1,-2,0,0,0.000000," ","integrate(sin(x)^4/(I+tan(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
2,-2,0,0,0.000000," ","integrate(sin(x)^3/(I+tan(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
3,-2,0,0,0.000000," ","integrate(sin(x)^2/(I+tan(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
4,-2,0,0,0.000000," ","integrate(sin(x)/(I+tan(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
5,1,28,0,0.313799," ","integrate(csc(x)/(I+tan(x)),x, algorithm=""maxima"")","\frac{2}{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + i} - i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"2/(sin(x)/(cos(x) + 1) + I) - I*log(sin(x)/(cos(x) + 1))","B",0
6,1,17,0,0.315361," ","integrate(csc(x)^2/(I+tan(x)),x, algorithm=""maxima"")","\frac{i}{\tan\left(x\right)} - \log\left(\tan\left(x\right) + i\right) + \log\left(\tan\left(x\right)\right)"," ",0,"I/tan(x) - log(tan(x) + I) + log(tan(x))","A",0
7,1,59,0,0.317544," ","integrate(csc(x)^3/(I+tan(x)),x, algorithm=""maxima"")","-\frac{{\left(\frac{4 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - i\right)} {\left(\cos\left(x\right) + 1\right)}^{2}}{8 \, \sin\left(x\right)^{2}} - \frac{\sin\left(x\right)}{2 \, {\left(\cos\left(x\right) + 1\right)}} - \frac{i \, \sin\left(x\right)^{2}}{8 \, {\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{1}{2} i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-1/8*(4*sin(x)/(cos(x) + 1) - I)*(cos(x) + 1)^2/sin(x)^2 - 1/2*sin(x)/(cos(x) + 1) - 1/8*I*sin(x)^2/(cos(x) + 1)^2 + 1/2*I*log(sin(x)/(cos(x) + 1))","B",0
8,1,12,0,0.574360," ","integrate(csc(x)^4/(I+tan(x)),x, algorithm=""maxima"")","-\frac{i \, {\left(-3 i \, \tan\left(x\right) - 2\right)}}{6 \, \tan\left(x\right)^{3}}"," ",0,"-1/6*I*(-3*I*tan(x) - 2)/tan(x)^3","A",0
9,1,83,0,0.511250," ","integrate(csc(x)^5/(I+tan(x)),x, algorithm=""maxima"")","-\frac{{\left(\frac{8 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{24 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - 3 i\right)} {\left(\cos\left(x\right) + 1\right)}^{4}}{192 \, \sin\left(x\right)^{4}} - \frac{\sin\left(x\right)}{8 \, {\left(\cos\left(x\right) + 1\right)}} - \frac{\sin\left(x\right)^{3}}{24 \, {\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{i \, \sin\left(x\right)^{4}}{64 \, {\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{1}{8} i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-1/192*(8*sin(x)/(cos(x) + 1) + 24*sin(x)^3/(cos(x) + 1)^3 - 3*I)*(cos(x) + 1)^4/sin(x)^4 - 1/8*sin(x)/(cos(x) + 1) - 1/24*sin(x)^3/(cos(x) + 1)^3 - 1/64*I*sin(x)^4/(cos(x) + 1)^4 + 1/8*I*log(sin(x)/(cos(x) + 1))","B",0
10,1,24,0,0.414743," ","integrate(csc(x)^6/(I+tan(x)),x, algorithm=""maxima"")","\frac{i \, {\left(30 i \, \tan\left(x\right)^{3} + 20 \, \tan\left(x\right)^{2} + 15 i \, \tan\left(x\right) + 12\right)}}{60 \, \tan\left(x\right)^{5}}"," ",0,"1/60*I*(30*I*tan(x)^3 + 20*tan(x)^2 + 15*I*tan(x) + 12)/tan(x)^5","A",0
11,1,91,0,0.374292," ","integrate(sin(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} a + {\left(6 \, \sin\left(d x + c\right)^{5} + 10 \, \sin\left(d x + c\right)^{3} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 30 \, \sin\left(d x + c\right)\right)} b}{30 \, d}"," ",0,"-1/30*(2*(3*cos(d*x + c)^5 - 10*cos(d*x + c)^3 + 15*cos(d*x + c))*a + (6*sin(d*x + c)^5 + 10*sin(d*x + c)^3 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 30*sin(d*x + c))*b)/d","A",0
12,1,87,0,0.530436," ","integrate(sin(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(d x + c\right)} a + 4 \, b \log\left(\tan\left(d x + c\right)^{2} + 1\right) - \frac{5 \, a \tan\left(d x + c\right)^{3} - 8 \, b \tan\left(d x + c\right)^{2} + 3 \, a \tan\left(d x + c\right) - 6 \, b}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*(3*(d*x + c)*a + 4*b*log(tan(d*x + c)^2 + 1) - (5*a*tan(d*x + c)^3 - 8*b*tan(d*x + c)^2 + 3*a*tan(d*x + c) - 6*b)/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
13,1,70,0,0.580429," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a - {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} b}{6 \, d}"," ",0,"1/6*(2*(cos(d*x + c)^3 - 3*cos(d*x + c))*a - (2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*b)/d","A",0
14,1,52,0,0.565734," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} a + b \log\left(\tan\left(d x + c\right)^{2} + 1\right) - \frac{a \tan\left(d x + c\right) - b}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*((d*x + c)*a + b*log(tan(d*x + c)^2 + 1) - (a*tan(d*x + c) - b)/(tan(d*x + c)^2 + 1))/d","A",0
15,1,46,0,0.413131," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} - 2 \, a \cos\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) - 2*a*cos(d*x + c))/d","A",0
16,1,46,0,0.538851," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 2 \, a \log\left(\cot\left(d x + c\right) + \csc\left(d x + c\right)\right)}{2 \, d}"," ",0,"1/2*(b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 2*a*log(cot(d*x + c) + csc(d*x + c)))/d","A",0
17,1,25,0,0.317671," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{b \log\left(\tan\left(d x + c\right)\right) - \frac{a}{\tan\left(d x + c\right)}}{d}"," ",0,"(b*log(tan(d*x + c)) - a/tan(d*x + c))/d","A",0
18,1,83,0,0.535297," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{a {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 2 \, b {\left(\frac{2}{\sin\left(d x + c\right)} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"1/4*(a*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 2*b*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
19,1,50,0,0.522076," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, b \log\left(\tan\left(d x + c\right)\right) - \frac{6 \, a \tan\left(d x + c\right)^{2} + 3 \, b \tan\left(d x + c\right) + 2 \, a}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*b*log(tan(d*x + c)) - (6*a*tan(d*x + c)^2 + 3*b*tan(d*x + c) + 2*a)/tan(d*x + c)^3)/d","A",0
20,1,123,0,0.514489," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, a {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 8 \, b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 1\right)}}{\sin\left(d x + c\right)^{3}} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(3*a*(2*(3*cos(d*x + c)^3 - 5*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 8*b*(2*(3*sin(d*x + c)^2 + 1)/sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)))/d","A",0
21,1,72,0,0.585505," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{60 \, b \log\left(\tan\left(d x + c\right)\right) - \frac{60 \, a \tan\left(d x + c\right)^{4} + 60 \, b \tan\left(d x + c\right)^{3} + 40 \, a \tan\left(d x + c\right)^{2} + 15 \, b \tan\left(d x + c\right) + 12 \, a}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*b*log(tan(d*x + c)) - (60*a*tan(d*x + c)^4 + 60*b*tan(d*x + c)^3 + 40*a*tan(d*x + c)^2 + 15*b*tan(d*x + c) + 12*a)/tan(d*x + c)^5)/d","A",0
22,1,128,0,0.892134," ","integrate(sin(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{8 \, a b \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 8 \, b^{2} \tan\left(d x + c\right) + 3 \, {\left(a^{2} - 5 \, b^{2}\right)} {\left(d x + c\right)} + \frac{16 \, a b \tan\left(d x + c\right)^{2} - {\left(5 \, a^{2} - 9 \, b^{2}\right)} \tan\left(d x + c\right)^{3} + 12 \, a b - {\left(3 \, a^{2} - 7 \, b^{2}\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*(8*a*b*log(tan(d*x + c)^2 + 1) + 8*b^2*tan(d*x + c) + 3*(a^2 - 5*b^2)*(d*x + c) + (16*a*b*tan(d*x + c)^2 - (5*a^2 - 9*b^2)*tan(d*x + c)^3 + 12*a*b - (3*a^2 - 7*b^2)*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
23,1,104,0,0.470208," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{2} - {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a b - {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} b^{2}}{3 \, d}"," ",0,"1/3*((cos(d*x + c)^3 - 3*cos(d*x + c))*a^2 - (2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a*b - (cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*b^2)/d","A",0
24,1,82,0,0.434868," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, a b \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, b^{2} \tan\left(d x + c\right) + {\left(a^{2} - 3 \, b^{2}\right)} {\left(d x + c\right)} + \frac{2 \, a b - {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*(2*a*b*log(tan(d*x + c)^2 + 1) + 2*b^2*tan(d*x + c) + (a^2 - 3*b^2)*(d*x + c) + (2*a*b - (a^2 - b^2)*tan(d*x + c))/(tan(d*x + c)^2 + 1))/d","A",0
25,1,67,0,0.365856," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{b^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} + a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} - a^{2} \cos\left(d x + c\right)}{d}"," ",0,"(b^2*(1/cos(d*x + c) + cos(d*x + c)) + a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) - a^2*cos(d*x + c))/d","A",0
26,1,60,0,0.546868," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - a^{2} \log\left(\cot\left(d x + c\right) + \csc\left(d x + c\right)\right) + \frac{b^{2}}{\cos\left(d x + c\right)}}{d}"," ",0,"(a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - a^2*log(cot(d*x + c) + csc(d*x + c)) + b^2/cos(d*x + c))/d","A",0
27,1,39,0,0.467675," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, a b \log\left(\tan\left(d x + c\right)\right) + b^{2} \tan\left(d x + c\right) - \frac{a^{2}}{\tan\left(d x + c\right)}}{d}"," ",0,"(2*a*b*log(tan(d*x + c)) + b^2*tan(d*x + c) - a^2/tan(d*x + c))/d","A",0
28,1,122,0,0.350299," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 2 \, b^{2} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 4 \, a b {\left(\frac{2}{\sin\left(d x + c\right)} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"1/4*(a^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 2*b^2*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 4*a*b*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
29,1,69,0,0.621151," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, a b \log\left(\tan\left(d x + c\right)\right) + 3 \, b^{2} \tan\left(d x + c\right) - \frac{3 \, a b \tan\left(d x + c\right) + 3 \, {\left(a^{2} + b^{2}\right)} \tan\left(d x + c\right)^{2} + a^{2}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(6*a*b*log(tan(d*x + c)) + 3*b^2*tan(d*x + c) - (3*a*b*tan(d*x + c) + 3*(a^2 + b^2)*tan(d*x + c)^2 + a^2)/tan(d*x + c)^3)/d","A",0
30,1,187,0,0.465855," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, a^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 12 \, b^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 16 \, a b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 1\right)}}{\sin\left(d x + c\right)^{3}} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(3*a^2*(2*(3*cos(d*x + c)^3 - 5*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 12*b^2*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 16*a*b*(2*(3*sin(d*x + c)^2 + 1)/sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)))/d","A",0
31,1,104,0,0.737650," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{60 \, a b \log\left(\tan\left(d x + c\right)\right) + 30 \, b^{2} \tan\left(d x + c\right) - \frac{60 \, a b \tan\left(d x + c\right)^{3} + 30 \, {\left(a^{2} + 2 \, b^{2}\right)} \tan\left(d x + c\right)^{4} + 15 \, a b \tan\left(d x + c\right) + 10 \, {\left(2 \, a^{2} + b^{2}\right)} \tan\left(d x + c\right)^{2} + 6 \, a^{2}}{\tan\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"1/30*(60*a*b*log(tan(d*x + c)) + 30*b^2*tan(d*x + c) - (60*a*b*tan(d*x + c)^3 + 30*(a^2 + 2*b^2)*tan(d*x + c)^4 + 15*a*b*tan(d*x + c) + 10*(2*a^2 + b^2)*tan(d*x + c)^2 + 6*a^2)/tan(d*x + c)^5)/d","A",0
32,1,173,0,0.707209," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{3} - 6 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a^{2} b - 12 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a b^{2} + {\left(4 \, \sin\left(d x + c\right)^{3} - \frac{6 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 24 \, \sin\left(d x + c\right)\right)} b^{3}}{12 \, d}"," ",0,"1/12*(4*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^3 - 6*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a^2*b - 12*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a*b^2 + (4*sin(d*x + c)^3 - 6*sin(d*x + c)/(sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 24*sin(d*x + c))*b^3)/d","A",0
33,1,113,0,0.450215," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{b^{3} \tan\left(d x + c\right)^{2} + 6 \, a b^{2} \tan\left(d x + c\right) + {\left(a^{3} - 9 \, a b^{2}\right)} {\left(d x + c\right)} + {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + \frac{3 \, a^{2} b - b^{3} - {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*(b^3*tan(d*x + c)^2 + 6*a*b^2*tan(d*x + c) + (a^3 - 9*a*b^2)*(d*x + c) + (3*a^2*b - 2*b^3)*log(tan(d*x + c)^2 + 1) + (3*a^2*b - b^3 - (a^3 - 3*a*b^2)*tan(d*x + c))/(tan(d*x + c)^2 + 1))/d","A",0
34,1,128,0,0.319282," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + 3 \, \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \log\left(\sin\left(d x + c\right) - 1\right) - 4 \, \sin\left(d x + c\right)\right)} - 12 \, a b^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - 6 \, a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} + 4 \, a^{3} \cos\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1) - 4*sin(d*x + c)) - 12*a*b^2*(1/cos(d*x + c) + cos(d*x + c)) - 6*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) + 4*a^3*cos(d*x + c))/d","A",0
35,1,111,0,0.327222," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, a^{3} \log\left(\cot\left(d x + c\right) + \csc\left(d x + c\right)\right) - \frac{12 \, a b^{2}}{\cos\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 6*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*a^3*log(cot(d*x + c) + csc(d*x + c)) - 12*a*b^2/cos(d*x + c))/d","A",0
36,1,56,0,0.318422," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{b^{3} \tan\left(d x + c\right)^{2} + 6 \, a^{2} b \log\left(\tan\left(d x + c\right)\right) + 6 \, a b^{2} \tan\left(d x + c\right) - \frac{2 \, a^{3}}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(b^3*tan(d*x + c)^2 + 6*a^2*b*log(tan(d*x + c)) + 6*a*b^2*tan(d*x + c) - 2*a^3/tan(d*x + c))/d","A",0
37,1,171,0,0.333738," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a b^{2} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 6 \, a^{2} b {\left(\frac{2}{\sin\left(d x + c\right)} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"1/4*(a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*a*b^2*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 6*a^2*b*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
38,1,98,0,0.457303," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, b^{3} \tan\left(d x + c\right)^{2} + 18 \, a b^{2} \tan\left(d x + c\right) + 6 \, {\left(3 \, a^{2} b + b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{9 \, a^{2} b \tan\left(d x + c\right) + 2 \, a^{3} + 6 \, {\left(a^{3} + 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(3*b^3*tan(d*x + c)^2 + 18*a*b^2*tan(d*x + c) + 6*(3*a^2*b + b^3)*log(tan(d*x + c)) - (9*a^2*b*tan(d*x + c) + 2*a^3 + 6*(a^3 + 3*a*b^2)*tan(d*x + c)^2)/tan(d*x + c)^3)/d","A",0
39,1,250,0,0.514221," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 12 \, a b^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 4 \, b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 2\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 8 \, a^{2} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 1\right)}}{\sin\left(d x + c\right)^{3}} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{16 \, d}"," ",0,"1/16*(a^3*(2*(3*cos(d*x + c)^3 - 5*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 12*a*b^2*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 4*b^3*(2*(3*sin(d*x + c)^2 - 2)/(sin(d*x + c)^3 - sin(d*x + c)) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 8*a^2*b*(2*(3*sin(d*x + c)^2 + 1)/sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)))/d","A",0
40,1,142,0,0.324231," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{30 \, b^{3} \tan\left(d x + c\right)^{2} + 180 \, a b^{2} \tan\left(d x + c\right) + 60 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{60 \, {\left(a^{3} + 6 \, a b^{2}\right)} \tan\left(d x + c\right)^{4} + 45 \, a^{2} b \tan\left(d x + c\right) + 30 \, {\left(6 \, a^{2} b + b^{3}\right)} \tan\left(d x + c\right)^{3} + 12 \, a^{3} + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(30*b^3*tan(d*x + c)^2 + 180*a*b^2*tan(d*x + c) + 60*(3*a^2*b + 2*b^3)*log(tan(d*x + c)) - (60*(a^3 + 6*a*b^2)*tan(d*x + c)^4 + 45*a^2*b*tan(d*x + c) + 30*(6*a^2*b + b^3)*tan(d*x + c)^3 + 12*a^3 + 20*(2*a^3 + 3*a*b^2)*tan(d*x + c)^2)/tan(d*x + c)^5)/d","A",0
41,1,218,0,0.537559," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{{\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{4} - 2 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a^{3} b - 6 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a^{2} b^{2} + {\left(4 \, \sin\left(d x + c\right)^{3} - \frac{6 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 24 \, \sin\left(d x + c\right)\right)} a b^{3} + {\left(\cos\left(d x + c\right)^{3} - \frac{9 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} - 9 \, \cos\left(d x + c\right)\right)} b^{4}}{3 \, d}"," ",0,"1/3*((cos(d*x + c)^3 - 3*cos(d*x + c))*a^4 - 2*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a^3*b - 6*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a^2*b^2 + (4*sin(d*x + c)^3 - 6*sin(d*x + c)/(sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 24*sin(d*x + c))*a*b^3 + (cos(d*x + c)^3 - (9*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 - 9*cos(d*x + c))*b^4)/d","A",0
42,1,154,0,0.452295," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{2 \, b^{4} \tan\left(d x + c\right)^{3} + 12 \, a b^{3} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{4} - 18 \, a^{2} b^{2} + 5 \, b^{4}\right)} {\left(d x + c\right)} + 12 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} \tan\left(d x + c\right) + \frac{3 \, {\left(4 \, a^{3} b - 4 \, a b^{3} - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)\right)}}{\tan\left(d x + c\right)^{2} + 1}}{6 \, d}"," ",0,"1/6*(2*b^4*tan(d*x + c)^3 + 12*a*b^3*tan(d*x + c)^2 + 3*(a^4 - 18*a^2*b^2 + 5*b^4)*(d*x + c) + 12*(a^3*b - 2*a*b^3)*log(tan(d*x + c)^2 + 1) + 12*(3*a^2*b^2 - b^4)*tan(d*x + c) + 3*(4*a^3*b - 4*a*b^3 - (a^4 - 6*a^2*b^2 + b^4)*tan(d*x + c))/(tan(d*x + c)^2 + 1))/d","A",0
43,1,166,0,0.695182," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + 3 \, \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \log\left(\sin\left(d x + c\right) - 1\right) - 4 \, \sin\left(d x + c\right)\right)} - 18 \, a^{2} b^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} + b^{4} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)} - 6 \, a^{3} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} + 3 \, a^{4} \cos\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(3*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1) - 4*sin(d*x + c)) - 18*a^2*b^2*(1/cos(d*x + c) + cos(d*x + c)) + b^4*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)) - 6*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) + 3*a^4*cos(d*x + c))/d","A",0
44,1,139,0,0.680674," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, a^{3} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 3 \, a^{4} \log\left(\cot\left(d x + c\right) + \csc\left(d x + c\right)\right) - \frac{18 \, a^{2} b^{2}}{\cos\left(d x + c\right)} + \frac{{\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} b^{4}}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"-1/3*(3*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 6*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 3*a^4*log(cot(d*x + c) + csc(d*x + c)) - 18*a^2*b^2/cos(d*x + c) + (3*cos(d*x + c)^2 - 1)*b^4/cos(d*x + c)^3)/d","A",0
45,1,72,0,0.416972," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{b^{4} \tan\left(d x + c\right)^{3} + 6 \, a b^{3} \tan\left(d x + c\right)^{2} + 12 \, a^{3} b \log\left(\tan\left(d x + c\right)\right) + 18 \, a^{2} b^{2} \tan\left(d x + c\right) - \frac{3 \, a^{4}}{\tan\left(d x + c\right)}}{3 \, d}"," ",0,"1/3*(b^4*tan(d*x + c)^3 + 6*a*b^3*tan(d*x + c)^2 + 12*a^3*b*log(tan(d*x + c)) + 18*a^2*b^2*tan(d*x + c) - 3*a^4/tan(d*x + c))/d","A",0
46,1,188,0,0.475732," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, a^{4} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 12 \, a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, a^{2} b^{2} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 24 \, a^{3} b {\left(\frac{2}{\sin\left(d x + c\right)} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{4 \, b^{4}}{\cos\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"1/12*(3*a^4*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 12*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 36*a^2*b^2*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 24*a^3*b*(2/sin(d*x + c) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 4*b^4/cos(d*x + c)^3)/d","A",0
47,1,120,0,0.403919," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{b^{4} \tan\left(d x + c\right)^{3} + 6 \, a b^{3} \tan\left(d x + c\right)^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) + 3 \, {\left(6 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right) - \frac{6 \, a^{3} b \tan\left(d x + c\right) + a^{4} + 3 \, {\left(a^{4} + 6 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(b^4*tan(d*x + c)^3 + 6*a*b^3*tan(d*x + c)^2 + 12*(a^3*b + a*b^3)*log(tan(d*x + c)) + 3*(6*a^2*b^2 + b^4)*tan(d*x + c) - (6*a^3*b*tan(d*x + c) + a^4 + 3*(a^4 + 6*a^2*b^2)*tan(d*x + c)^2)/tan(d*x + c)^3)/d","A",0
48,1,304,0,0.632663," ","integrate(csc(d*x+c)^5*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, a^{4} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 72 \, a^{2} b^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 48 \, a b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} - 2\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, b^{4} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{\cos\left(d x + c\right)^{3}} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 32 \, a^{3} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 1\right)}}{\sin\left(d x + c\right)^{3}} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(3*a^4*(2*(3*cos(d*x + c)^3 - 5*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 72*a^2*b^2*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 48*a*b^3*(2*(3*sin(d*x + c)^2 - 2)/(sin(d*x + c)^3 - sin(d*x + c)) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 8*b^4*(2*(3*cos(d*x + c)^2 + 1)/cos(d*x + c)^3 - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 32*a^3*b*(2*(3*sin(d*x + c)^2 + 1)/sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)))/d","A",0
49,1,171,0,0.629160," ","integrate(csc(d*x+c)^6*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{5 \, b^{4} \tan\left(d x + c\right)^{3} + 30 \, a b^{3} \tan\left(d x + c\right)^{2} + 60 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) + 30 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right) - \frac{15 \, a^{3} b \tan\left(d x + c\right) + 15 \, {\left(a^{4} + 12 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{4} + 3 \, a^{4} + 30 \, {\left(2 \, a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)^{3} + 10 \, {\left(a^{4} + 3 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*(5*b^4*tan(d*x + c)^3 + 30*a*b^3*tan(d*x + c)^2 + 60*(a^3*b + 2*a*b^3)*log(tan(d*x + c)) + 30*(3*a^2*b^2 + b^4)*tan(d*x + c) - (15*a^3*b*tan(d*x + c) + 15*(a^4 + 12*a^2*b^2 + b^4)*tan(d*x + c)^4 + 3*a^4 + 30*(2*a^3*b + a*b^3)*tan(d*x + c)^3 + 10*(a^4 + 3*a^2*b^2)*tan(d*x + c)^2)/tan(d*x + c)^5)/d","A",0
50,1,387,0,0.401278," ","integrate(csc(d*x+c)^7*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{5 \, a^{4} {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{5} - 40 \, \cos\left(d x + c\right)^{3} + 33 \, \cos\left(d x + c\right)\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 40 \, b^{4} {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{3}} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 180 \, a^{2} b^{2} {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 25 \, \cos\left(d x + c\right)^{2} + 8\right)}}{\cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 160 \, a b^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} - 10 \, \sin\left(d x + c\right)^{2} - 2\right)}}{\sin\left(d x + c\right)^{5} - \sin\left(d x + c\right)^{3}} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 64 \, a^{3} b {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} + 5 \, \sin\left(d x + c\right)^{2} + 3\right)}}{\sin\left(d x + c\right)^{5}} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{480 \, d}"," ",0,"1/480*(5*a^4*(2*(15*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 33*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 40*b^4*(2*(15*cos(d*x + c)^4 - 10*cos(d*x + c)^2 - 2)/(cos(d*x + c)^5 - cos(d*x + c)^3) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 180*a^2*b^2*(2*(15*cos(d*x + c)^4 - 25*cos(d*x + c)^2 + 8)/(cos(d*x + c)^5 - 2*cos(d*x + c)^3 + cos(d*x + c)) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) - 160*a*b^3*(2*(15*sin(d*x + c)^4 - 10*sin(d*x + c)^2 - 2)/(sin(d*x + c)^5 - sin(d*x + c)^3) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 64*a^3*b*(2*(15*sin(d*x + c)^4 + 5*sin(d*x + c)^2 + 3)/sin(d*x + c)^5 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)))/d","A",0
51,1,658,0,0.799150," ","integrate(sin(d*x+c)^5/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{15 \, a^{5} b \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(8 \, a^{5} - 9 \, a^{3} b^{2} - 2 \, a b^{4} - \frac{15 \, a^{4} b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15 \, a^{3} b^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{15 \, a^{4} b \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{10 \, {\left(4 \, a^{5} - 3 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{20 \, {\left(4 \, a^{4} b + a^{2} b^{3}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{10 \, {\left(8 \, a^{5} + a b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2 \, {\left(89 \, a^{4} b + 68 \, a^{2} b^{3} + 24 \, b^{5}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{30 \, {\left(3 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{20 \, {\left(4 \, a^{4} b + a^{2} b^{3}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6} + \frac{5 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}}}{15 \, d}"," ",0,"1/15*(15*a^5*b*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 2*(8*a^5 - 9*a^3*b^2 - 2*a*b^4 - 15*a^4*b*sin(d*x + c)/(cos(d*x + c) + 1) - 15*a^3*b^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 15*a^4*b*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 10*(4*a^5 - 3*a^3*b^2 - a*b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 20*(4*a^4*b + a^2*b^3)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 10*(8*a^5 + a*b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2*(89*a^4*b + 68*a^2*b^3 + 24*b^5)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 30*(3*a^3*b^2 + a*b^4)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 20*(4*a^4*b + a^2*b^3)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6 + 5*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10))/d","B",0
52,1,280,0,0.625342," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, a^{4} b \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{4 \, a^{4} b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{5} - 6 \, a^{3} b^{2} - a b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(5 \, a^{3} + a b^{2}\right)} \tan\left(d x + c\right)^{3} + 6 \, a^{2} b + 2 \, b^{3} + 4 \, {\left(2 \, a^{2} b + b^{3}\right)} \tan\left(d x + c\right)^{2} + {\left(3 \, a^{3} - a b^{2}\right)} \tan\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \tan\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)} \tan\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"1/8*(8*a^4*b*log(b*tan(d*x + c) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 4*a^4*b*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*a^5 - 6*a^3*b^2 - a*b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((5*a^3 + a*b^2)*tan(d*x + c)^3 + 6*a^2*b + 2*b^3 + 4*(2*a^2*b + b^3)*tan(d*x + c)^2 + (3*a^3 - a*b^2)*tan(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*tan(d*x + c)^4 + a^4 + 2*a^2*b^2 + b^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*tan(d*x + c)^2))/d","A",0
53,1,364,0,0.643048," ","integrate(sin(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{3 \, a^{3} b \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(2 \, a^{3} - a b^{2} - \frac{3 \, a^{2} b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3 \, a b^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3 \, a^{2} b \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, {\left(5 \, a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}}{3 \, d}"," ",0,"1/3*(3*a^3*b*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(2*a^3 - a*b^2 - 3*a^2*b*sin(d*x + c)/(cos(d*x + c) + 1) + 6*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 3*a*b^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3*a^2*b*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*(5*a^2*b + 2*b^3)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 + 2*a^2*b^2 + b^4 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6))/d","B",0
54,1,144,0,0.579152," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, a^{2} b \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a^{2} b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{3} - a b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{a \tan\left(d x + c\right) + b}{{\left(a^{2} + b^{2}\right)} \tan\left(d x + c\right)^{2} + a^{2} + b^{2}}}{2 \, d}"," ",0,"1/2*(2*a^2*b*log(b*tan(d*x + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - a^2*b*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^3 - a*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - (a*tan(d*x + c) + b)/((a^2 + b^2)*tan(d*x + c)^2 + a^2 + b^2))/d","A",0
55,1,141,0,0.788486," ","integrate(sin(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{a b \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(a - \frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}}{a^{2} + b^{2} + \frac{{\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{d}"," ",0,"(a*b*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(a - b*sin(d*x + c)/(cos(d*x + c) + 1))/(a^2 + b^2 + (a^2 + b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","A",0
56,1,107,0,0.470542," ","integrate(csc(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{b \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} a} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{d}"," ",0,"(b*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a) + log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","A",0
57,1,47,0,0.584674," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{b \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2}} - \frac{b \log\left(\tan\left(d x + c\right)\right)}{a^{2}} - \frac{1}{a \tan\left(d x + c\right)}}{d}"," ",0,"(b*log(b*tan(d*x + c) + a)/a^2 - b*log(tan(d*x + c))/a^2 - 1/(a*tan(d*x + c)))/d","A",0
58,1,215,0,0.662703," ","integrate(csc(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{4 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{2}} + \frac{4 \, {\left(a^{2} + 2 \, b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{{\left(a - \frac{4 \, b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{a^{2} \sin\left(d x + c\right)^{2}} + \frac{8 \, {\left(a^{2} b + b^{3}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} a^{3}}}{8 \, d}"," ",0,"1/8*((4*b*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^2 + 4*(a^2 + 2*b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - (a - 4*b*sin(d*x + c)/(cos(d*x + c) + 1))*(cos(d*x + c) + 1)^2/(a^2*sin(d*x + c)^2) + 8*(a^2*b + b^3)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a^3))/d","A",0
59,1,97,0,0.494481," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(a^{2} b + b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4}} - \frac{6 \, {\left(a^{2} b + b^{3}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{4}} + \frac{3 \, a b \tan\left(d x + c\right) - 6 \, {\left(a^{2} + b^{2}\right)} \tan\left(d x + c\right)^{2} - 2 \, a^{2}}{a^{3} \tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(a^2*b + b^3)*log(b*tan(d*x + c) + a)/a^4 - 6*(a^2*b + b^3)*log(tan(d*x + c))/a^4 + (3*a*b*tan(d*x + c) - 6*(a^2 + b^2)*tan(d*x + c)^2 - 2*a^2)/(a^3*tan(d*x + c)^3))/d","A",0
60,1,168,0,0.540479," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{60 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6}} - \frac{60 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{6}} + \frac{15 \, a^{3} b \tan\left(d x + c\right) - 60 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{4} - 12 \, a^{4} + 30 \, {\left(2 \, a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)^{3} - 20 \, {\left(2 \, a^{4} + a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{a^{5} \tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*(a^4*b + 2*a^2*b^3 + b^5)*log(b*tan(d*x + c) + a)/a^6 - 60*(a^4*b + 2*a^2*b^3 + b^5)*log(tan(d*x + c))/a^6 + (15*a^3*b*tan(d*x + c) - 60*(a^4 + 2*a^2*b^2 + b^4)*tan(d*x + c)^4 - 12*a^4 + 30*(2*a^3*b + a*b^3)*tan(d*x + c)^3 - 20*(2*a^4 + a^2*b^2)*tan(d*x + c)^2)/(a^5*tan(d*x + c)^5))/d","A",0
61,1,799,0,0.961565," ","integrate(sin(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(5 \, a^{8} - 80 \, a^{6} b^{2} + 50 \, a^{4} b^{4} + 8 \, a^{2} b^{6} + b^{8}\right)} {\left(d x + c\right)}}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} + \frac{96 \, {\left(a^{7} b - 3 \, a^{5} b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{48 \, {\left(a^{7} b - 3 \, a^{5} b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{136 \, a^{6} b - 64 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + 3 \, {\left(27 \, a^{6} b - 43 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - b^{7}\right)} \tan\left(d x + c\right)^{6} + 3 \, {\left(11 \, a^{7} + 5 \, a^{5} b^{2} - 7 \, a^{3} b^{4} - a b^{6}\right)} \tan\left(d x + c\right)^{5} + 8 \, {\left(41 \, a^{6} b - 31 \, a^{4} b^{3} + a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{4} + 8 \, {\left(5 \, a^{7} - 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(125 \, a^{6} b - 69 \, a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{2} + {\left(15 \, a^{7} - 23 \, a^{5} b^{2} - 43 \, a^{3} b^{4} - 5 \, a b^{6}\right)} \tan\left(d x + c\right)}{a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8} + {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)^{7} + {\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(d x + c\right)^{6} + 3 \, {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)^{5} + 3 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)}}{48 \, d}"," ",0,"1/48*(3*(5*a^8 - 80*a^6*b^2 + 50*a^4*b^4 + 8*a^2*b^6 + b^8)*(d*x + c)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) + 96*(a^7*b - 3*a^5*b^3)*log(b*tan(d*x + c) + a)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - 48*(a^7*b - 3*a^5*b^3)*log(tan(d*x + c)^2 + 1)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - (136*a^6*b - 64*a^4*b^3 - 8*a^2*b^5 + 3*(27*a^6*b - 43*a^4*b^3 - 7*a^2*b^5 - b^7)*tan(d*x + c)^6 + 3*(11*a^7 + 5*a^5*b^2 - 7*a^3*b^4 - a*b^6)*tan(d*x + c)^5 + 8*(41*a^6*b - 31*a^4*b^3 + a^2*b^5 + b^7)*tan(d*x + c)^4 + 8*(5*a^7 - 4*a^5*b^2 - 11*a^3*b^4 - 2*a*b^6)*tan(d*x + c)^3 + 3*(125*a^6*b - 69*a^4*b^3 - a^2*b^5 + b^7)*tan(d*x + c)^2 + (15*a^7 - 23*a^5*b^2 - 43*a^3*b^4 - 5*a*b^6)*tan(d*x + c))/(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8 + (a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*tan(d*x + c)^7 + (a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*tan(d*x + c)^6 + 3*(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*tan(d*x + c)^5 + 3*(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*tan(d*x + c)^4 + 3*(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*tan(d*x + c)^3 + 3*(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*tan(d*x + c)^2 + (a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*tan(d*x + c)))/d","B",0
62,1,507,0,0.923038," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, a^{6} - 33 \, a^{4} b^{2} + 13 \, a^{2} b^{4} + b^{6}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{16 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{8 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{20 \, a^{4} b - 4 \, a^{2} b^{3} + {\left(13 \, a^{4} b - 12 \, a^{2} b^{3} - b^{5}\right)} \tan\left(d x + c\right)^{4} + {\left(5 \, a^{5} + 4 \, a^{3} b^{2} - a b^{4}\right)} \tan\left(d x + c\right)^{3} + {\left(35 \, a^{4} b - 12 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{5} - a b^{4}\right)} \tan\left(d x + c\right)}{a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{5} + {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)}}{8 \, d}"," ",0,"1/8*((3*a^6 - 33*a^4*b^2 + 13*a^2*b^4 + b^6)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 16*(a^5*b - 2*a^3*b^3)*log(b*tan(d*x + c) + a)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 8*(a^5*b - 2*a^3*b^3)*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - (20*a^4*b - 4*a^2*b^3 + (13*a^4*b - 12*a^2*b^3 - b^5)*tan(d*x + c)^4 + (5*a^5 + 4*a^3*b^2 - a*b^4)*tan(d*x + c)^3 + (35*a^4*b - 12*a^2*b^3 + b^5)*tan(d*x + c)^2 + 3*(a^5 - a*b^4)*tan(d*x + c))/(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6 + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*tan(d*x + c)^5 + (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*tan(d*x + c)^4 + 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*tan(d*x + c)^3 + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*tan(d*x + c)^2 + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*tan(d*x + c)))/d","B",0
63,1,293,0,0.814939," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{4 \, {\left(a^{3} b - a b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{4 \, a^{2} b + {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} \tan\left(d x + c\right)}{a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*((a^4 - 6*a^2*b^2 + b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 4*(a^3*b - a*b^3)*log(b*tan(d*x + c) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(a^3*b - a*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (4*a^2*b + (3*a^2*b - b^3)*tan(d*x + c)^2 + (a^3 + a*b^2)*tan(d*x + c))/(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*tan(d*x + c)^3 + (a^5 + 2*a^3*b^2 + a*b^4)*tan(d*x + c)^2 + (a^4*b + 2*a^2*b^3 + b^5)*tan(d*x + c)))/d","B",0
64,1,74,0,0.570618," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, b \tan\left(d x + c\right) + a}{a^{2} b \tan\left(d x + c\right)^{2} + a^{3} \tan\left(d x + c\right)} - \frac{2 \, b \log\left(b \tan\left(d x + c\right) + a\right)}{a^{3}} + \frac{2 \, b \log\left(\tan\left(d x + c\right)\right)}{a^{3}}}{d}"," ",0,"-((2*b*tan(d*x + c) + a)/(a^2*b*tan(d*x + c)^2 + a^3*tan(d*x + c)) - 2*b*log(b*tan(d*x + c) + a)/a^3 + 2*b*log(tan(d*x + c))/a^3)/d","A",0
65,1,144,0,0.424467," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, a^{2} b \tan\left(d x + c\right) - 6 \, {\left(a^{2} b + 2 \, b^{3}\right)} \tan\left(d x + c\right)^{3} - a^{3} - 3 \, {\left(a^{3} + 2 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}}{a^{4} b \tan\left(d x + c\right)^{4} + a^{5} \tan\left(d x + c\right)^{3}} + \frac{6 \, {\left(a^{2} b + 2 \, b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{5}} - \frac{6 \, {\left(a^{2} b + 2 \, b^{3}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{5}}}{3 \, d}"," ",0,"1/3*((2*a^2*b*tan(d*x + c) - 6*(a^2*b + 2*b^3)*tan(d*x + c)^3 - a^3 - 3*(a^3 + 2*a*b^2)*tan(d*x + c)^2)/(a^4*b*tan(d*x + c)^4 + a^5*tan(d*x + c)^3) + 6*(a^2*b + 2*b^3)*log(b*tan(d*x + c) + a)/a^5 - 6*(a^2*b + 2*b^3)*log(tan(d*x + c))/a^5)/d","A",0
66,1,225,0,0.602244," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{9 \, a^{4} b \tan\left(d x + c\right) - 60 \, {\left(a^{4} b + 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \tan\left(d x + c\right)^{5} - 6 \, a^{5} - 30 \, {\left(a^{5} + 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \tan\left(d x + c\right)^{4} + 10 \, {\left(4 \, a^{4} b + 3 \, a^{2} b^{3}\right)} \tan\left(d x + c\right)^{3} - 5 \, {\left(4 \, a^{5} + 3 \, a^{3} b^{2}\right)} \tan\left(d x + c\right)^{2}}{a^{6} b \tan\left(d x + c\right)^{6} + a^{7} \tan\left(d x + c\right)^{5}} + \frac{60 \, {\left(a^{4} b + 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{7}} - \frac{60 \, {\left(a^{4} b + 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{7}}}{30 \, d}"," ",0,"1/30*((9*a^4*b*tan(d*x + c) - 60*(a^4*b + 4*a^2*b^3 + 3*b^5)*tan(d*x + c)^5 - 6*a^5 - 30*(a^5 + 4*a^3*b^2 + 3*a*b^4)*tan(d*x + c)^4 + 10*(4*a^4*b + 3*a^2*b^3)*tan(d*x + c)^3 - 5*(4*a^5 + 3*a^3*b^2)*tan(d*x + c)^2)/(a^6*b*tan(d*x + c)^6 + a^7*tan(d*x + c)^5) + 60*(a^4*b + 4*a^2*b^3 + 3*b^5)*log(b*tan(d*x + c) + a)/a^7 - 60*(a^4*b + 4*a^2*b^3 + 3*b^5)*log(tan(d*x + c))/a^7)/d","A",0
67,1,1088,0,0.556032," ","integrate(sin(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(5 \, a^{9} - 180 \, a^{7} b^{2} + 390 \, a^{5} b^{4} - 68 \, a^{3} b^{6} - 3 \, a b^{8}\right)} {\left(d x + c\right)}}{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}} + \frac{48 \, {\left(3 \, a^{8} b - 22 \, a^{6} b^{3} + 15 \, a^{4} b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}} - \frac{24 \, {\left(3 \, a^{8} b - 22 \, a^{6} b^{3} + 15 \, a^{4} b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}} - \frac{252 \, a^{8} b - 644 \, a^{6} b^{3} + 68 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + 3 \, {\left(43 \, a^{7} b^{2} - 215 \, a^{5} b^{4} + 65 \, a^{3} b^{6} + 3 \, a b^{8}\right)} \tan\left(d x + c\right)^{7} + 6 \, {\left(31 \, a^{8} b - 127 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + 3 \, a^{2} b^{7}\right)} \tan\left(d x + c\right)^{6} + {\left(33 \, a^{9} + 403 \, a^{7} b^{2} - 2005 \, a^{5} b^{4} + 529 \, a^{3} b^{6} + 24 \, a b^{8}\right)} \tan\left(d x + c\right)^{5} + 4 \, {\left(164 \, a^{8} b - 515 \, a^{6} b^{3} + 65 \, a^{4} b^{5} + 27 \, a^{2} b^{7} + 3 \, b^{9}\right)} \tan\left(d x + c\right)^{4} + {\left(40 \, a^{9} + 335 \, a^{7} b^{2} - 2171 \, a^{5} b^{4} + 429 \, a^{3} b^{6} + 15 \, a b^{8}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(357 \, a^{8} b - 987 \, a^{6} b^{3} + 125 \, a^{4} b^{5} + 31 \, a^{2} b^{7} + 2 \, b^{9}\right)} \tan\left(d x + c\right)^{2} + {\left(15 \, a^{9} + 93 \, a^{7} b^{2} - 763 \, a^{5} b^{4} + 127 \, a^{3} b^{6} + 8 \, a b^{8}\right)} \tan\left(d x + c\right)}{a^{12} + 5 \, a^{10} b^{2} + 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} + a^{2} b^{10} + {\left(a^{10} b^{2} + 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} + b^{12}\right)} \tan\left(d x + c\right)^{8} + 2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \tan\left(d x + c\right)^{7} + {\left(a^{12} + 8 \, a^{10} b^{2} + 25 \, a^{8} b^{4} + 40 \, a^{6} b^{6} + 35 \, a^{4} b^{8} + 16 \, a^{2} b^{10} + 3 \, b^{12}\right)} \tan\left(d x + c\right)^{6} + 6 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \tan\left(d x + c\right)^{5} + 3 \, {\left(a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}\right)} \tan\left(d x + c\right)^{4} + 6 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \tan\left(d x + c\right)^{3} + {\left(3 \, a^{12} + 16 \, a^{10} b^{2} + 35 \, a^{8} b^{4} + 40 \, a^{6} b^{6} + 25 \, a^{4} b^{8} + 8 \, a^{2} b^{10} + b^{12}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} \tan\left(d x + c\right)}}{48 \, d}"," ",0,"1/48*(3*(5*a^9 - 180*a^7*b^2 + 390*a^5*b^4 - 68*a^3*b^6 - 3*a*b^8)*(d*x + c)/(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12) + 48*(3*a^8*b - 22*a^6*b^3 + 15*a^4*b^5)*log(b*tan(d*x + c) + a)/(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12) - 24*(3*a^8*b - 22*a^6*b^3 + 15*a^4*b^5)*log(tan(d*x + c)^2 + 1)/(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12) - (252*a^8*b - 644*a^6*b^3 + 68*a^4*b^5 + 4*a^2*b^7 + 3*(43*a^7*b^2 - 215*a^5*b^4 + 65*a^3*b^6 + 3*a*b^8)*tan(d*x + c)^7 + 6*(31*a^8*b - 127*a^6*b^3 + 5*a^4*b^5 + 3*a^2*b^7)*tan(d*x + c)^6 + (33*a^9 + 403*a^7*b^2 - 2005*a^5*b^4 + 529*a^3*b^6 + 24*a*b^8)*tan(d*x + c)^5 + 4*(164*a^8*b - 515*a^6*b^3 + 65*a^4*b^5 + 27*a^2*b^7 + 3*b^9)*tan(d*x + c)^4 + (40*a^9 + 335*a^7*b^2 - 2171*a^5*b^4 + 429*a^3*b^6 + 15*a*b^8)*tan(d*x + c)^3 + 2*(357*a^8*b - 987*a^6*b^3 + 125*a^4*b^5 + 31*a^2*b^7 + 2*b^9)*tan(d*x + c)^2 + (15*a^9 + 93*a^7*b^2 - 763*a^5*b^4 + 127*a^3*b^6 + 8*a*b^8)*tan(d*x + c))/(a^12 + 5*a^10*b^2 + 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 + a^2*b^10 + (a^10*b^2 + 5*a^8*b^4 + 10*a^6*b^6 + 10*a^4*b^8 + 5*a^2*b^10 + b^12)*tan(d*x + c)^8 + 2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*tan(d*x + c)^7 + (a^12 + 8*a^10*b^2 + 25*a^8*b^4 + 40*a^6*b^6 + 35*a^4*b^8 + 16*a^2*b^10 + 3*b^12)*tan(d*x + c)^6 + 6*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*tan(d*x + c)^5 + 3*(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12)*tan(d*x + c)^4 + 6*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*tan(d*x + c)^3 + (3*a^12 + 16*a^10*b^2 + 35*a^8*b^4 + 40*a^6*b^6 + 25*a^4*b^8 + 8*a^2*b^10 + b^12)*tan(d*x + c)^2 + 2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*tan(d*x + c)))/d","B",0
68,1,744,0,0.700576," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a^{7} - 25 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 3 \, a b^{6}\right)} {\left(d x + c\right)}}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} + \frac{24 \, {\left(a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{12 \, {\left(a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{38 \, a^{6} b - 56 \, a^{4} b^{3} + 2 \, a^{2} b^{5} + 3 \, {\left(7 \, a^{5} b^{2} - 22 \, a^{3} b^{4} + 3 \, a b^{6}\right)} \tan\left(d x + c\right)^{5} + 6 \, {\left(5 \, a^{6} b - 12 \, a^{4} b^{3} - a^{2} b^{5}\right)} \tan\left(d x + c\right)^{4} + {\left(5 \, a^{7} + 49 \, a^{5} b^{2} - 133 \, a^{3} b^{4} + 15 \, a b^{6}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(35 \, a^{6} b - 61 \, a^{4} b^{3} + a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 22 \, a^{5} b^{2} - 73 \, a^{3} b^{4} + 4 \, a b^{6}\right)} \tan\left(d x + c\right)}{a^{10} + 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} + 4 \, a^{4} b^{6} + a^{2} b^{8} + {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} \tan\left(d x + c\right)^{6} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)^{5} + {\left(a^{10} + 6 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 16 \, a^{4} b^{6} + 9 \, a^{2} b^{8} + 2 \, b^{10}\right)} \tan\left(d x + c\right)^{4} + 4 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)^{3} + {\left(2 \, a^{10} + 9 \, a^{8} b^{2} + 16 \, a^{6} b^{4} + 14 \, a^{4} b^{6} + 6 \, a^{2} b^{8} + b^{10}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)}}{8 \, d}"," ",0,"1/8*(3*(a^7 - 25*a^5*b^2 + 35*a^3*b^4 - 3*a*b^6)*(d*x + c)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) + 24*(a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*log(b*tan(d*x + c) + a)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - 12*(a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*log(tan(d*x + c)^2 + 1)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - (38*a^6*b - 56*a^4*b^3 + 2*a^2*b^5 + 3*(7*a^5*b^2 - 22*a^3*b^4 + 3*a*b^6)*tan(d*x + c)^5 + 6*(5*a^6*b - 12*a^4*b^3 - a^2*b^5)*tan(d*x + c)^4 + (5*a^7 + 49*a^5*b^2 - 133*a^3*b^4 + 15*a*b^6)*tan(d*x + c)^3 + 2*(35*a^6*b - 61*a^4*b^3 + a^2*b^5 + b^7)*tan(d*x + c)^2 + (3*a^7 + 22*a^5*b^2 - 73*a^3*b^4 + 4*a*b^6)*tan(d*x + c))/(a^10 + 4*a^8*b^2 + 6*a^6*b^4 + 4*a^4*b^6 + a^2*b^8 + (a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*tan(d*x + c)^6 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*tan(d*x + c)^5 + (a^10 + 6*a^8*b^2 + 14*a^6*b^4 + 16*a^4*b^6 + 9*a^2*b^8 + 2*b^10)*tan(d*x + c)^4 + 4*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*tan(d*x + c)^3 + (2*a^10 + 9*a^8*b^2 + 16*a^6*b^4 + 14*a^4*b^6 + 6*a^2*b^8 + b^10)*tan(d*x + c)^2 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*tan(d*x + c)))/d","B",0
69,1,463,0,0.909171," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(a^{5} - 14 \, a^{3} b^{2} + 9 \, a b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{2 \, {\left(3 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{{\left(3 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{8 \, a^{4} b - 4 \, a^{2} b^{3} + {\left(5 \, a^{3} b^{2} - 7 \, a b^{4}\right)} \tan\left(d x + c\right)^{3} + {\left(7 \, a^{4} b - 6 \, a^{2} b^{3} - b^{5}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{5} + 7 \, a^{3} b^{2} - 6 \, a b^{4}\right)} \tan\left(d x + c\right)}{a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*((a^5 - 14*a^3*b^2 + 9*a*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 2*(3*a^4*b - 8*a^2*b^3 + b^5)*log(b*tan(d*x + c) + a)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - (3*a^4*b - 8*a^2*b^3 + b^5)*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - (8*a^4*b - 4*a^2*b^3 + (5*a^3*b^2 - 7*a*b^4)*tan(d*x + c)^3 + (7*a^4*b - 6*a^2*b^3 - b^5)*tan(d*x + c)^2 + (a^5 + 7*a^3*b^2 - 6*a*b^4)*tan(d*x + c))/(a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6 + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*tan(d*x + c)^4 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*tan(d*x + c)^3 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*tan(d*x + c)))/d","B",0
70,1,108,0,0.483738," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{6 \, b^{2} \tan\left(d x + c\right)^{2} + 9 \, a b \tan\left(d x + c\right) + 2 \, a^{2}}{a^{3} b^{2} \tan\left(d x + c\right)^{3} + 2 \, a^{4} b \tan\left(d x + c\right)^{2} + a^{5} \tan\left(d x + c\right)} - \frac{6 \, b \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4}} + \frac{6 \, b \log\left(\tan\left(d x + c\right)\right)}{a^{4}}}{2 \, d}"," ",0,"-1/2*((6*b^2*tan(d*x + c)^2 + 9*a*b*tan(d*x + c) + 2*a^2)/(a^3*b^2*tan(d*x + c)^3 + 2*a^4*b*tan(d*x + c)^2 + a^5*tan(d*x + c)) - 6*b*log(b*tan(d*x + c) + a)/a^4 + 6*b*log(tan(d*x + c))/a^4)/d","A",0
71,1,192,0,0.404124," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{5 \, a^{3} b \tan\left(d x + c\right) - 6 \, {\left(3 \, a^{2} b^{2} + 10 \, b^{4}\right)} \tan\left(d x + c\right)^{4} - 2 \, a^{4} - 9 \, {\left(3 \, a^{3} b + 10 \, a b^{3}\right)} \tan\left(d x + c\right)^{3} - 2 \, {\left(3 \, a^{4} + 10 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{a^{5} b^{2} \tan\left(d x + c\right)^{5} + 2 \, a^{6} b \tan\left(d x + c\right)^{4} + a^{7} \tan\left(d x + c\right)^{3}} + \frac{6 \, {\left(3 \, a^{2} b + 10 \, b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6}} - \frac{6 \, {\left(3 \, a^{2} b + 10 \, b^{3}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{6}}}{6 \, d}"," ",0,"1/6*((5*a^3*b*tan(d*x + c) - 6*(3*a^2*b^2 + 10*b^4)*tan(d*x + c)^4 - 2*a^4 - 9*(3*a^3*b + 10*a*b^3)*tan(d*x + c)^3 - 2*(3*a^4 + 10*a^2*b^2)*tan(d*x + c)^2)/(a^5*b^2*tan(d*x + c)^5 + 2*a^6*b*tan(d*x + c)^4 + a^7*tan(d*x + c)^3) + 6*(3*a^2*b + 10*b^3)*log(b*tan(d*x + c) + a)/a^6 - 6*(3*a^2*b + 10*b^3)*log(tan(d*x + c))/a^6)/d","A",0
72,1,281,0,0.776477," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{21 \, a^{5} b \tan\left(d x + c\right) - 60 \, {\left(3 \, a^{4} b^{2} + 20 \, a^{2} b^{4} + 21 \, b^{6}\right)} \tan\left(d x + c\right)^{6} - 12 \, a^{6} - 90 \, {\left(3 \, a^{5} b + 20 \, a^{3} b^{3} + 21 \, a b^{5}\right)} \tan\left(d x + c\right)^{5} - 20 \, {\left(3 \, a^{6} + 20 \, a^{4} b^{2} + 21 \, a^{2} b^{4}\right)} \tan\left(d x + c\right)^{4} + 5 \, {\left(20 \, a^{5} b + 21 \, a^{3} b^{3}\right)} \tan\left(d x + c\right)^{3} - 2 \, {\left(20 \, a^{6} + 21 \, a^{4} b^{2}\right)} \tan\left(d x + c\right)^{2}}{a^{7} b^{2} \tan\left(d x + c\right)^{7} + 2 \, a^{8} b \tan\left(d x + c\right)^{6} + a^{9} \tan\left(d x + c\right)^{5}} + \frac{60 \, {\left(3 \, a^{4} b + 20 \, a^{2} b^{3} + 21 \, b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{8}} - \frac{60 \, {\left(3 \, a^{4} b + 20 \, a^{2} b^{3} + 21 \, b^{5}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{8}}}{60 \, d}"," ",0,"1/60*((21*a^5*b*tan(d*x + c) - 60*(3*a^4*b^2 + 20*a^2*b^4 + 21*b^6)*tan(d*x + c)^6 - 12*a^6 - 90*(3*a^5*b + 20*a^3*b^3 + 21*a*b^5)*tan(d*x + c)^5 - 20*(3*a^6 + 20*a^4*b^2 + 21*a^2*b^4)*tan(d*x + c)^4 + 5*(20*a^5*b + 21*a^3*b^3)*tan(d*x + c)^3 - 2*(20*a^6 + 21*a^4*b^2)*tan(d*x + c)^2)/(a^7*b^2*tan(d*x + c)^7 + 2*a^8*b*tan(d*x + c)^6 + a^9*tan(d*x + c)^5) + 60*(3*a^4*b + 20*a^2*b^3 + 21*b^5)*log(b*tan(d*x + c) + a)/a^8 - 60*(3*a^4*b + 20*a^2*b^3 + 21*b^5)*log(tan(d*x + c))/a^8)/d","A",0
73,1,997,0,0.935442," ","integrate(sin(d*x+c)^4/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(3 \, a^{8} - 132 \, a^{6} b^{2} + 370 \, a^{4} b^{4} - 132 \, a^{2} b^{6} + 3 \, b^{8}\right)} {\left(d x + c\right)}}{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}} + \frac{96 \, {\left(a^{7} b - 9 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - a b^{7}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}} - \frac{48 \, {\left(a^{7} b - 9 \, a^{5} b^{3} + 9 \, a^{3} b^{5} - a b^{7}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{12} + 6 \, a^{10} b^{2} + 15 \, a^{8} b^{4} + 20 \, a^{6} b^{6} + 15 \, a^{4} b^{8} + 6 \, a^{2} b^{10} + b^{12}} - \frac{176 \, a^{8} b - 608 \, a^{6} b^{3} + 176 \, a^{4} b^{5} + 3 \, {\left(29 \, a^{6} b^{3} - 185 \, a^{4} b^{5} + 103 \, a^{2} b^{7} - 3 \, b^{9}\right)} \tan\left(d x + c\right)^{6} + 3 \, {\left(71 \, a^{7} b^{2} - 411 \, a^{5} b^{4} + 165 \, a^{3} b^{6} + 7 \, a b^{8}\right)} \tan\left(d x + c\right)^{5} + {\left(149 \, a^{8} b - 512 \, a^{6} b^{3} - 1006 \, a^{4} b^{5} + 600 \, a^{2} b^{7} - 15 \, b^{9}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{9} + 152 \, a^{7} b^{2} - 822 \, a^{5} b^{4} + 320 \, a^{3} b^{6} + 9 \, a b^{8}\right)} \tan\left(d x + c\right)^{3} + {\left(331 \, a^{8} b - 1183 \, a^{6} b^{3} - 239 \, a^{4} b^{5} + 315 \, a^{2} b^{7}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(3 \, a^{9} + 73 \, a^{7} b^{2} - 423 \, a^{5} b^{4} + 147 \, a^{3} b^{6}\right)} \tan\left(d x + c\right)}{a^{13} + 5 \, a^{11} b^{2} + 10 \, a^{9} b^{4} + 10 \, a^{7} b^{6} + 5 \, a^{5} b^{8} + a^{3} b^{10} + {\left(a^{10} b^{3} + 5 \, a^{8} b^{5} + 10 \, a^{6} b^{7} + 10 \, a^{4} b^{9} + 5 \, a^{2} b^{11} + b^{13}\right)} \tan\left(d x + c\right)^{7} + 3 \, {\left(a^{11} b^{2} + 5 \, a^{9} b^{4} + 10 \, a^{7} b^{6} + 10 \, a^{5} b^{8} + 5 \, a^{3} b^{10} + a b^{12}\right)} \tan\left(d x + c\right)^{6} + {\left(3 \, a^{12} b + 17 \, a^{10} b^{3} + 40 \, a^{8} b^{5} + 50 \, a^{6} b^{7} + 35 \, a^{4} b^{9} + 13 \, a^{2} b^{11} + 2 \, b^{13}\right)} \tan\left(d x + c\right)^{5} + {\left(a^{13} + 11 \, a^{11} b^{2} + 40 \, a^{9} b^{4} + 70 \, a^{7} b^{6} + 65 \, a^{5} b^{8} + 31 \, a^{3} b^{10} + 6 \, a b^{12}\right)} \tan\left(d x + c\right)^{4} + {\left(6 \, a^{12} b + 31 \, a^{10} b^{3} + 65 \, a^{8} b^{5} + 70 \, a^{6} b^{7} + 40 \, a^{4} b^{9} + 11 \, a^{2} b^{11} + b^{13}\right)} \tan\left(d x + c\right)^{3} + {\left(2 \, a^{13} + 13 \, a^{11} b^{2} + 35 \, a^{9} b^{4} + 50 \, a^{7} b^{6} + 40 \, a^{5} b^{8} + 17 \, a^{3} b^{10} + 3 \, a b^{12}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{12} b + 5 \, a^{10} b^{3} + 10 \, a^{8} b^{5} + 10 \, a^{6} b^{7} + 5 \, a^{4} b^{9} + a^{2} b^{11}\right)} \tan\left(d x + c\right)}}{24 \, d}"," ",0,"1/24*(3*(3*a^8 - 132*a^6*b^2 + 370*a^4*b^4 - 132*a^2*b^6 + 3*b^8)*(d*x + c)/(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12) + 96*(a^7*b - 9*a^5*b^3 + 9*a^3*b^5 - a*b^7)*log(b*tan(d*x + c) + a)/(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12) - 48*(a^7*b - 9*a^5*b^3 + 9*a^3*b^5 - a*b^7)*log(tan(d*x + c)^2 + 1)/(a^12 + 6*a^10*b^2 + 15*a^8*b^4 + 20*a^6*b^6 + 15*a^4*b^8 + 6*a^2*b^10 + b^12) - (176*a^8*b - 608*a^6*b^3 + 176*a^4*b^5 + 3*(29*a^6*b^3 - 185*a^4*b^5 + 103*a^2*b^7 - 3*b^9)*tan(d*x + c)^6 + 3*(71*a^7*b^2 - 411*a^5*b^4 + 165*a^3*b^6 + 7*a*b^8)*tan(d*x + c)^5 + (149*a^8*b - 512*a^6*b^3 - 1006*a^4*b^5 + 600*a^2*b^7 - 15*b^9)*tan(d*x + c)^4 + 3*(5*a^9 + 152*a^7*b^2 - 822*a^5*b^4 + 320*a^3*b^6 + 9*a*b^8)*tan(d*x + c)^3 + (331*a^8*b - 1183*a^6*b^3 - 239*a^4*b^5 + 315*a^2*b^7)*tan(d*x + c)^2 + 3*(3*a^9 + 73*a^7*b^2 - 423*a^5*b^4 + 147*a^3*b^6)*tan(d*x + c))/(a^13 + 5*a^11*b^2 + 10*a^9*b^4 + 10*a^7*b^6 + 5*a^5*b^8 + a^3*b^10 + (a^10*b^3 + 5*a^8*b^5 + 10*a^6*b^7 + 10*a^4*b^9 + 5*a^2*b^11 + b^13)*tan(d*x + c)^7 + 3*(a^11*b^2 + 5*a^9*b^4 + 10*a^7*b^6 + 10*a^5*b^8 + 5*a^3*b^10 + a*b^12)*tan(d*x + c)^6 + (3*a^12*b + 17*a^10*b^3 + 40*a^8*b^5 + 50*a^6*b^7 + 35*a^4*b^9 + 13*a^2*b^11 + 2*b^13)*tan(d*x + c)^5 + (a^13 + 11*a^11*b^2 + 40*a^9*b^4 + 70*a^7*b^6 + 65*a^5*b^8 + 31*a^3*b^10 + 6*a*b^12)*tan(d*x + c)^4 + (6*a^12*b + 31*a^10*b^3 + 65*a^8*b^5 + 70*a^6*b^7 + 40*a^4*b^9 + 11*a^2*b^11 + b^13)*tan(d*x + c)^3 + (2*a^13 + 13*a^11*b^2 + 35*a^9*b^4 + 50*a^7*b^6 + 40*a^5*b^8 + 17*a^3*b^10 + 3*a*b^12)*tan(d*x + c)^2 + 3*(a^12*b + 5*a^10*b^3 + 10*a^8*b^5 + 10*a^6*b^7 + 5*a^4*b^9 + a^2*b^11)*tan(d*x + c)))/d","B",0
74,1,662,0,0.596156," ","integrate(sin(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a^{6} - 25 \, a^{4} b^{2} + 35 \, a^{2} b^{4} - 3 \, b^{6}\right)} {\left(d x + c\right)}}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} + \frac{24 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{12 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{38 \, a^{6} b - 56 \, a^{4} b^{3} + 2 \, a^{2} b^{5} + 3 \, {\left(7 \, a^{4} b^{3} - 22 \, a^{2} b^{5} + 3 \, b^{7}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(17 \, a^{5} b^{2} - 46 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)^{3} + {\left(35 \, a^{6} b - 44 \, a^{4} b^{3} - 73 \, a^{2} b^{5} + 6 \, b^{7}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{7} + 20 \, a^{5} b^{2} - 43 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \tan\left(d x + c\right)}{a^{11} + 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} + 4 \, a^{5} b^{6} + a^{3} b^{8} + {\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} \tan\left(d x + c\right)^{5} + 3 \, {\left(a^{9} b^{2} + 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} + 4 \, a^{3} b^{8} + a b^{10}\right)} \tan\left(d x + c\right)^{4} + {\left(3 \, a^{10} b + 13 \, a^{8} b^{3} + 22 \, a^{6} b^{5} + 18 \, a^{4} b^{7} + 7 \, a^{2} b^{9} + b^{11}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{11} + 7 \, a^{9} b^{2} + 18 \, a^{7} b^{4} + 22 \, a^{5} b^{6} + 13 \, a^{3} b^{8} + 3 \, a b^{10}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b + 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} + 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} \tan\left(d x + c\right)}}{6 \, d}"," ",0,"1/6*(3*(a^6 - 25*a^4*b^2 + 35*a^2*b^4 - 3*b^6)*(d*x + c)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) + 24*(a^5*b - 5*a^3*b^3 + 2*a*b^5)*log(b*tan(d*x + c) + a)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - 12*(a^5*b - 5*a^3*b^3 + 2*a*b^5)*log(tan(d*x + c)^2 + 1)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - (38*a^6*b - 56*a^4*b^3 + 2*a^2*b^5 + 3*(7*a^4*b^3 - 22*a^2*b^5 + 3*b^7)*tan(d*x + c)^4 + 3*(17*a^5*b^2 - 46*a^3*b^4 + a*b^6)*tan(d*x + c)^3 + (35*a^6*b - 44*a^4*b^3 - 73*a^2*b^5 + 6*b^7)*tan(d*x + c)^2 + 3*(a^7 + 20*a^5*b^2 - 43*a^3*b^4 + 2*a*b^6)*tan(d*x + c))/(a^11 + 4*a^9*b^2 + 6*a^7*b^4 + 4*a^5*b^6 + a^3*b^8 + (a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*tan(d*x + c)^5 + 3*(a^9*b^2 + 4*a^7*b^4 + 6*a^5*b^6 + 4*a^3*b^8 + a*b^10)*tan(d*x + c)^4 + (3*a^10*b + 13*a^8*b^3 + 22*a^6*b^5 + 18*a^4*b^7 + 7*a^2*b^9 + b^11)*tan(d*x + c)^3 + (a^11 + 7*a^9*b^2 + 18*a^7*b^4 + 22*a^5*b^6 + 13*a^3*b^8 + 3*a*b^10)*tan(d*x + c)^2 + 3*(a^10*b + 4*a^8*b^3 + 6*a^6*b^5 + 4*a^4*b^7 + a^2*b^9)*tan(d*x + c)))/d","B",0
75,1,140,0,0.380424," ","integrate(csc(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{12 \, b^{3} \tan\left(d x + c\right)^{3} + 30 \, a b^{2} \tan\left(d x + c\right)^{2} + 22 \, a^{2} b \tan\left(d x + c\right) + 3 \, a^{3}}{a^{4} b^{3} \tan\left(d x + c\right)^{4} + 3 \, a^{5} b^{2} \tan\left(d x + c\right)^{3} + 3 \, a^{6} b \tan\left(d x + c\right)^{2} + a^{7} \tan\left(d x + c\right)} - \frac{12 \, b \log\left(b \tan\left(d x + c\right) + a\right)}{a^{5}} + \frac{12 \, b \log\left(\tan\left(d x + c\right)\right)}{a^{5}}}{3 \, d}"," ",0,"-1/3*((12*b^3*tan(d*x + c)^3 + 30*a*b^2*tan(d*x + c)^2 + 22*a^2*b*tan(d*x + c) + 3*a^3)/(a^4*b^3*tan(d*x + c)^4 + 3*a^5*b^2*tan(d*x + c)^3 + 3*a^6*b*tan(d*x + c)^2 + a^7*tan(d*x + c)) - 12*b*log(b*tan(d*x + c) + a)/a^5 + 12*b*log(tan(d*x + c))/a^5)/d","A",0
76,1,228,0,0.557680," ","integrate(csc(d*x+c)^4/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{3 \, a^{4} b \tan\left(d x + c\right) - 12 \, {\left(a^{2} b^{3} + 5 \, b^{5}\right)} \tan\left(d x + c\right)^{5} - a^{5} - 30 \, {\left(a^{3} b^{2} + 5 \, a b^{4}\right)} \tan\left(d x + c\right)^{4} - 22 \, {\left(a^{4} b + 5 \, a^{2} b^{3}\right)} \tan\left(d x + c\right)^{3} - 3 \, {\left(a^{5} + 5 \, a^{3} b^{2}\right)} \tan\left(d x + c\right)^{2}}{a^{6} b^{3} \tan\left(d x + c\right)^{6} + 3 \, a^{7} b^{2} \tan\left(d x + c\right)^{5} + 3 \, a^{8} b \tan\left(d x + c\right)^{4} + a^{9} \tan\left(d x + c\right)^{3}} + \frac{12 \, {\left(a^{2} b + 5 \, b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{7}} - \frac{12 \, {\left(a^{2} b + 5 \, b^{3}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{7}}}{3 \, d}"," ",0,"1/3*((3*a^4*b*tan(d*x + c) - 12*(a^2*b^3 + 5*b^5)*tan(d*x + c)^5 - a^5 - 30*(a^3*b^2 + 5*a*b^4)*tan(d*x + c)^4 - 22*(a^4*b + 5*a^2*b^3)*tan(d*x + c)^3 - 3*(a^5 + 5*a^3*b^2)*tan(d*x + c)^2)/(a^6*b^3*tan(d*x + c)^6 + 3*a^7*b^2*tan(d*x + c)^5 + 3*a^8*b*tan(d*x + c)^4 + a^9*tan(d*x + c)^3) + 12*(a^2*b + 5*b^3)*log(b*tan(d*x + c) + a)/a^7 - 12*(a^2*b + 5*b^3)*log(tan(d*x + c))/a^7)/d","A",0
77,1,325,0,0.614579," ","integrate(csc(d*x+c)^6/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{6 \, a^{6} b \tan\left(d x + c\right) - 60 \, {\left(a^{4} b^{3} + 10 \, a^{2} b^{5} + 14 \, b^{7}\right)} \tan\left(d x + c\right)^{7} - 3 \, a^{7} - 150 \, {\left(a^{5} b^{2} + 10 \, a^{3} b^{4} + 14 \, a b^{6}\right)} \tan\left(d x + c\right)^{6} - 110 \, {\left(a^{6} b + 10 \, a^{4} b^{3} + 14 \, a^{2} b^{5}\right)} \tan\left(d x + c\right)^{5} - 15 \, {\left(a^{7} + 10 \, a^{5} b^{2} + 14 \, a^{3} b^{4}\right)} \tan\left(d x + c\right)^{4} + 6 \, {\left(5 \, a^{6} b + 7 \, a^{4} b^{3}\right)} \tan\left(d x + c\right)^{3} - 2 \, {\left(5 \, a^{7} + 7 \, a^{5} b^{2}\right)} \tan\left(d x + c\right)^{2}}{a^{8} b^{3} \tan\left(d x + c\right)^{8} + 3 \, a^{9} b^{2} \tan\left(d x + c\right)^{7} + 3 \, a^{10} b \tan\left(d x + c\right)^{6} + a^{11} \tan\left(d x + c\right)^{5}} + \frac{60 \, {\left(a^{4} b + 10 \, a^{2} b^{3} + 14 \, b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{9}} - \frac{60 \, {\left(a^{4} b + 10 \, a^{2} b^{3} + 14 \, b^{5}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{9}}}{15 \, d}"," ",0,"1/15*((6*a^6*b*tan(d*x + c) - 60*(a^4*b^3 + 10*a^2*b^5 + 14*b^7)*tan(d*x + c)^7 - 3*a^7 - 150*(a^5*b^2 + 10*a^3*b^4 + 14*a*b^6)*tan(d*x + c)^6 - 110*(a^6*b + 10*a^4*b^3 + 14*a^2*b^5)*tan(d*x + c)^5 - 15*(a^7 + 10*a^5*b^2 + 14*a^3*b^4)*tan(d*x + c)^4 + 6*(5*a^6*b + 7*a^4*b^3)*tan(d*x + c)^3 - 2*(5*a^7 + 7*a^5*b^2)*tan(d*x + c)^2)/(a^8*b^3*tan(d*x + c)^8 + 3*a^9*b^2*tan(d*x + c)^7 + 3*a^10*b*tan(d*x + c)^6 + a^11*tan(d*x + c)^5) + 60*(a^4*b + 10*a^2*b^3 + 14*b^5)*log(b*tan(d*x + c) + a)/a^9 - 60*(a^4*b + 10*a^2*b^3 + 14*b^5)*log(tan(d*x + c))/a^9)/d","A",0
78,1,50,0,0.852862," ","integrate(csc(x)/(1+tan(x)),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1}{\sqrt{2} + \frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1}\right) + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"1/2*sqrt(2)*log(-(sqrt(2) - sin(x)/(cos(x) + 1) + 1)/(sqrt(2) + sin(x)/(cos(x) + 1) - 1)) + log(sin(x)/(cos(x) + 1))","B",0
79,0,0,0,0.000000," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{3} \sin\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3*sin(d*x + c)^m, x)","F",0
80,0,0,0,0.000000," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2*sin(d*x + c)^m, x)","F",0
81,0,0,0,0.000000," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)*sin(d*x + c)^m, x)","F",0
82,0,0,0,0.000000," ","integrate(sin(d*x+c)^m/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{m}}{b \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^m/(b*tan(d*x + c) + a), x)","F",0
83,0,0,0,0.000000," ","integrate(sin(d*x+c)^m*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sin(d*x + c)^m, x)","F",0
84,0,0,0,0.000000," ","integrate(sin(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sin(d*x + c)^4, x)","F",0
85,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sin(d*x + c)^2, x)","F",0
86,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
87,0,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*csc(d*x + c)^4, x)","F",0
88,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sin(d*x + c)^3, x)","F",0
89,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sin(d*x + c), x)","F",0
90,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*csc(d*x + c), x)","F",0
91,0,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*csc(d*x + c)^3, x)","F",0
