt(2)*e^(5/2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e) - sqrt(2)*e^(5/2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e) - 8*sqrt(e*tan(d*x + c))*e^2)*a^2/e)/d","A",0
113,1,177,0,0.455230," ","integrate((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{3 \, a^{2} e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}}\right)} + \frac{8 \, \left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}} a^{2}}{e}}{12 \, d}"," ",0,"1/12*(3*a^2*e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) + sqrt(2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e)) + 8*(e*tan(d*x + c))^(3/2)*a^2/e)/d","A",0
114,1,178,0,0.457368," ","integrate((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{{\left(2 \, \sqrt{2} \sqrt{e} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right) + 2 \, \sqrt{2} \sqrt{e} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right) + \sqrt{2} \sqrt{e} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right) - \sqrt{2} \sqrt{e} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)\right)} a^{2}}{e} + \frac{8 \, \sqrt{e \tan\left(d x + c\right)} a^{2}}{e}}{4 \, d}"," ",0,"1/4*((2*sqrt(2)*sqrt(e)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e)) + 2*sqrt(2)*sqrt(e)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e)) + sqrt(2)*sqrt(e)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e) - sqrt(2)*sqrt(e)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e))*a^2/e + 8*sqrt(e*tan(d*x + c))*a^2/e)/d","A",0
115,1,190,0,0.483358," ","integrate((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{a^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} + \frac{8}{\sqrt{e \tan\left(d x + c\right)}}\right)}}{e} + \frac{8 \, a^{2}}{\sqrt{e \tan\left(d x + c\right)} e}}{4 \, d}"," ",0,"-1/4*(a^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) + sqrt(2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) + 8/sqrt(e*tan(d*x + c)))/e + 8*a^2/(sqrt(e*tan(d*x + c))*e))/d","A",0
116,1,191,0,0.439792," ","integrate((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{a^{2} {\left(\frac{6 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{6 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{3 \, \sqrt{2} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{e^{\frac{3}{2}}} - \frac{3 \, \sqrt{2} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{e^{\frac{3}{2}}} + \frac{8}{\left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}\right)}}{e} + \frac{8 \, a^{2}}{\left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}} e}}{12 \, d}"," ",0,"-1/12*(a^2*(6*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/e^(3/2) + 6*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/e^(3/2) + 3*sqrt(2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/e^(3/2) - 3*sqrt(2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/e^(3/2) + 8/(e*tan(d*x + c))^(3/2))/e + 8*a^2/((e*tan(d*x + c))^(3/2)*e))/d","A",0
117,1,218,0,0.437165," ","integrate((a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{\frac{a^{2} {\left(\frac{5 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}}\right)}}{e^{2}} + \frac{8 \, {\left(5 \, e^{2} \tan\left(d x + c\right)^{2} - e^{2}\right)}}{\left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}} e^{2}}\right)}}{e} - \frac{8 \, a^{2}}{\left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}} e}}{20 \, d}"," ",0,"1/20*(a^2*(5*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) + sqrt(2)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e))/e^2 + 8*(5*e^2*tan(d*x + c)^2 - e^2)/((e*tan(d*x + c))^(5/2)*e^2))/e - 8*a^2/((e*tan(d*x + c))^(5/2)*e))/d","A",0
118,-1,0,0,0.000000," ","integrate((e*tan(d*x+c))^(11/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(9/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{9}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(9/2)/(a*sec(d*x + c) + a), x)","F",0
120,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(7/2)/(a*sec(d*x + c) + a), x)","F",0
121,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(5/2)/(a*sec(d*x + c) + a), x)","F",0
122,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(3/2)/(a*sec(d*x + c) + a), x)","F",0
123,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{e \tan\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*tan(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*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \sqrt{e \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*sqrt(e*tan(d*x + c))), x)","F",0
125,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*(e*tan(d*x + c))^(3/2)), x)","F",0
126,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)*(e*tan(d*x + c))^(5/2)), x)","F",0
127,-1,0,0,0.000000," ","integrate((e*tan(d*x+c))^(13/2)/(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*tan(d*x+c))^(11/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((e*tan(d*x+c))^(9/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate((e*tan(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(5/2)/(a*sec(d*x + c) + a)^2, x)","F",0
132,-1,0,0,0.000000," ","integrate((e*tan(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{e \tan\left(d x + c\right)}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*tan(d*x + c))/(a*sec(d*x + c) + a)^2, x)","F",0
134,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sec\left(d x + c\right) + a\right)}^{2} \sqrt{e \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*sec(d*x + c) + a)^2*sqrt(e*tan(d*x + c))), x)","F",0
135,1,145,0,0.625253," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^5,x, algorithm=""maxima"")","\frac{315 \, \sqrt{a} \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 630 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \frac{70 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{9}{2}}}{a^{4}} - \frac{270 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{7}{2}}}{a^{3}} + \frac{126 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}}}{a^{2}} + \frac{210 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}}}{a}}{315 \, d}"," ",0,"1/315*(315*sqrt(a)*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a))) + 630*sqrt(a + a/cos(d*x + c)) + 70*(a + a/cos(d*x + c))^(9/2)/a^4 - 270*(a + a/cos(d*x + c))^(7/2)/a^3 + 126*(a + a/cos(d*x + c))^(5/2)/a^2 + 210*(a + a/cos(d*x + c))^(3/2)/a)/d","A",0
136,1,107,0,0.565983," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^3,x, algorithm=""maxima"")","-\frac{15 \, \sqrt{a} \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 30 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \frac{6 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}}}{a^{2}} + \frac{10 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}}}{a}}{15 \, d}"," ",0,"-1/15*(15*sqrt(a)*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a))) + 30*sqrt(a + a/cos(d*x + c)) - 6*(a + a/cos(d*x + c))^(5/2)/a^2 + 10*(a + a/cos(d*x + c))^(3/2)/a)/d","A",0
137,1,67,0,0.581605," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c),x, algorithm=""maxima"")","\frac{\sqrt{a} \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 2 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}}}{d}"," ",0,"(sqrt(a)*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a))) + 2*sqrt(a + a/cos(d*x + c)))/d","A",0
138,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*cot(d*x + c), x)","F",0
139,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*cot(d*x + c)^3, x)","F",0
140,-1,0,0,0.000000," ","integrate(cot(d*x+c)^5*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^6,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)*tan(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*cot(d*x + c)^2, x)","F",0
145,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*cot(d*x + c)^4, x)","F",0
146,-1,0,0,0.000000," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,1,162,0,0.462463," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^5,x, algorithm=""maxima"")","\frac{1155 \, a^{\frac{3}{2}} \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 770 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} + \frac{210 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{11}{2}}}{a^{4}} - \frac{770 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{9}{2}}}{a^{3}} + \frac{330 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{7}{2}}}{a^{2}} + \frac{462 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}}}{a} + 2310 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}} a}{1155 \, d}"," ",0,"1/1155*(1155*a^(3/2)*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a))) + 770*(a + a/cos(d*x + c))^(3/2) + 210*(a + a/cos(d*x + c))^(11/2)/a^4 - 770*(a + a/cos(d*x + c))^(9/2)/a^3 + 330*(a + a/cos(d*x + c))^(7/2)/a^2 + 462*(a + a/cos(d*x + c))^(5/2)/a + 2310*sqrt(a + a/cos(d*x + c))*a)/d","A",0
148,1,124,0,0.424930," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^3,x, algorithm=""maxima"")","-\frac{105 \, a^{\frac{3}{2}} \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 70 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} - \frac{30 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{7}{2}}}{a^{2}} + \frac{42 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}}}{a} + 210 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}} a}{105 \, d}"," ",0,"-1/105*(105*a^(3/2)*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a))) + 70*(a + a/cos(d*x + c))^(3/2) - 30*(a + a/cos(d*x + c))^(7/2)/a^2 + 42*(a + a/cos(d*x + c))^(5/2)/a + 210*sqrt(a + a/cos(d*x + c))*a)/d","A",0
149,1,86,0,0.454369," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c),x, algorithm=""maxima"")","\frac{3 \, a^{\frac{3}{2}} \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 2 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} + 6 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}} a}{3 \, d}"," ",0,"1/3*(3*a^(3/2)*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a))) + 2*(a + a/cos(d*x + c))^(3/2) + 6*sqrt(a + a/cos(d*x + c))*a)/d","A",0
150,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*cot(d*x + c), x)","F",0
151,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*cot(d*x + c)^3, x)","F",0
152,-1,0,0,0.000000," ","integrate(cot(d*x+c)^5*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^6,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*tan(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*cot(d*x + c)^2, x)","F",0
157,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,1,181,0,0.599347," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^5,x, algorithm=""maxima"")","\frac{45045 \, a^{\frac{5}{2}} \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 18018 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}} + \frac{6930 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{13}{2}}}{a^{4}} - \frac{24570 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{11}{2}}}{a^{3}} + \frac{10010 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{9}{2}}}{a^{2}} + \frac{12870 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{7}{2}}}{a} + 30030 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a + 90090 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}} a^{2}}{45045 \, d}"," ",0,"1/45045*(45045*a^(5/2)*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a))) + 18018*(a + a/cos(d*x + c))^(5/2) + 6930*(a + a/cos(d*x + c))^(13/2)/a^4 - 24570*(a + a/cos(d*x + c))^(11/2)/a^3 + 10010*(a + a/cos(d*x + c))^(9/2)/a^2 + 12870*(a + a/cos(d*x + c))^(7/2)/a + 30030*(a + a/cos(d*x + c))^(3/2)*a + 90090*sqrt(a + a/cos(d*x + c))*a^2)/d","A",0
160,1,143,0,0.605421," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^3,x, algorithm=""maxima"")","-\frac{315 \, a^{\frac{5}{2}} \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 126 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}} - \frac{70 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{9}{2}}}{a^{2}} + \frac{90 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{7}{2}}}{a} + 210 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a + 630 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}} a^{2}}{315 \, d}"," ",0,"-1/315*(315*a^(5/2)*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a))) + 126*(a + a/cos(d*x + c))^(5/2) - 70*(a + a/cos(d*x + c))^(9/2)/a^2 + 90*(a + a/cos(d*x + c))^(7/2)/a + 210*(a + a/cos(d*x + c))^(3/2)*a + 630*sqrt(a + a/cos(d*x + c))*a^2)/d","A",0
161,1,105,0,0.638444," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c),x, algorithm=""maxima"")","\frac{15 \, a^{\frac{5}{2}} \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 6 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}} + 10 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a + 30 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}} a^{2}}{15 \, d}"," ",0,"1/15*(15*a^(5/2)*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a))) + 6*(a + a/cos(d*x + c))^(5/2) + 10*(a + a/cos(d*x + c))^(3/2)*a + 30*sqrt(a + a/cos(d*x + c))*a^2)/d","A",0
162,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)*cot(d*x + c), x)","F",0
163,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)*cot(d*x + c)^3, x)","F",0
164,-1,0,0,0.000000," ","integrate(cot(d*x+c)^5*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^6,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/2)*tan(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(5/2)*cot(d*x + c)^2, x)","F",0
169,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate(cot(d*x+c)^6*(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,1,129,0,0.537568," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{105 \, \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{\sqrt{a}} + \frac{30 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{7}{2}}}{a^{4}} - \frac{126 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}}}{a^{3}} + \frac{70 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}}}{a^{2}} + \frac{210 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}}}{a}}{105 \, d}"," ",0,"1/105*(105*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a)))/sqrt(a) + 30*(a + a/cos(d*x + c))^(7/2)/a^4 - 126*(a + a/cos(d*x + c))^(5/2)/a^3 + 70*(a + a/cos(d*x + c))^(3/2)/a^2 + 210*sqrt(a + a/cos(d*x + c))/a)/d","A",0
172,1,91,0,0.992797," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{\sqrt{a}} - \frac{2 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}}}{a^{2}} + \frac{6 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}}}{a}}{3 \, d}"," ",0,"-1/3*(3*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a)))/sqrt(a) - 2*(a + a/cos(d*x + c))^(3/2)/a^2 + 6*sqrt(a + a/cos(d*x + c))/a)/d","A",0
173,1,49,0,0.606657," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{\sqrt{a} d}"," ",0,"log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a)))/(sqrt(a)*d)","A",0
174,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)/sqrt(a*sec(d*x + c) + a), x)","F",0
175,0,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{3}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^3/sqrt(a*sec(d*x + c) + a), x)","F",0
176,0,0,0,0.000000," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{5}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^5/sqrt(a*sec(d*x + c) + a), x)","F",0
177,-1,0,0,0.000000," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{2}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/sqrt(a*sec(d*x + c) + a), x)","F",0
181,0,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{4}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^4/sqrt(a*sec(d*x + c) + a), x)","F",0
182,-1,0,0,0.000000," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,1,110,0,0.547472," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{5 \, \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}}}{a^{4}} - \frac{10 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}}}{a^{3}} + \frac{10 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}}}{a^{2}}}{5 \, d}"," ",0,"1/5*(5*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a)))/a^(3/2) + 2*(a + a/cos(d*x + c))^(5/2)/a^4 - 10*(a + a/cos(d*x + c))^(3/2)/a^3 + 10*sqrt(a + a/cos(d*x + c))/a^2)/d","A",0
184,1,71,0,0.810001," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} - \frac{2 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}}}{a^{2}}}{d}"," ",0,"-(log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a)))/a^(3/2) - 2*sqrt(a + a/cos(d*x + c))/a^2)/d","A",0
185,1,70,0,0.590803," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{\log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} a}}{d}"," ",0,"(log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a)))/a^(3/2) + 2/(sqrt(a + a/cos(d*x + c))*a))/d","A",0
186,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)/(a*sec(d*x + c) + a)^(3/2), x)","F",0
187,0,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^3/(a*sec(d*x + c) + a)^(3/2), x)","F",0
188,-1,0,0,0.000000," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
192,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/(a*sec(d*x + c) + a)^(3/2), x)","F",0
193,0,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{4}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^4/(a*sec(d*x + c) + a)^(3/2), x)","F",0
194,-1,0,0,0.000000," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,1,163,0,0.457301," ","integrate(tan(d*x+c)^5/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{3 \, \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{a^{\frac{5}{2}}} + \frac{2 \, {\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}}}{a^{4}} - \frac{18 \, \sqrt{a + \frac{a}{\cos\left(d x + c\right)}}}{a^{3}} + \frac{2 \, {\left(4 \, a + \frac{3 \, a}{\cos\left(d x + c\right)}\right)}}{{\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a^{2}} - \frac{6}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} a^{2}} - \frac{2}{{\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a}}{3 \, d}"," ",0,"1/3*(3*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a)))/a^(5/2) + 2*(a + a/cos(d*x + c))^(3/2)/a^4 - 18*sqrt(a + a/cos(d*x + c))/a^3 + 2*(4*a + 3*a/cos(d*x + c))/((a + a/cos(d*x + c))^(3/2)*a^2) - 6/(sqrt(a + a/cos(d*x + c))*a^2) - 2/((a + a/cos(d*x + c))^(3/2)*a))/d","B",0
196,1,125,0,0.452652," ","integrate(tan(d*x+c)^3/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{a^{\frac{5}{2}}} + \frac{2 \, {\left(4 \, a + \frac{3 \, a}{\cos\left(d x + c\right)}\right)}}{{\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a^{2}} + \frac{6}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} a^{2}} - \frac{2}{{\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a}}{3 \, d}"," ",0,"-1/3*(3*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a)))/a^(5/2) + 2*(4*a + 3*a/cos(d*x + c))/((a + a/cos(d*x + c))^(3/2)*a^2) + 6/(sqrt(a + a/cos(d*x + c))*a^2) - 2/((a + a/cos(d*x + c))^(3/2)*a))/d","B",0
197,1,87,0,0.440824," ","integrate(tan(d*x+c)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{3 \, \log\left(\frac{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{a}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{a^{\frac{5}{2}}} + \frac{2 \, {\left(4 \, a + \frac{3 \, a}{\cos\left(d x + c\right)}\right)}}{{\left(a + \frac{a}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a^{2}}}{3 \, d}"," ",0,"1/3*(3*log((sqrt(a + a/cos(d*x + c)) - sqrt(a))/(sqrt(a + a/cos(d*x + c)) + sqrt(a)))/a^(5/2) + 2*(4*a + 3*a/cos(d*x + c))/((a + a/cos(d*x + c))^(3/2)*a^2))/d","A",0
198,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)/(a*sec(d*x + c) + a)^(5/2), x)","F",0
199,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,-1,0,0,0.000000," ","integrate(cot(d*x+c)^5/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate(tan(d*x+c)^6/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,0,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{4}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^4/(a*sec(d*x + c) + a)^(5/2), x)","F",0
203,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/(a*sec(d*x + c) + a)^(5/2), x)","F",0
204,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/(a*sec(d*x + c) + a)^(5/2), x)","F",0
205,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate(cot(d*x+c)^6/(a+a*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+a*sec(f*x+e))^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*(e*tan(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*(e*tan(d*x + c))^m, x)","F",0
209,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^3*(e*tan(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{3} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^3*(e*tan(d*x + c))^m, x)","F",0
210,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^2*(e*tan(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{2} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^2*(e*tan(d*x + c))^m, x)","F",0
211,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))*(e*tan(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)*(e*tan(d*x + c))^m, x)","F",0
212,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{m}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^m/(a*sec(d*x + c) + a), x)","F",0
213,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{m}}{{\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^m/(a*sec(d*x + c) + a)^2, x)","F",0
214,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{m}}{{\left(a \sec\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^m/(a*sec(d*x + c) + a)^3, x)","F",0
215,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(3/2)*(e*tan(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^(3/2)*(e*tan(d*x + c))^m, x)","F",0
216,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(1/2)*(e*tan(d*x+c))^m,x, algorithm=""maxima"")","\int \sqrt{a \sec\left(d x + c\right) + a} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(a*sec(d*x + c) + a)*(e*tan(d*x + c))^m, x)","F",0
217,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{m}}{\sqrt{a \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^m/sqrt(a*sec(d*x + c) + a), x)","F",0
218,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+a*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(e \tan\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*tan(d*x + c))^m/(a*sec(d*x + c) + a)^(3/2), x)","F",0
219,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^7,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^7, x)","F",0
220,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^5, x)","F",0
221,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^3, x)","F",0
222,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c), x)","F",0
223,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*cot(d*x + c), x)","F",0
224,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*cot(d*x + c)^3, x)","F",0
225,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^4, x)","F",0
226,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^2, x)","F",0
227,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*cot(d*x + c)^2, x)","F",0
228,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*cot(d*x + c)^4, x)","F",0
229,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*tan(d*x + c)^(3/2), x)","F",0
230,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n*tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(a \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n*sqrt(tan(d*x + c)), x)","F",0
231,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{n}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n/sqrt(tan(d*x + c)), x)","F",0
232,0,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^n/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sec\left(d x + c\right) + a\right)}^{n}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sec(d*x + c) + a)^n/tan(d*x + c)^(3/2), x)","F",0
233,1,186,0,0.471316," ","integrate((e*cot(d*x+c))^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, e^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} - 8 \, \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}\right)} a e}{12 \, d}"," ",0,"1/12*(3*e^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e)) - 8*(e/tan(d*x + c))^(3/2))*a*e/d","A",0
234,1,180,0,0.496836," ","integrate((e*cot(d*x+c))^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, \sqrt{2} \sqrt{e} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right) + 2 \, \sqrt{2} \sqrt{e} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right) + \sqrt{2} \sqrt{e} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right) - \sqrt{2} \sqrt{e} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right) - 8 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)} a e}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*sqrt(e)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e)) + 2*sqrt(2)*sqrt(e)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e)) + sqrt(2)*sqrt(e)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c)) - sqrt(2)*sqrt(e)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c)) - 8*sqrt(e/tan(d*x + c)))*a*e/d","A",0
235,1,166,0,0.466571," ","integrate((a+a*sec(d*x+c))*(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{a e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)}}{4 \, d}"," ",0,"-1/4*a*e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/d","A",0
236,1,166,0,0.496954," ","integrate((a+a*sec(d*x+c))/(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{a e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{e^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{e^{\frac{3}{2}}}\right)}}{4 \, d}"," ",0,"-1/4*a*e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/e^(3/2) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/e^(3/2) + sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/e^(3/2) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/e^(3/2))/d","A",0
237,1,188,0,0.452175," ","integrate((a+a*sec(d*x+c))/(e*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{a e {\left(\frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{e^{2}} + \frac{8}{e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}\right)}}{4 \, d}"," ",0,"1/4*a*e*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^2 + 8/(e^2*sqrt(e/tan(d*x + c))))/d","A",0
238,1,214,0,0.496314," ","integrate((e*cot(d*x+c))^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{8 \, a^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{5}{2}} \tan\left(d x + c\right) - {\left(3 \, e^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} - 8 \, \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}\right)} a^{2} e}{12 \, d}"," ",0,"-1/12*(8*a^2*(e/tan(d*x + c))^(5/2)*tan(d*x + c) - (3*e^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e)) - 8*(e/tan(d*x + c))^(3/2))*a^2*e)/d","A",0
239,1,208,0,0.464804," ","integrate((e*cot(d*x+c))^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{8 \, a^{2} \left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}} \tan\left(d x + c\right) - {\left(2 \, \sqrt{2} \sqrt{e} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right) + 2 \, \sqrt{2} \sqrt{e} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right) + \sqrt{2} \sqrt{e} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right) - \sqrt{2} \sqrt{e} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right) - 8 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)} a^{2} e}{4 \, d}"," ",0,"-1/4*(8*a^2*(e/tan(d*x + c))^(3/2)*tan(d*x + c) - (2*sqrt(2)*sqrt(e)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e)) + 2*sqrt(2)*sqrt(e)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e)) + sqrt(2)*sqrt(e)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c)) - sqrt(2)*sqrt(e)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c)) - 8*sqrt(e/tan(d*x + c)))*a^2*e)/d","A",0
240,1,193,0,0.467874," ","integrate((a+a*sec(d*x+c))^2*(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{a^{2} e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}\right)} - 8 \, a^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}} \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(a^2*e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e)) - 8*a^2*sqrt(e/tan(d*x + c))*tan(d*x + c))/d","A",0
241,1,194,0,0.514142," ","integrate((a+a*sec(d*x+c))^2/(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{3 \, a^{2} e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{e^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{e^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{e^{\frac{3}{2}}}\right)} - \frac{8 \, a^{2} \tan\left(d x + c\right)}{\sqrt{\frac{e}{\tan\left(d x + c\right)}}}}{12 \, d}"," ",0,"-1/12*(3*a^2*e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/e^(3/2) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/e^(3/2) + sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/e^(3/2) - sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/e^(3/2)) - 8*a^2*tan(d*x + c)/sqrt(e/tan(d*x + c)))/d","A",0
242,1,216,0,0.488554," ","integrate((a+a*sec(d*x+c))^2/(e*cot(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{5 \, a^{2} e {\left(\frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{\frac{e}{\tan\left(d x + c\right)}}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e}{\tan\left(d x + c\right)}} + e + \frac{e}{\tan\left(d x + c\right)}\right)}{\sqrt{e}}}{e^{2}} + \frac{8}{e^{2} \sqrt{\frac{e}{\tan\left(d x + c\right)}}}\right)} + \frac{8 \, a^{2} \tan\left(d x + c\right)}{\left(\frac{e}{\tan\left(d x + c\right)}\right)^{\frac{3}{2}}}}{20 \, d}"," ",0,"1/20*(5*a^2*e*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e/tan(d*x + c)))/sqrt(e))/sqrt(e) - sqrt(2)*log(sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e) + sqrt(2)*log(-sqrt(2)*sqrt(e)*sqrt(e/tan(d*x + c)) + e + e/tan(d*x + c))/sqrt(e))/e^2 + 8/(e^2*sqrt(e/tan(d*x + c)))) + 8*a^2*tan(d*x + c)/(e/tan(d*x + c))^(3/2))/d","A",0
243,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,0,0,0,0.000000," ","integrate((e*cot(d*x+c))^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{e \cot\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*cot(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
245,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))/(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e \cot\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cot(d*x + c))*(a*sec(d*x + c) + a)), x)","F",0
246,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cot\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*cot(d*x + c))^(3/2)*(a*sec(d*x + c) + a)), x)","F",0
247,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cot\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*cot(d*x + c))^(5/2)*(a*sec(d*x + c) + a)), x)","F",0
248,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cot\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*cot(d*x + c))^(7/2)*(a*sec(d*x + c) + a)), x)","F",0
249,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(9/2)/(a+a*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cot\left(d x + c\right)\right)^{\frac{9}{2}} {\left(a \sec\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cot(d*x + c))^(9/2)*(a*sec(d*x + c) + a)), x)","F",0
250,0,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^2/(e*cot(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e \cot\left(d x + c\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cot(d*x + c))*(a*sec(d*x + c) + a)^2), x)","F",0
251,-1,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(e \cot\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cot(d*x + c))^(5/2)*(a*sec(d*x + c) + a)^2), x)","F",0
253,-1,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(9/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(e \cot\left(d x + c\right)\right)^{\frac{9}{2}} {\left(a \sec\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cot(d*x + c))^(9/2)*(a*sec(d*x + c) + a)^2), x)","F",0
255,-1,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(11/2)/(a+a*sec(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,1,94,0,0.322821," ","integrate((a+b*sec(d*x+c))*tan(d*x+c)^7,x, algorithm=""maxima"")","\frac{420 \, a \log\left(\cos\left(d x + c\right)\right) - \frac{420 \, b \cos\left(d x + c\right)^{6} - 630 \, a \cos\left(d x + c\right)^{5} - 420 \, b \cos\left(d x + c\right)^{4} + 315 \, a \cos\left(d x + c\right)^{3} + 252 \, b \cos\left(d x + c\right)^{2} - 70 \, a \cos\left(d x + c\right) - 60 \, b}{\cos\left(d x + c\right)^{7}}}{420 \, d}"," ",0,"1/420*(420*a*log(cos(d*x + c)) - (420*b*cos(d*x + c)^6 - 630*a*cos(d*x + c)^5 - 420*b*cos(d*x + c)^4 + 315*a*cos(d*x + c)^3 + 252*b*cos(d*x + c)^2 - 70*a*cos(d*x + c) - 60*b)/cos(d*x + c)^7)/d","A",0
257,1,72,0,0.503962," ","integrate((a+b*sec(d*x+c))*tan(d*x+c)^5,x, algorithm=""maxima"")","-\frac{60 \, a \log\left(\cos\left(d x + c\right)\right) - \frac{60 \, b \cos\left(d x + c\right)^{4} - 60 \, a \cos\left(d x + c\right)^{3} - 40 \, b \cos\left(d x + c\right)^{2} + 15 \, a \cos\left(d x + c\right) + 12 \, b}{\cos\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*a*log(cos(d*x + c)) - (60*b*cos(d*x + c)^4 - 60*a*cos(d*x + c)^3 - 40*b*cos(d*x + c)^2 + 15*a*cos(d*x + c) + 12*b)/cos(d*x + c)^5)/d","A",0
258,1,50,0,0.506451," ","integrate((a+b*sec(d*x+c))*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{6 \, a \log\left(\cos\left(d x + c\right)\right) - \frac{6 \, b \cos\left(d x + c\right)^{2} - 3 \, a \cos\left(d x + c\right) - 2 \, b}{\cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*a*log(cos(d*x + c)) - (6*b*cos(d*x + c)^2 - 3*a*cos(d*x + c) - 2*b)/cos(d*x + c)^3)/d","A",0
259,1,26,0,0.562921," ","integrate((a+b*sec(d*x+c))*tan(d*x+c),x, algorithm=""maxima"")","-\frac{a \log\left(\cos\left(d x + c\right)\right) - \frac{b}{\cos\left(d x + c\right)}}{d}"," ",0,"-(a*log(cos(d*x + c)) - b/cos(d*x + c))/d","A",0
260,1,34,0,0.522306," ","integrate(cot(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 \, d}"," ",0,"1/2*((a - b)*log(cos(d*x + c) + 1) + (a + b)*log(cos(d*x + c) - 1))/d","A",0
261,1,62,0,0.353438," ","integrate(cot(d*x+c)^3*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(2 \, a - b\right)} \log\left(\cos\left(d x + c\right) + 1\right) + {\left(2 \, a + b\right)} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"-1/4*((2*a - b)*log(cos(d*x + c) + 1) + (2*a + b)*log(cos(d*x + c) - 1) - 2*(b*cos(d*x + c) + a)/(cos(d*x + c)^2 - 1))/d","A",0
262,1,99,0,0.500709," ","integrate(cot(d*x+c)^5*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(8 \, a - 3 \, b\right)} \log\left(\cos\left(d x + c\right) + 1\right) + {\left(8 \, a + 3 \, b\right)} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, {\left(5 \, b \cos\left(d x + c\right)^{3} + 8 \, a \cos\left(d x + c\right)^{2} - 3 \, b \cos\left(d x + c\right) - 6 \, a\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*((8*a - 3*b)*log(cos(d*x + c) + 1) + (8*a + 3*b)*log(cos(d*x + c) - 1) - 2*(5*b*cos(d*x + c)^3 + 8*a*cos(d*x + c)^2 - 3*b*cos(d*x + c) - 6*a)/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1))/d","A",0
263,1,133,0,0.368608," ","integrate(cot(d*x+c)^7*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, {\left(16 \, a - 5 \, b\right)} \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, {\left(16 \, a + 5 \, b\right)} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, {\left(33 \, b \cos\left(d x + c\right)^{5} + 72 \, a \cos\left(d x + c\right)^{4} - 40 \, b \cos\left(d x + c\right)^{3} - 108 \, a \cos\left(d x + c\right)^{2} + 15 \, b \cos\left(d x + c\right) + 44 \, a\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*(16*a - 5*b)*log(cos(d*x + c) + 1) + 3*(16*a + 5*b)*log(cos(d*x + c) - 1) - 2*(33*b*cos(d*x + c)^5 + 72*a*cos(d*x + c)^4 - 40*b*cos(d*x + c)^3 - 108*a*cos(d*x + c)^2 + 15*b*cos(d*x + c) + 44*a)/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1))/d","A",0
264,1,134,0,0.866718," ","integrate((a+b*sec(d*x+c))*tan(d*x+c)^6,x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a - 5 \, b {\left(\frac{2 \, {\left(33 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \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)\right)}}{480 \, d}"," ",0,"1/480*(32*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a - 5*b*(2*(33*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 15*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) + 15*log(sin(d*x + c) + 1) - 15*log(sin(d*x + c) - 1)))/d","A",0
265,1,102,0,0.619987," ","integrate((a+b*sec(d*x+c))*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a + 3 \, b {\left(\frac{2 \, {\left(5 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \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)\right)}}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a + 3*b*(2*(5*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1)))/d","A",0
266,1,65,0,0.743295," ","integrate((a+b*sec(d*x+c))*tan(d*x+c)^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a + b {\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)}}{4 \, d}"," ",0,"-1/4*(4*(d*x + c - tan(d*x + c))*a + b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)))/d","A",0
267,1,31,0,0.542501," ","integrate(cot(d*x+c)^2*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a + \frac{b}{\sin\left(d x + c\right)}}{d}"," ",0,"-((d*x + c + 1/tan(d*x + c))*a + b/sin(d*x + c))/d","A",0
268,1,59,0,0.573997," ","integrate(cot(d*x+c)^4*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a + \frac{{\left(3 \, \sin\left(d x + c\right)^{2} - 1\right)} b}{\sin\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*((3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a + (3*sin(d*x + c)^2 - 1)*b/sin(d*x + c)^3)/d","A",0
269,1,79,0,0.693623," ","integrate(cot(d*x+c)^6*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a + \frac{{\left(15 \, \sin\left(d x + c\right)^{4} - 10 \, \sin\left(d x + c\right)^{2} + 3\right)} b}{\sin\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*((15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a + (15*sin(d*x + c)^4 - 10*sin(d*x + c)^2 + 3)*b/sin(d*x + c)^5)/d","A",0
270,1,100,0,0.661529," ","integrate(cot(d*x+c)^8*(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(105 \, d x + 105 \, c + \frac{105 \, \tan\left(d x + c\right)^{6} - 35 \, \tan\left(d x + c\right)^{4} + 21 \, \tan\left(d x + c\right)^{2} - 15}{\tan\left(d x + c\right)^{7}}\right)} a + \frac{3 \, {\left(35 \, \sin\left(d x + c\right)^{6} - 35 \, \sin\left(d x + c\right)^{4} + 21 \, \sin\left(d x + c\right)^{2} - 5\right)} b}{\sin\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*((105*d*x + 105*c + (105*tan(d*x + c)^6 - 35*tan(d*x + c)^4 + 21*tan(d*x + c)^2 - 15)/tan(d*x + c)^7)*a + 3*(35*sin(d*x + c)^6 - 35*sin(d*x + c)^4 + 21*sin(d*x + c)^2 - 5)*b/sin(d*x + c)^7)/d","A",0
271,1,174,0,0.705284," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^9,x, algorithm=""maxima"")","-\frac{2520 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{5040 \, a b \cos\left(d x + c\right)^{9} - 6720 \, a b \cos\left(d x + c\right)^{7} - 1260 \, {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{8} + 6048 \, a b \cos\left(d x + c\right)^{5} + 1260 \, {\left(3 \, a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 2880 \, a b \cos\left(d x + c\right)^{3} - 840 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 560 \, a b \cos\left(d x + c\right) + 315 \, {\left(a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 252 \, b^{2}}{\cos\left(d x + c\right)^{10}}}{2520 \, d}"," ",0,"-1/2520*(2520*a^2*log(cos(d*x + c)) - (5040*a*b*cos(d*x + c)^9 - 6720*a*b*cos(d*x + c)^7 - 1260*(4*a^2 - b^2)*cos(d*x + c)^8 + 6048*a*b*cos(d*x + c)^5 + 1260*(3*a^2 - 2*b^2)*cos(d*x + c)^6 - 2880*a*b*cos(d*x + c)^3 - 840*(2*a^2 - 3*b^2)*cos(d*x + c)^4 + 560*a*b*cos(d*x + c) + 315*(a^2 - 4*b^2)*cos(d*x + c)^2 + 252*b^2)/cos(d*x + c)^10)/d","A",0
272,1,139,0,0.441456," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^7,x, algorithm=""maxima"")","\frac{840 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{1680 \, a b \cos\left(d x + c\right)^{7} - 1680 \, a b \cos\left(d x + c\right)^{5} - 420 \, {\left(3 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} + 1008 \, a b \cos\left(d x + c\right)^{3} + 630 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} - 240 \, a b \cos\left(d x + c\right) - 140 \, {\left(a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 105 \, b^{2}}{\cos\left(d x + c\right)^{8}}}{840 \, d}"," ",0,"1/840*(840*a^2*log(cos(d*x + c)) - (1680*a*b*cos(d*x + c)^7 - 1680*a*b*cos(d*x + c)^5 - 420*(3*a^2 - b^2)*cos(d*x + c)^6 + 1008*a*b*cos(d*x + c)^3 + 630*(a^2 - b^2)*cos(d*x + c)^4 - 240*a*b*cos(d*x + c) - 140*(a^2 - 3*b^2)*cos(d*x + c)^2 - 105*b^2)/cos(d*x + c)^8)/d","A",0
273,1,108,0,0.331093," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^5,x, algorithm=""maxima"")","-\frac{60 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{120 \, a b \cos\left(d x + c\right)^{5} - 80 \, a b \cos\left(d x + c\right)^{3} - 30 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 24 \, a b \cos\left(d x + c\right) + 15 \, {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 10 \, b^{2}}{\cos\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(60*a^2*log(cos(d*x + c)) - (120*a*b*cos(d*x + c)^5 - 80*a*b*cos(d*x + c)^3 - 30*(2*a^2 - b^2)*cos(d*x + c)^4 + 24*a*b*cos(d*x + c) + 15*(a^2 - 2*b^2)*cos(d*x + c)^2 + 10*b^2)/cos(d*x + c)^6)/d","A",0
274,1,75,0,0.500017," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^3,x, algorithm=""maxima"")","\frac{12 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{24 \, a b \cos\left(d x + c\right)^{3} - 8 \, a b \cos\left(d x + c\right) - 6 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, b^{2}}{\cos\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*a^2*log(cos(d*x + c)) - (24*a*b*cos(d*x + c)^3 - 8*a*b*cos(d*x + c) - 6*(a^2 - b^2)*cos(d*x + c)^2 - 3*b^2)/cos(d*x + c)^4)/d","A",0
275,1,42,0,0.378372," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c),x, algorithm=""maxima"")","-\frac{2 \, a^{2} \log\left(\cos\left(d x + c\right)\right) - \frac{4 \, a b \cos\left(d x + c\right) + b^{2}}{\cos\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*a^2*log(cos(d*x + c)) - (4*a*b*cos(d*x + c) + b^2)/cos(d*x + c)^2)/d","A",0
276,1,62,0,0.419315," ","integrate(cot(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, b^{2} \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)}{2 \, d}"," ",0,"-1/2*(2*b^2*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))/d","A",0
277,1,72,0,0.501796," ","integrate(cot(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} - a b\right)} \log\left(\cos\left(d x + c\right) + 1\right) + {\left(a^{2} + a b\right)} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, a b \cos\left(d x + c\right) + a^{2} + b^{2}}{\cos\left(d x + c\right)^{2} - 1}}{2 \, d}"," ",0,"-1/2*((a^2 - a*b)*log(cos(d*x + c) + 1) + (a^2 + a*b)*log(cos(d*x + c) - 1) - (2*a*b*cos(d*x + c) + a^2 + b^2)/(cos(d*x + c)^2 - 1))/d","A",0
278,1,122,0,0.434308," ","integrate(cot(d*x+c)^5*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(4 \, a^{2} - 3 \, a b\right)} \log\left(\cos\left(d x + c\right) + 1\right) + {\left(4 \, a^{2} + 3 \, a b\right)} \log\left(\cos\left(d x + c\right) - 1\right) - \frac{2 \, {\left(5 \, a b \cos\left(d x + c\right)^{3} - 3 \, a b \cos\left(d x + c\right) + 2 \, {\left(2 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, a^{2} - b^{2}\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*((4*a^2 - 3*a*b)*log(cos(d*x + c) + 1) + (4*a^2 + 3*a*b)*log(cos(d*x + c) - 1) - 2*(5*a*b*cos(d*x + c)^3 - 3*a*b*cos(d*x + c) + 2*(2*a^2 + b^2)*cos(d*x + c)^2 - 3*a^2 - b^2)/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1))/d","A",0
279,1,150,0,0.693874," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^6,x, algorithm=""maxima"")","\frac{240 \, b^{2} \tan\left(d x + c\right)^{7} + 112 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a^{2} - 35 \, a b {\left(\frac{2 \, {\left(33 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \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)\right)}}{1680 \, d}"," ",0,"1/1680*(240*b^2*tan(d*x + c)^7 + 112*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a^2 - 35*a*b*(2*(33*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 15*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) + 15*log(sin(d*x + c) + 1) - 15*log(sin(d*x + c) - 1)))/d","A",0
280,1,118,0,0.597368," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{24 \, b^{2} \tan\left(d x + c\right)^{5} + 40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{2} + 15 \, a b {\left(\frac{2 \, {\left(5 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \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)\right)}}{120 \, d}"," ",0,"1/120*(24*b^2*tan(d*x + c)^5 + 40*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^2 + 15*a*b*(2*(5*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1)))/d","A",0
281,1,82,0,0.658201," ","integrate((a+b*sec(d*x+c))^2*tan(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, b^{2} \tan\left(d x + c\right)^{3} - 6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} - 3 \, a b {\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 \, d}"," ",0,"1/6*(2*b^2*tan(d*x + c)^3 - 6*(d*x + c - tan(d*x + c))*a^2 - 3*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)))/d","A",0
282,1,47,0,0.556096," ","integrate(cot(d*x+c)^2*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{2} + \frac{2 \, a b}{\sin\left(d x + c\right)} + \frac{b^{2}}{\tan\left(d x + c\right)}}{d}"," ",0,"-((d*x + c + 1/tan(d*x + c))*a^2 + 2*a*b/sin(d*x + c) + b^2/tan(d*x + c))/d","A",0
283,1,76,0,0.572321," ","integrate(cot(d*x+c)^4*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{2} + \frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 1\right)} a b}{\sin\left(d x + c\right)^{3}} - \frac{b^{2}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*((3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^2 + 2*(3*sin(d*x + c)^2 - 1)*a*b/sin(d*x + c)^3 - b^2/tan(d*x + c)^3)/d","A",0
284,1,96,0,0.659464," ","integrate(cot(d*x+c)^6*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{2} + \frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} - 10 \, \sin\left(d x + c\right)^{2} + 3\right)} a b}{\sin\left(d x + c\right)^{5}} + \frac{3 \, b^{2}}{\tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*((15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^2 + 2*(15*sin(d*x + c)^4 - 10*sin(d*x + c)^2 + 3)*a*b/sin(d*x + c)^5 + 3*b^2/tan(d*x + c)^5)/d","A",0
285,1,116,0,0.526246," ","integrate(cot(d*x+c)^8*(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(105 \, d x + 105 \, c + \frac{105 \, \tan\left(d x + c\right)^{6} - 35 \, \tan\left(d x + c\right)^{4} + 21 \, \tan\left(d x + c\right)^{2} - 15}{\tan\left(d x + c\right)^{7}}\right)} a^{2} + \frac{6 \, {\left(35 \, \sin\left(d x + c\right)^{6} - 35 \, \sin\left(d x + c\right)^{4} + 21 \, \sin\left(d x + c\right)^{2} - 5\right)} a b}{\sin\left(d x + c\right)^{7}} - \frac{15 \, b^{2}}{\tan\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*((105*d*x + 105*c + (105*tan(d*x + c)^6 - 35*tan(d*x + c)^4 + 21*tan(d*x + c)^2 - 15)/tan(d*x + c)^7)*a^2 + 6*(35*sin(d*x + c)^6 - 35*sin(d*x + c)^4 + 21*sin(d*x + c)^2 - 5)*a*b/sin(d*x + c)^7 - 15*b^2/tan(d*x + c)^7)/d","A",0
286,1,268,0,0.622689," ","integrate(tan(d*x+c)^9/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{420 \, {\left(a^{7} - 4 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 4 \, a b^{6}\right)} \log\left(\cos\left(d x + c\right)\right)}{b^{8}} - \frac{420 \, {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a b^{8}} - \frac{70 \, a b^{5} \cos\left(d x + c\right) - 420 \, {\left(a^{6} - 4 \, a^{4} b^{2} + 6 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 60 \, b^{6} + 210 \, {\left(a^{5} b - 4 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} - 140 \, {\left(a^{4} b^{2} - 4 \, a^{2} b^{4} + 6 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 105 \, {\left(a^{3} b^{3} - 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 84 \, {\left(a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2}}{b^{7} \cos\left(d x + c\right)^{7}}}{420 \, d}"," ",0,"1/420*(420*(a^7 - 4*a^5*b^2 + 6*a^3*b^4 - 4*a*b^6)*log(cos(d*x + c))/b^8 - 420*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*log(a*cos(d*x + c) + b)/(a*b^8) - (70*a*b^5*cos(d*x + c) - 420*(a^6 - 4*a^4*b^2 + 6*a^2*b^4 - 4*b^6)*cos(d*x + c)^6 - 60*b^6 + 210*(a^5*b - 4*a^3*b^3 + 6*a*b^5)*cos(d*x + c)^5 - 140*(a^4*b^2 - 4*a^2*b^4 + 6*b^6)*cos(d*x + c)^4 + 105*(a^3*b^3 - 4*a*b^5)*cos(d*x + c)^3 - 84*(a^2*b^4 - 4*b^6)*cos(d*x + c)^2)/(b^7*cos(d*x + c)^7))/d","A",0
287,1,183,0,0.601364," ","integrate(tan(d*x+c)^7/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{60 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left(\cos\left(d x + c\right)\right)}{b^{6}} - \frac{60 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a b^{6}} - \frac{15 \, a b^{3} \cos\left(d x + c\right) - 60 \, {\left(a^{4} - 3 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{4} - 12 \, b^{4} + 30 \, {\left(a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} - 20 \, {\left(a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(d x + c\right)^{2}}{b^{5} \cos\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*(a^5 - 3*a^3*b^2 + 3*a*b^4)*log(cos(d*x + c))/b^6 - 60*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*log(a*cos(d*x + c) + b)/(a*b^6) - (15*a*b^3*cos(d*x + c) - 60*(a^4 - 3*a^2*b^2 + 3*b^4)*cos(d*x + c)^4 - 12*b^4 + 30*(a^3*b - 3*a*b^3)*cos(d*x + c)^3 - 20*(a^2*b^2 - 3*b^4)*cos(d*x + c)^2)/(b^5*cos(d*x + c)^5))/d","A",0
288,1,110,0,0.402624," ","integrate(tan(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(a^{3} - 2 \, a b^{2}\right)} \log\left(\cos\left(d x + c\right)\right)}{b^{4}} - \frac{6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a b^{4}} - \frac{3 \, a b \cos\left(d x + c\right) - 6 \, {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, b^{2}}{b^{3} \cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(a^3 - 2*a*b^2)*log(cos(d*x + c))/b^4 - 6*(a^4 - 2*a^2*b^2 + b^4)*log(a*cos(d*x + c) + b)/(a*b^4) - (3*a*b*cos(d*x + c) - 6*(a^2 - 2*b^2)*cos(d*x + c)^2 - 2*b^2)/(b^3*cos(d*x + c)^3))/d","A",0
289,1,57,0,0.421976," ","integrate(tan(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{a \log\left(\cos\left(d x + c\right)\right)}{b^{2}} - \frac{{\left(a^{2} - b^{2}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a b^{2}} + \frac{1}{b \cos\left(d x + c\right)}}{d}"," ",0,"(a*log(cos(d*x + c))/b^2 - (a^2 - b^2)*log(a*cos(d*x + c) + b)/(a*b^2) + 1/(b*cos(d*x + c)))/d","A",0
290,1,19,0,0.437041," ","integrate(tan(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\log\left(a \cos\left(d x + c\right) + b\right)}{a d}"," ",0,"-log(a*cos(d*x + c) + b)/(a*d)","A",0
291,1,68,0,0.503678," ","integrate(cot(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, b^{2} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{3} - a 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^2*log(a*cos(d*x + c) + b)/(a^3 - a*b^2) - log(cos(d*x + c) + 1)/(a - b) - log(cos(d*x + c) - 1)/(a + b))/d","A",0
292,1,144,0,0.341743," ","integrate(cot(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{4 \, b^{4} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{5} - 2 \, a^{3} b^{2} + a b^{4}} + \frac{{\left(2 \, a - 3 \, b\right)} \log\left(\cos\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{{\left(2 \, a + 3 \, b\right)} \log\left(\cos\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(b \cos\left(d x + c\right) - a\right)}}{{\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + b^{2}}}{4 \, d}"," ",0,"-1/4*(4*b^4*log(a*cos(d*x + c) + b)/(a^5 - 2*a^3*b^2 + a*b^4) + (2*a - 3*b)*log(cos(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + (2*a + 3*b)*log(cos(d*x + c) - 1)/(a^2 + 2*a*b + b^2) + 2*(b*cos(d*x + c) - a)/((a^2 - b^2)*cos(d*x + c)^2 - a^2 + b^2))/d","A",0
293,1,289,0,0.516412," ","integrate(cot(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{16 \, b^{6} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}} - \frac{{\left(8 \, a^{2} - 21 \, a b + 15 \, b^{2}\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(8 \, a^{2} + 21 \, a b + 15 \, b^{2}\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({\left(5 \, a^{2} b - 9 \, b^{3}\right)} \cos\left(d x + c\right)^{3} + 6 \, a^{3} - 10 \, a b^{2} - 4 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, a^{2} b - 7 \, b^{3}\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*b^6*log(a*cos(d*x + c) + b)/(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6) - (8*a^2 - 21*a*b + 15*b^2)*log(cos(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (8*a^2 + 21*a*b + 15*b^2)*log(cos(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*((5*a^2*b - 9*b^3)*cos(d*x + c)^3 + 6*a^3 - 10*a*b^2 - 4*(2*a^3 - 3*a*b^2)*cos(d*x + c)^2 - (3*a^2*b - 7*b^3)*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
294,-2,0,0,0.000000," ","integrate(tan(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
295,-2,0,0,0.000000," ","integrate(tan(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
296,-2,0,0,0.000000," ","integrate(tan(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
297,-2,0,0,0.000000," ","integrate(cot(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
298,-2,0,0,0.000000," ","integrate(cot(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
299,1,321,0,0.429419," ","integrate(tan(d*x+c)^9/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{14 \, a^{3} b^{5} \cos\left(d x + c\right) - 10 \, a^{2} b^{6} + 60 \, {\left(7 \, a^{8} - 20 \, a^{6} b^{2} + 18 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{6} + 30 \, {\left(7 \, a^{7} b - 20 \, a^{5} b^{3} + 18 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(7 \, a^{6} b^{2} - 20 \, a^{4} b^{4} + 18 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(7 \, a^{5} b^{3} - 20 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(7 \, a^{4} b^{4} - 20 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2}}{a^{3} b^{7} \cos\left(d x + c\right)^{7} + a^{2} b^{8} \cos\left(d x + c\right)^{6}} + \frac{60 \, {\left(7 \, a^{6} - 20 \, a^{4} b^{2} + 18 \, a^{2} b^{4} - 4 \, b^{6}\right)} \log\left(\cos\left(d x + c\right)\right)}{b^{8}} - \frac{60 \, {\left(7 \, a^{8} - 20 \, a^{6} b^{2} + 18 \, a^{4} b^{4} - 4 \, a^{2} b^{6} - b^{8}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{2} b^{8}}}{60 \, d}"," ",0,"-1/60*((14*a^3*b^5*cos(d*x + c) - 10*a^2*b^6 + 60*(7*a^8 - 20*a^6*b^2 + 18*a^4*b^4 - 4*a^2*b^6 + b^8)*cos(d*x + c)^6 + 30*(7*a^7*b - 20*a^5*b^3 + 18*a^3*b^5)*cos(d*x + c)^5 - 10*(7*a^6*b^2 - 20*a^4*b^4 + 18*a^2*b^6)*cos(d*x + c)^4 + 5*(7*a^5*b^3 - 20*a^3*b^5)*cos(d*x + c)^3 - 3*(7*a^4*b^4 - 20*a^2*b^6)*cos(d*x + c)^2)/(a^3*b^7*cos(d*x + c)^7 + a^2*b^8*cos(d*x + c)^6) + 60*(7*a^6 - 20*a^4*b^2 + 18*a^2*b^4 - 4*b^6)*log(cos(d*x + c))/b^8 - 60*(7*a^8 - 20*a^6*b^2 + 18*a^4*b^4 - 4*a^2*b^6 - b^8)*log(a*cos(d*x + c) + b)/(a^2*b^8))/d","A",0
300,1,227,0,0.512141," ","integrate(tan(d*x+c)^7/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{5 \, a^{3} b^{3} \cos\left(d x + c\right) - 3 \, a^{2} b^{4} + 12 \, {\left(5 \, a^{6} - 9 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(5 \, a^{5} b - 9 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(5 \, a^{4} b^{2} - 9 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2}}{a^{3} b^{5} \cos\left(d x + c\right)^{5} + a^{2} b^{6} \cos\left(d x + c\right)^{4}} + \frac{12 \, {\left(5 \, a^{4} - 9 \, a^{2} b^{2} + 3 \, b^{4}\right)} \log\left(\cos\left(d x + c\right)\right)}{b^{6}} - \frac{12 \, {\left(5 \, a^{6} - 9 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{2} b^{6}}}{12 \, d}"," ",0,"-1/12*((5*a^3*b^3*cos(d*x + c) - 3*a^2*b^4 + 12*(5*a^6 - 9*a^4*b^2 + 3*a^2*b^4 - b^6)*cos(d*x + c)^4 + 6*(5*a^5*b - 9*a^3*b^3)*cos(d*x + c)^3 - 2*(5*a^4*b^2 - 9*a^2*b^4)*cos(d*x + c)^2)/(a^3*b^5*cos(d*x + c)^5 + a^2*b^6*cos(d*x + c)^4) + 12*(5*a^4 - 9*a^2*b^2 + 3*b^4)*log(cos(d*x + c))/b^6 - 12*(5*a^6 - 9*a^4*b^2 + 3*a^2*b^4 + b^6)*log(a*cos(d*x + c) + b)/(a^2*b^6))/d","A",0
301,1,149,0,0.340080," ","integrate(tan(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, a^{3} b \cos\left(d x + c\right) - a^{2} b^{2} + 2 \, {\left(3 \, a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}}{a^{3} b^{3} \cos\left(d x + c\right)^{3} + a^{2} b^{4} \cos\left(d x + c\right)^{2}} + \frac{2 \, {\left(3 \, a^{2} - 2 \, b^{2}\right)} \log\left(\cos\left(d x + c\right)\right)}{b^{4}} - \frac{2 \, {\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{2} b^{4}}}{2 \, d}"," ",0,"-1/2*((3*a^3*b*cos(d*x + c) - a^2*b^2 + 2*(3*a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)/(a^3*b^3*cos(d*x + c)^3 + a^2*b^4*cos(d*x + c)^2) + 2*(3*a^2 - 2*b^2)*log(cos(d*x + c))/b^4 - 2*(3*a^4 - 2*a^2*b^2 - b^4)*log(a*cos(d*x + c) + b)/(a^2*b^4))/d","A",0
302,1,74,0,0.386618," ","integrate(tan(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{a^{2} - b^{2}}{a^{3} b \cos\left(d x + c\right) + a^{2} b^{2}} + \frac{\log\left(\cos\left(d x + c\right)\right)}{b^{2}} - \frac{{\left(a^{2} + b^{2}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{2} b^{2}}}{d}"," ",0,"-((a^2 - b^2)/(a^3*b*cos(d*x + c) + a^2*b^2) + log(cos(d*x + c))/b^2 - (a^2 + b^2)*log(a*cos(d*x + c) + b)/(a^2*b^2))/d","A",0
303,1,41,0,0.439309," ","integrate(tan(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{b}{a^{3} \cos\left(d x + c\right) + a^{2} b} + \frac{\log\left(a \cos\left(d x + c\right) + b\right)}{a^{2}}}{d}"," ",0,"-(b/(a^3*cos(d*x + c) + a^2*b) + log(a*cos(d*x + c) + b)/a^2)/d","A",0
304,1,142,0,0.319259," ","integrate(cot(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, b^{3}}{a^{4} b - a^{2} b^{3} + {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(d x + c\right)} + \frac{2 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}} - \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*(2*b^3/(a^4*b - a^2*b^3 + (a^5 - a^3*b^2)*cos(d*x + c)) + 2*(3*a^2*b^2 - b^4)*log(a*cos(d*x + c) + b)/(a^6 - 2*a^4*b^2 + a^2*b^4) - 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
305,1,303,0,0.544106," ","integrate(cot(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(5 \, a^{2} b^{4} - b^{6}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}} + \frac{{\left(a - 2 \, 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 + 2 \, 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{a^{4} b + a^{2} b^{3} + 2 \, b^{5} - 2 \, {\left(a^{4} b + b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(d x + c\right)}{a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \cos\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(5*a^2*b^4 - b^6)*log(a*cos(d*x + c) + b)/(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6) + (a - 2*b)*log(cos(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (a + 2*b)*log(cos(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + (a^4*b + a^2*b^3 + 2*b^5 - 2*(a^4*b + b^5)*cos(d*x + c)^2 + (a^5 - a^3*b^2)*cos(d*x + c))/(a^6*b - 2*a^4*b^3 + a^2*b^5 - (a^7 - 2*a^5*b^2 + a^3*b^4)*cos(d*x + c)^3 - (a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c)^2 + (a^7 - 2*a^5*b^2 + a^3*b^4)*cos(d*x + c)))/d","A",0
306,1,558,0,0.375183," ","integrate(cot(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(7 \, a^{2} b^{6} - b^{8}\right)} \log\left(a \cos\left(d x + c\right) + b\right)}{a^{10} - 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + a^{2} b^{8}} - \frac{{\left(4 \, a^{2} - 13 \, a b + 12 \, 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(4 \, a^{2} + 13 \, a b + 12 \, 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(3 \, a^{6} b - 6 \, a^{4} b^{3} - 5 \, a^{2} b^{5} - 4 \, b^{7} + {\left(5 \, a^{6} b - 13 \, a^{4} b^{3} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(4 \, a^{7} - 11 \, a^{5} b^{2} + 7 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{3} - {\left(7 \, a^{6} b - 17 \, a^{4} b^{3} - 6 \, a^{2} b^{5} - 8 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 2 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)\right)}}{a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7} + {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} \cos\left(d x + c\right)^{5} + {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} \cos\left(d x + c\right)}}{8 \, d}"," ",0,"-1/8*(8*(7*a^2*b^6 - b^8)*log(a*cos(d*x + c) + b)/(a^10 - 4*a^8*b^2 + 6*a^6*b^4 - 4*a^4*b^6 + a^2*b^8) - (4*a^2 - 13*a*b + 12*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) - (4*a^2 + 13*a*b + 12*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*(3*a^6*b - 6*a^4*b^3 - 5*a^2*b^5 - 4*b^7 + (5*a^6*b - 13*a^4*b^3 - 4*b^7)*cos(d*x + c)^4 - (4*a^7 - 11*a^5*b^2 + 7*a^3*b^4)*cos(d*x + c)^3 - (7*a^6*b - 17*a^4*b^3 - 6*a^2*b^5 - 8*b^7)*cos(d*x + c)^2 + 3*(a^7 - 3*a^5*b^2 + 2*a^3*b^4)*cos(d*x + c))/(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7 + (a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*cos(d*x + c)^5 + (a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*cos(d*x + c)^4 - 2*(a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*cos(d*x + c)^3 - 2*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*cos(d*x + c)^2 + (a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*cos(d*x + c)))/d","B",0
307,-2,0,0,0.000000," ","integrate(tan(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
308,-2,0,0,0.000000," ","integrate(tan(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
309,-2,0,0,0.000000," ","integrate(tan(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
310,-2,0,0,0.000000," ","integrate(cot(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
311,-2,0,0,0.000000," ","integrate(cot(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
312,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(5/2)/(b*sec(d*x + c) + a), x)","F",0
313,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^(3/2)/(b*sec(d*x + c) + a), x)","F",0
314,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{e \tan\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*tan(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \sqrt{e \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*sqrt(e*tan(d*x + c))), x)","F",0
316,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*(e*tan(d*x + c))^(3/2)), x)","F",0
317,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/(e*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)} \left(e \tan\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(d*x + c) + a)*(e*tan(d*x + c))^(5/2)), x)","F",0
318,1,191,0,0.428468," ","integrate((a+b*sec(d*x+c))^(1/2)*tan(d*x+c)^5,x, algorithm=""maxima"")","\frac{315 \, \sqrt{a} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 630 \, \sqrt{a + \frac{b}{\cos\left(d x + c\right)}} + \frac{70 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{9}{2}}}{b^{4}} - \frac{270 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{7}{2}} a}{b^{4}} + \frac{378 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}} a^{2}}{b^{4}} - \frac{210 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a^{3}}{b^{4}} - \frac{252 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}}}{b^{2}} + \frac{420 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a}{b^{2}}}{315 \, d}"," ",0,"1/315*(315*sqrt(a)*log((sqrt(a + b/cos(d*x + c)) - sqrt(a))/(sqrt(a + b/cos(d*x + c)) + sqrt(a))) + 630*sqrt(a + b/cos(d*x + c)) + 70*(a + b/cos(d*x + c))^(9/2)/b^4 - 270*(a + b/cos(d*x + c))^(7/2)*a/b^4 + 378*(a + b/cos(d*x + c))^(5/2)*a^2/b^4 - 210*(a + b/cos(d*x + c))^(3/2)*a^3/b^4 - 252*(a + b/cos(d*x + c))^(5/2)/b^2 + 420*(a + b/cos(d*x + c))^(3/2)*a/b^2)/d","A",0
319,1,108,0,0.422472," ","integrate((a+b*sec(d*x+c))^(1/2)*tan(d*x+c)^3,x, algorithm=""maxima"")","-\frac{15 \, \sqrt{a} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 30 \, \sqrt{a + \frac{b}{\cos\left(d x + c\right)}} - \frac{6 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}}}{b^{2}} + \frac{10 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a}{b^{2}}}{15 \, d}"," ",0,"-1/15*(15*sqrt(a)*log((sqrt(a + b/cos(d*x + c)) - sqrt(a))/(sqrt(a + b/cos(d*x + c)) + sqrt(a))) + 30*sqrt(a + b/cos(d*x + c)) - 6*(a + b/cos(d*x + c))^(5/2)/b^2 + 10*(a + b/cos(d*x + c))^(3/2)*a/b^2)/d","A",0
320,1,67,0,0.423942," ","integrate((a+b*sec(d*x+c))^(1/2)*tan(d*x+c),x, algorithm=""maxima"")","\frac{\sqrt{a} \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} + \sqrt{a}}\right) + 2 \, \sqrt{a + \frac{b}{\cos\left(d x + c\right)}}}{d}"," ",0,"(sqrt(a)*log((sqrt(a + b/cos(d*x + c)) - sqrt(a))/(sqrt(a + b/cos(d*x + c)) + sqrt(a))) + 2*sqrt(a + b/cos(d*x + c)))/d","A",0
321,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cot(d*x + c), x)","F",0
322,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cot(d*x + c)^3, x)","F",0
323,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)*tan(d*x+c)^2,x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*tan(d*x + c)^2, x)","F",0
324,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a), x)","F",0
325,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*cot(d*x + c)^2, x)","F",0
326,1,175,0,0.427204," ","integrate(tan(d*x+c)^5/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{105 \, \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{\sqrt{a}} + \frac{30 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{7}{2}}}{b^{4}} - \frac{126 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}} a}{b^{4}} + \frac{210 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a^{2}}{b^{4}} - \frac{210 \, \sqrt{a + \frac{b}{\cos\left(d x + c\right)}} a^{3}}{b^{4}} - \frac{140 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}}}{b^{2}} + \frac{420 \, \sqrt{a + \frac{b}{\cos\left(d x + c\right)}} a}{b^{2}}}{105 \, d}"," ",0,"1/105*(105*log((sqrt(a + b/cos(d*x + c)) - sqrt(a))/(sqrt(a + b/cos(d*x + c)) + sqrt(a)))/sqrt(a) + 30*(a + b/cos(d*x + c))^(7/2)/b^4 - 126*(a + b/cos(d*x + c))^(5/2)*a/b^4 + 210*(a + b/cos(d*x + c))^(3/2)*a^2/b^4 - 210*sqrt(a + b/cos(d*x + c))*a^3/b^4 - 140*(a + b/cos(d*x + c))^(3/2)/b^2 + 420*sqrt(a + b/cos(d*x + c))*a/b^2)/d","A",0
327,1,92,0,0.425073," ","integrate(tan(d*x+c)^3/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{\sqrt{a}} - \frac{2 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}}}{b^{2}} + \frac{6 \, \sqrt{a + \frac{b}{\cos\left(d x + c\right)}} a}{b^{2}}}{3 \, d}"," ",0,"-1/3*(3*log((sqrt(a + b/cos(d*x + c)) - sqrt(a))/(sqrt(a + b/cos(d*x + c)) + sqrt(a)))/sqrt(a) - 2*(a + b/cos(d*x + c))^(3/2)/b^2 + 6*sqrt(a + b/cos(d*x + c))*a/b^2)/d","A",0
328,1,49,0,0.413728," ","integrate(tan(d*x+c)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\frac{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{\sqrt{a} d}"," ",0,"log((sqrt(a + b/cos(d*x + c)) - sqrt(a))/(sqrt(a + b/cos(d*x + c)) + sqrt(a)))/(sqrt(a)*d)","A",0
329,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
330,0,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
331,0,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{4}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^4/sqrt(b*sec(d*x + c) + a), x)","F",0
332,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
333,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sec(d*x + c) + a), x)","F",0
334,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
335,1,194,0,0.432884," ","integrate(tan(d*x+c)^5/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{5 \, \log\left(\frac{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{10}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} a} + \frac{2 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{5}{2}}}{b^{4}} - \frac{10 \, {\left(a + \frac{b}{\cos\left(d x + c\right)}\right)}^{\frac{3}{2}} a}{b^{4}} + \frac{30 \, \sqrt{a + \frac{b}{\cos\left(d x + c\right)}} a^{2}}{b^{4}} + \frac{10 \, a^{3}}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} b^{4}} - \frac{20 \, \sqrt{a + \frac{b}{\cos\left(d x + c\right)}}}{b^{2}} - \frac{20 \, a}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} b^{2}}}{5 \, d}"," ",0,"1/5*(5*log((sqrt(a + b/cos(d*x + c)) - sqrt(a))/(sqrt(a + b/cos(d*x + c)) + sqrt(a)))/a^(3/2) + 10/(sqrt(a + b/cos(d*x + c))*a) + 2*(a + b/cos(d*x + c))^(5/2)/b^4 - 10*(a + b/cos(d*x + c))^(3/2)*a/b^4 + 30*sqrt(a + b/cos(d*x + c))*a^2/b^4 + 10*a^3/(sqrt(a + b/cos(d*x + c))*b^4) - 20*sqrt(a + b/cos(d*x + c))/b^2 - 20*a/(sqrt(a + b/cos(d*x + c))*b^2))/d","A",0
336,1,110,0,0.424523," ","integrate(tan(d*x+c)^3/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\frac{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} a} - \frac{2 \, \sqrt{a + \frac{b}{\cos\left(d x + c\right)}}}{b^{2}} - \frac{2 \, a}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} b^{2}}}{d}"," ",0,"-(log((sqrt(a + b/cos(d*x + c)) - sqrt(a))/(sqrt(a + b/cos(d*x + c)) + sqrt(a)))/a^(3/2) + 2/(sqrt(a + b/cos(d*x + c))*a) - 2*sqrt(a + b/cos(d*x + c))/b^2 - 2*a/(sqrt(a + b/cos(d*x + c))*b^2))/d","A",0
337,1,70,0,0.419953," ","integrate(tan(d*x+c)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{\log\left(\frac{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} - \sqrt{a}}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2}{\sqrt{a + \frac{b}{\cos\left(d x + c\right)}} a}}{d}"," ",0,"(log((sqrt(a + b/cos(d*x + c)) - sqrt(a))/(sqrt(a + b/cos(d*x + c)) + sqrt(a)))/a^(3/2) + 2/(sqrt(a + b/cos(d*x + c))*a))/d","A",0
338,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)/(b*sec(d*x + c) + a)^(3/2), x)","F",0
339,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-1,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/(b*sec(d*x + c) + a)^(3/2), x)","F",0
342,0,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(-3/2), x)","F",0
343,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
344,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^3*(d*tan(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{3} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^3*(d*tan(f*x + e))^n, x)","F",0
345,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^2*(d*tan(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)}^{2} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)^2*(d*tan(f*x + e))^n, x)","F",0
346,0,0,0,0.000000," ","integrate((a+b*sec(f*x+e))*(d*tan(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(b \sec\left(f x + e\right) + a\right)} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sec(f*x + e) + a)*(d*tan(f*x + e))^n, x)","F",0
347,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+b*sec(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{b \sec\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/(b*sec(f*x + e) + a), x)","F",0
348,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)*(e*tan(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^(3/2)*(e*tan(d*x + c))^m, x)","F",0
349,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)*(e*tan(d*x+c))^m,x, algorithm=""maxima"")","\int \sqrt{b \sec\left(d x + c\right) + a} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)*(e*tan(d*x + c))^m, x)","F",0
350,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+b*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \tan\left(d x + c\right)\right)^{m}}{\sqrt{b \sec\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*tan(d*x + c))^m/sqrt(b*sec(d*x + c) + a), x)","F",0
351,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m/(a+b*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(e \tan\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*tan(d*x + c))^m/(b*sec(d*x + c) + a)^(3/2), x)","F",0
352,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*(e*tan(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \left(e \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*(e*tan(d*x + c))^m, x)","F",0
353,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c)^5, x)","F",0
354,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c)^3, x)","F",0
355,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c), x)","F",0
356,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*cot(d*x + c), x)","F",0
357,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*cot(d*x + c)^3, x)","F",0
358,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c)^4, x)","F",0
359,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c)^2, x)","F",0
360,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*cot(d*x + c)^2, x)","F",0
361,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*cot(d*x + c)^4, x)","F",0
362,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*tan(d*x + c)^(3/2), x)","F",0
363,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n*tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(d x + c\right) + a\right)}^{n} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n*sqrt(tan(d*x + c)), x)","F",0
364,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{n}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n/sqrt(tan(d*x + c)), x)","F",0
365,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^n/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(d x + c\right) + a\right)}^{n}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(d*x + c) + a)^n/tan(d*x + c)^(3/2), x)","F",0
