1,1,91,0,0.366698," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^7,x, algorithm=""maxima"")","\frac{429 \, \sin\left(15 \, b x + 15 \, a\right) - 495 \, \sin\left(13 \, b x + 13 \, a\right) - 4095 \, \sin\left(11 \, b x + 11 \, a\right) + 5005 \, \sin\left(9 \, b x + 9 \, a\right) + 19305 \, \sin\left(7 \, b x + 7 \, a\right) - 27027 \, \sin\left(5 \, b x + 5 \, a\right) - 75075 \, \sin\left(3 \, b x + 3 \, a\right) + 225225 \, \sin\left(b x + a\right)}{823680 \, b}"," ",0,"1/823680*(429*sin(15*b*x + 15*a) - 495*sin(13*b*x + 13*a) - 4095*sin(11*b*x + 11*a) + 5005*sin(9*b*x + 9*a) + 19305*sin(7*b*x + 7*a) - 27027*sin(5*b*x + 5*a) - 75075*sin(3*b*x + 3*a) + 225225*sin(b*x + a))/b","A",0
2,1,80,0,0.348951," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^6,x, algorithm=""maxima"")","\frac{231 \, \cos\left(13 \, b x + 13 \, a\right) - 273 \, \cos\left(11 \, b x + 11 \, a\right) - 2002 \, \cos\left(9 \, b x + 9 \, a\right) + 2574 \, \cos\left(7 \, b x + 7 \, a\right) + 9009 \, \cos\left(5 \, b x + 5 \, a\right) - 15015 \, \cos\left(3 \, b x + 3 \, a\right) - 60060 \, \cos\left(b x + a\right)}{192192 \, b}"," ",0,"1/192192*(231*cos(13*b*x + 13*a) - 273*cos(11*b*x + 11*a) - 2002*cos(9*b*x + 9*a) + 2574*cos(7*b*x + 7*a) + 9009*cos(5*b*x + 5*a) - 15015*cos(3*b*x + 3*a) - 60060*cos(b*x + a))/b","A",0
3,1,69,0,0.339315," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","-\frac{63 \, \sin\left(11 \, b x + 11 \, a\right) - 77 \, \sin\left(9 \, b x + 9 \, a\right) - 495 \, \sin\left(7 \, b x + 7 \, a\right) + 693 \, \sin\left(5 \, b x + 5 \, a\right) + 2310 \, \sin\left(3 \, b x + 3 \, a\right) - 6930 \, \sin\left(b x + a\right)}{22176 \, b}"," ",0,"-1/22176*(63*sin(11*b*x + 11*a) - 77*sin(9*b*x + 9*a) - 495*sin(7*b*x + 7*a) + 693*sin(5*b*x + 5*a) + 2310*sin(3*b*x + 3*a) - 6930*sin(b*x + a))/b","A",0
4,1,58,0,0.335629," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","-\frac{35 \, \cos\left(9 \, b x + 9 \, a\right) - 45 \, \cos\left(7 \, b x + 7 \, a\right) - 252 \, \cos\left(5 \, b x + 5 \, a\right) + 420 \, \cos\left(3 \, b x + 3 \, a\right) + 1890 \, \cos\left(b x + a\right)}{5040 \, b}"," ",0,"-1/5040*(35*cos(9*b*x + 9*a) - 45*cos(7*b*x + 7*a) - 252*cos(5*b*x + 5*a) + 420*cos(3*b*x + 3*a) + 1890*cos(b*x + a))/b","A",0
5,1,47,0,0.338809," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{5 \, \sin\left(7 \, b x + 7 \, a\right) - 7 \, \sin\left(5 \, b x + 5 \, a\right) - 35 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)}{280 \, b}"," ",0,"1/280*(5*sin(7*b*x + 7*a) - 7*sin(5*b*x + 5*a) - 35*sin(3*b*x + 3*a) + 105*sin(b*x + a))/b","A",0
6,1,36,0,0.338277," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","\frac{3 \, \cos\left(5 \, b x + 5 \, a\right) - 5 \, \cos\left(3 \, b x + 3 \, a\right) - 30 \, \cos\left(b x + a\right)}{60 \, b}"," ",0,"1/60*(3*cos(5*b*x + 5*a) - 5*cos(3*b*x + 3*a) - 30*cos(b*x + a))/b","A",0
7,1,26,0,0.320882," ","integrate(sin(b*x+a)*sin(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{\sin\left(3 \, b x + 3 \, a\right)}{6 \, b} + \frac{\sin\left(b x + a\right)}{2 \, b}"," ",0,"-1/6*sin(3*b*x + 3*a)/b + 1/2*sin(b*x + a)/b","A",0
8,1,115,0,0.463058," ","integrate(csc(2*b*x+2*a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{\log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right)}{4 \, b}"," ",0,"-1/4*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2))/b","B",0
9,1,236,0,0.349966," ","integrate(csc(2*b*x+2*a)^2*sin(b*x+a),x, algorithm=""maxima"")","\frac{4 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) - {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, \cos\left(b x + a\right)}{8 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"1/8*(4*cos(2*b*x + 2*a)*cos(b*x + a) - (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*sin(2*b*x + 2*a)*sin(b*x + a) + 4*cos(b*x + a))/(b*cos(2*b*x + 2*a)^2 + b*sin(2*b*x + 2*a)^2 + 2*b*cos(2*b*x + 2*a) + b)","B",0
10,1,808,0,0.502264," ","integrate(csc(2*b*x+2*a)^3*sin(b*x+a),x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \sin\left(5 \, b x + 5 \, a\right) + 2 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(5 \, b x + 5 \, a\right) + 4 \, {\left(2 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 3 \, {\left(2 \, {\left(\cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) + \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + \sin\left(6 \, b x + 6 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(3 \, \cos\left(5 \, b x + 5 \, a\right) + 2 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 12 \, {\left(\cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(5 \, b x + 5 \, a\right) - 4 \, {\left(2 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) - 8 \, {\left(\cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 8 \, \cos\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 12 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 12 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 12 \, \sin\left(b x + a\right)}{32 \, {\left(b \cos\left(6 \, b x + 6 \, a\right)^{2} + b \cos\left(4 \, b x + 4 \, a\right)^{2} + b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(6 \, b x + 6 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) - 2 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/32*(4*(3*sin(5*b*x + 5*a) + 2*sin(3*b*x + 3*a) + 3*sin(b*x + a))*cos(6*b*x + 6*a) - 12*(sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(5*b*x + 5*a) + 4*(2*sin(3*b*x + 3*a) + 3*sin(b*x + a))*cos(4*b*x + 4*a) - 3*(2*(cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) + cos(6*b*x + 6*a)^2 - 2*(cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + cos(2*b*x + 2*a)^2 + 2*(sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + sin(6*b*x + 6*a)^2 + sin(4*b*x + 4*a)^2 - 2*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(3*cos(5*b*x + 5*a) + 2*cos(3*b*x + 3*a) + 3*cos(b*x + a))*sin(6*b*x + 6*a) + 12*(cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*sin(5*b*x + 5*a) - 4*(2*cos(3*b*x + 3*a) + 3*cos(b*x + a))*sin(4*b*x + 4*a) - 8*(cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a) + 8*cos(3*b*x + 3*a)*sin(2*b*x + 2*a) + 12*cos(b*x + a)*sin(2*b*x + 2*a) - 12*cos(2*b*x + 2*a)*sin(b*x + a) - 12*sin(b*x + a))/(b*cos(6*b*x + 6*a)^2 + b*cos(4*b*x + 4*a)^2 + b*cos(2*b*x + 2*a)^2 + b*sin(6*b*x + 6*a)^2 + b*sin(4*b*x + 4*a)^2 - 2*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + b*sin(2*b*x + 2*a)^2 + 2*(b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) - 2*(b*cos(2*b*x + 2*a) + b)*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) + 2*(b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
11,1,2174,0,0.404656," ","integrate(csc(2*b*x+2*a)^4*sin(b*x+a),x, algorithm=""maxima"")","\frac{4 \, {\left(15 \, \cos\left(9 \, b x + 9 \, a\right) + 20 \, \cos\left(7 \, b x + 7 \, a\right) - 22 \, \cos\left(5 \, b x + 5 \, a\right) + 20 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) + 60 \, {\left(\cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(9 \, b x + 9 \, a\right) + 4 \, {\left(20 \, \cos\left(7 \, b x + 7 \, a\right) - 22 \, \cos\left(5 \, b x + 5 \, a\right) + 20 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) - 80 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(7 \, b x + 7 \, a\right) + 8 \, {\left(22 \, \cos\left(5 \, b x + 5 \, a\right) - 20 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 88 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(5 \, b x + 5 \, a\right) - 40 \, {\left(4 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 80 \, {\left(\cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right) + 60 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) - 15 \, {\left(2 \, {\left(\cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) + \cos\left(10 \, b x + 10 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(8 \, b x + 8 \, a\right) + \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) + 4 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 4 \, {\left(\cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, \cos\left(4 \, b x + 4 \, a\right)^{2} + \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + \sin\left(10 \, b x + 10 \, a\right)^{2} - 2 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) + 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 4 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 15 \, {\left(2 \, {\left(\cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) + \cos\left(10 \, b x + 10 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(8 \, b x + 8 \, a\right) + \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) + 4 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 4 \, {\left(\cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, \cos\left(4 \, b x + 4 \, a\right)^{2} + \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + \sin\left(10 \, b x + 10 \, a\right)^{2} - 2 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) + 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 4 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(15 \, \sin\left(9 \, b x + 9 \, a\right) + 20 \, \sin\left(7 \, b x + 7 \, a\right) - 22 \, \sin\left(5 \, b x + 5 \, a\right) + 20 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 60 \, {\left(\sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(9 \, b x + 9 \, a\right) + 4 \, {\left(20 \, \sin\left(7 \, b x + 7 \, a\right) - 22 \, \sin\left(5 \, b x + 5 \, a\right) + 20 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 80 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) + 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(7 \, b x + 7 \, a\right) + 8 \, {\left(22 \, \sin\left(5 \, b x + 5 \, a\right) - 20 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 88 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(5 \, b x + 5 \, a\right) - 40 \, {\left(4 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 80 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 60 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 60 \, \cos\left(b x + a\right)}{192 \, {\left(b \cos\left(10 \, b x + 10 \, a\right)^{2} + b \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(10 \, b x + 10 \, a\right)^{2} + b \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b \cos\left(8 \, b x + 8 \, a\right) - 2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(10 \, b x + 10 \, a\right) - 2 \, {\left(2 \, b \cos\left(6 \, b x + 6 \, a\right) + 2 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(8 \, b x + 8 \, a\right) + 4 \, {\left(2 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(b \sin\left(8 \, b x + 8 \, a\right) - 2 \, b \sin\left(6 \, b x + 6 \, a\right) - 2 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 2 \, {\left(2 \, b \sin\left(6 \, b x + 6 \, a\right) + 2 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 4 \, {\left(2 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/192*(4*(15*cos(9*b*x + 9*a) + 20*cos(7*b*x + 7*a) - 22*cos(5*b*x + 5*a) + 20*cos(3*b*x + 3*a) + 15*cos(b*x + a))*cos(10*b*x + 10*a) + 60*(cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) + 1)*cos(9*b*x + 9*a) + 4*(20*cos(7*b*x + 7*a) - 22*cos(5*b*x + 5*a) + 20*cos(3*b*x + 3*a) + 15*cos(b*x + a))*cos(8*b*x + 8*a) - 80*(2*cos(6*b*x + 6*a) + 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*cos(7*b*x + 7*a) + 8*(22*cos(5*b*x + 5*a) - 20*cos(3*b*x + 3*a) - 15*cos(b*x + a))*cos(6*b*x + 6*a) + 88*(2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*cos(5*b*x + 5*a) - 40*(4*cos(3*b*x + 3*a) + 3*cos(b*x + a))*cos(4*b*x + 4*a) + 80*(cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a) + 60*cos(2*b*x + 2*a)*cos(b*x + a) - 15*(2*(cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) + cos(10*b*x + 10*a)^2 - 2*(2*cos(6*b*x + 6*a) + 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*cos(8*b*x + 8*a) + cos(8*b*x + 8*a)^2 + 4*(2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) + 4*cos(6*b*x + 6*a)^2 - 4*(cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 4*cos(4*b*x + 4*a)^2 + cos(2*b*x + 2*a)^2 + 2*(sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + sin(10*b*x + 10*a)^2 - 2*(2*sin(6*b*x + 6*a) + 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + sin(8*b*x + 8*a)^2 + 4*(2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + 4*sin(6*b*x + 6*a)^2 + 4*sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + 15*(2*(cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) + cos(10*b*x + 10*a)^2 - 2*(2*cos(6*b*x + 6*a) + 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*cos(8*b*x + 8*a) + cos(8*b*x + 8*a)^2 + 4*(2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) + 4*cos(6*b*x + 6*a)^2 - 4*(cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 4*cos(4*b*x + 4*a)^2 + cos(2*b*x + 2*a)^2 + 2*(sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + sin(10*b*x + 10*a)^2 - 2*(2*sin(6*b*x + 6*a) + 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + sin(8*b*x + 8*a)^2 + 4*(2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + 4*sin(6*b*x + 6*a)^2 + 4*sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(15*sin(9*b*x + 9*a) + 20*sin(7*b*x + 7*a) - 22*sin(5*b*x + 5*a) + 20*sin(3*b*x + 3*a) + 15*sin(b*x + a))*sin(10*b*x + 10*a) + 60*(sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(9*b*x + 9*a) + 4*(20*sin(7*b*x + 7*a) - 22*sin(5*b*x + 5*a) + 20*sin(3*b*x + 3*a) + 15*sin(b*x + a))*sin(8*b*x + 8*a) - 80*(2*sin(6*b*x + 6*a) + 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(7*b*x + 7*a) + 8*(22*sin(5*b*x + 5*a) - 20*sin(3*b*x + 3*a) - 15*sin(b*x + a))*sin(6*b*x + 6*a) + 88*(2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(5*b*x + 5*a) - 40*(4*sin(3*b*x + 3*a) + 3*sin(b*x + a))*sin(4*b*x + 4*a) + 80*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) + 60*sin(2*b*x + 2*a)*sin(b*x + a) + 60*cos(b*x + a))/(b*cos(10*b*x + 10*a)^2 + b*cos(8*b*x + 8*a)^2 + 4*b*cos(6*b*x + 6*a)^2 + 4*b*cos(4*b*x + 4*a)^2 + b*cos(2*b*x + 2*a)^2 + b*sin(10*b*x + 10*a)^2 + b*sin(8*b*x + 8*a)^2 + 4*b*sin(6*b*x + 6*a)^2 + 4*b*sin(4*b*x + 4*a)^2 - 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + b*sin(2*b*x + 2*a)^2 + 2*(b*cos(8*b*x + 8*a) - 2*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) + b)*cos(10*b*x + 10*a) - 2*(2*b*cos(6*b*x + 6*a) + 2*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) - b)*cos(8*b*x + 8*a) + 4*(2*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) - 4*(b*cos(2*b*x + 2*a) + b)*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) + 2*(b*sin(8*b*x + 8*a) - 2*b*sin(6*b*x + 6*a) - 2*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 2*(2*b*sin(6*b*x + 6*a) + 2*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 4*(2*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
12,1,3088,0,0.619057," ","integrate(csc(2*b*x+2*a)^5*sin(b*x+a),x, algorithm=""maxima"")","\frac{4 \, {\left(105 \, \sin\left(13 \, b x + 13 \, a\right) + 70 \, \sin\left(11 \, b x + 11 \, a\right) - 329 \, \sin\left(9 \, b x + 9 \, a\right) - 204 \, \sin\left(7 \, b x + 7 \, a\right) - 329 \, \sin\left(5 \, b x + 5 \, a\right) + 70 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)\right)} \cos\left(14 \, b x + 14 \, a\right) - 420 \, {\left(\sin\left(12 \, b x + 12 \, a\right) - 3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) + 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(13 \, b x + 13 \, a\right) + 4 \, {\left(70 \, \sin\left(11 \, b x + 11 \, a\right) - 329 \, \sin\left(9 \, b x + 9 \, a\right) - 204 \, \sin\left(7 \, b x + 7 \, a\right) - 329 \, \sin\left(5 \, b x + 5 \, a\right) + 70 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) + 280 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) + 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(11 \, b x + 11 \, a\right) + 12 \, {\left(329 \, \sin\left(9 \, b x + 9 \, a\right) + 204 \, \sin\left(7 \, b x + 7 \, a\right) + 329 \, \sin\left(5 \, b x + 5 \, a\right) - 70 \, \sin\left(3 \, b x + 3 \, a\right) - 105 \, \sin\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) - 1316 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(9 \, b x + 9 \, a\right) + 12 \, {\left(204 \, \sin\left(7 \, b x + 7 \, a\right) + 329 \, \sin\left(5 \, b x + 5 \, a\right) - 70 \, \sin\left(3 \, b x + 3 \, a\right) - 105 \, \sin\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) + 816 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(7 \, b x + 7 \, a\right) - 84 \, {\left(47 \, \sin\left(5 \, b x + 5 \, a\right) - 10 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 1316 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(5 \, b x + 5 \, a\right) + 420 \, {\left(2 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 105 \, {\left(2 \, {\left(\cos\left(12 \, b x + 12 \, a\right) - 3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) + 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(14 \, b x + 14 \, a\right) + \cos\left(14 \, b x + 14 \, a\right)^{2} - 2 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) + 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(12 \, b x + 12 \, a\right) + \cos\left(12 \, b x + 12 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) + 9 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 6 \, {\left(3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(8 \, b x + 8 \, a\right) + 9 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) + 9 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 6 \, {\left(\cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} + \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(12 \, b x + 12 \, a\right) - 3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) + 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) + \sin\left(14 \, b x + 14 \, a\right)^{2} - 2 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) + 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + \sin\left(12 \, b x + 12 \, a\right)^{2} + 6 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 9 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 6 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 9 \, \sin\left(8 \, b x + 8 \, a\right)^{2} + 6 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 9 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 6 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(105 \, \cos\left(13 \, b x + 13 \, a\right) + 70 \, \cos\left(11 \, b x + 11 \, a\right) - 329 \, \cos\left(9 \, b x + 9 \, a\right) - 204 \, \cos\left(7 \, b x + 7 \, a\right) - 329 \, \cos\left(5 \, b x + 5 \, a\right) + 70 \, \cos\left(3 \, b x + 3 \, a\right) + 105 \, \cos\left(b x + a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) + 420 \, {\left(\cos\left(12 \, b x + 12 \, a\right) - 3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) + 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(13 \, b x + 13 \, a\right) - 4 \, {\left(70 \, \cos\left(11 \, b x + 11 \, a\right) - 329 \, \cos\left(9 \, b x + 9 \, a\right) - 204 \, \cos\left(7 \, b x + 7 \, a\right) - 329 \, \cos\left(5 \, b x + 5 \, a\right) + 70 \, \cos\left(3 \, b x + 3 \, a\right) + 105 \, \cos\left(b x + a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 280 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) + 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(11 \, b x + 11 \, a\right) - 12 \, {\left(329 \, \cos\left(9 \, b x + 9 \, a\right) + 204 \, \cos\left(7 \, b x + 7 \, a\right) + 329 \, \cos\left(5 \, b x + 5 \, a\right) - 70 \, \cos\left(3 \, b x + 3 \, a\right) - 105 \, \cos\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 1316 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(9 \, b x + 9 \, a\right) - 12 \, {\left(204 \, \cos\left(7 \, b x + 7 \, a\right) + 329 \, \cos\left(5 \, b x + 5 \, a\right) - 70 \, \cos\left(3 \, b x + 3 \, a\right) - 105 \, \cos\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 816 \, {\left(3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(7 \, b x + 7 \, a\right) + 84 \, {\left(47 \, \cos\left(5 \, b x + 5 \, a\right) - 10 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 1316 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(5 \, b x + 5 \, a\right) - 420 \, {\left(2 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) - 280 \, {\left(\cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 280 \, \cos\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 420 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 420 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 420 \, \sin\left(b x + a\right)}{1536 \, {\left(b \cos\left(14 \, b x + 14 \, a\right)^{2} + b \cos\left(12 \, b x + 12 \, a\right)^{2} + 9 \, b \cos\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \cos\left(8 \, b x + 8 \, a\right)^{2} + 9 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(14 \, b x + 14 \, a\right)^{2} + b \sin\left(12 \, b x + 12 \, a\right)^{2} + 9 \, b \sin\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \sin\left(8 \, b x + 8 \, a\right)^{2} + 9 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} - 6 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b \cos\left(12 \, b x + 12 \, a\right) - 3 \, b \cos\left(10 \, b x + 10 \, a\right) - 3 \, b \cos\left(8 \, b x + 8 \, a\right) + 3 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(14 \, b x + 14 \, a\right) - 2 \, {\left(3 \, b \cos\left(10 \, b x + 10 \, a\right) + 3 \, b \cos\left(8 \, b x + 8 \, a\right) - 3 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(12 \, b x + 12 \, a\right) + 6 \, {\left(3 \, b \cos\left(8 \, b x + 8 \, a\right) - 3 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(10 \, b x + 10 \, a\right) - 6 \, {\left(3 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(8 \, b x + 8 \, a\right) + 6 \, {\left(3 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(b \sin\left(12 \, b x + 12 \, a\right) - 3 \, b \sin\left(10 \, b x + 10 \, a\right) - 3 \, b \sin\left(8 \, b x + 8 \, a\right) + 3 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 2 \, {\left(3 \, b \sin\left(10 \, b x + 10 \, a\right) + 3 \, b \sin\left(8 \, b x + 8 \, a\right) - 3 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 6 \, {\left(3 \, b \sin\left(8 \, b x + 8 \, a\right) - 3 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 6 \, {\left(3 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 6 \, {\left(3 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/1536*(4*(105*sin(13*b*x + 13*a) + 70*sin(11*b*x + 11*a) - 329*sin(9*b*x + 9*a) - 204*sin(7*b*x + 7*a) - 329*sin(5*b*x + 5*a) + 70*sin(3*b*x + 3*a) + 105*sin(b*x + a))*cos(14*b*x + 14*a) - 420*(sin(12*b*x + 12*a) - 3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) + 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(13*b*x + 13*a) + 4*(70*sin(11*b*x + 11*a) - 329*sin(9*b*x + 9*a) - 204*sin(7*b*x + 7*a) - 329*sin(5*b*x + 5*a) + 70*sin(3*b*x + 3*a) + 105*sin(b*x + a))*cos(12*b*x + 12*a) + 280*(3*sin(10*b*x + 10*a) + 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*cos(11*b*x + 11*a) + 12*(329*sin(9*b*x + 9*a) + 204*sin(7*b*x + 7*a) + 329*sin(5*b*x + 5*a) - 70*sin(3*b*x + 3*a) - 105*sin(b*x + a))*cos(10*b*x + 10*a) - 1316*(3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*cos(9*b*x + 9*a) + 12*(204*sin(7*b*x + 7*a) + 329*sin(5*b*x + 5*a) - 70*sin(3*b*x + 3*a) - 105*sin(b*x + a))*cos(8*b*x + 8*a) + 816*(3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(7*b*x + 7*a) - 84*(47*sin(5*b*x + 5*a) - 10*sin(3*b*x + 3*a) - 15*sin(b*x + a))*cos(6*b*x + 6*a) + 1316*(3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(5*b*x + 5*a) + 420*(2*sin(3*b*x + 3*a) + 3*sin(b*x + a))*cos(4*b*x + 4*a) - 105*(2*(cos(12*b*x + 12*a) - 3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) + 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*cos(14*b*x + 14*a) + cos(14*b*x + 14*a)^2 - 2*(3*cos(10*b*x + 10*a) + 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) + 1)*cos(12*b*x + 12*a) + cos(12*b*x + 12*a)^2 + 6*(3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) + 9*cos(10*b*x + 10*a)^2 - 6*(3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*cos(8*b*x + 8*a) + 9*cos(8*b*x + 8*a)^2 + 6*(3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) + 9*cos(6*b*x + 6*a)^2 - 6*(cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 9*cos(4*b*x + 4*a)^2 + cos(2*b*x + 2*a)^2 + 2*(sin(12*b*x + 12*a) - 3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) + 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(14*b*x + 14*a) + sin(14*b*x + 14*a)^2 - 2*(3*sin(10*b*x + 10*a) + 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + sin(12*b*x + 12*a)^2 + 6*(3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 9*sin(10*b*x + 10*a)^2 - 6*(3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 9*sin(8*b*x + 8*a)^2 + 6*(3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + 9*sin(6*b*x + 6*a)^2 + 9*sin(4*b*x + 4*a)^2 - 6*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(105*cos(13*b*x + 13*a) + 70*cos(11*b*x + 11*a) - 329*cos(9*b*x + 9*a) - 204*cos(7*b*x + 7*a) - 329*cos(5*b*x + 5*a) + 70*cos(3*b*x + 3*a) + 105*cos(b*x + a))*sin(14*b*x + 14*a) + 420*(cos(12*b*x + 12*a) - 3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) + 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*sin(13*b*x + 13*a) - 4*(70*cos(11*b*x + 11*a) - 329*cos(9*b*x + 9*a) - 204*cos(7*b*x + 7*a) - 329*cos(5*b*x + 5*a) + 70*cos(3*b*x + 3*a) + 105*cos(b*x + a))*sin(12*b*x + 12*a) - 280*(3*cos(10*b*x + 10*a) + 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) + 1)*sin(11*b*x + 11*a) - 12*(329*cos(9*b*x + 9*a) + 204*cos(7*b*x + 7*a) + 329*cos(5*b*x + 5*a) - 70*cos(3*b*x + 3*a) - 105*cos(b*x + a))*sin(10*b*x + 10*a) + 1316*(3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) + 1)*sin(9*b*x + 9*a) - 12*(204*cos(7*b*x + 7*a) + 329*cos(5*b*x + 5*a) - 70*cos(3*b*x + 3*a) - 105*cos(b*x + a))*sin(8*b*x + 8*a) - 816*(3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*sin(7*b*x + 7*a) + 84*(47*cos(5*b*x + 5*a) - 10*cos(3*b*x + 3*a) - 15*cos(b*x + a))*sin(6*b*x + 6*a) - 1316*(3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) - 1)*sin(5*b*x + 5*a) - 420*(2*cos(3*b*x + 3*a) + 3*cos(b*x + a))*sin(4*b*x + 4*a) - 280*(cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a) + 280*cos(3*b*x + 3*a)*sin(2*b*x + 2*a) + 420*cos(b*x + a)*sin(2*b*x + 2*a) - 420*cos(2*b*x + 2*a)*sin(b*x + a) - 420*sin(b*x + a))/(b*cos(14*b*x + 14*a)^2 + b*cos(12*b*x + 12*a)^2 + 9*b*cos(10*b*x + 10*a)^2 + 9*b*cos(8*b*x + 8*a)^2 + 9*b*cos(6*b*x + 6*a)^2 + 9*b*cos(4*b*x + 4*a)^2 + b*cos(2*b*x + 2*a)^2 + b*sin(14*b*x + 14*a)^2 + b*sin(12*b*x + 12*a)^2 + 9*b*sin(10*b*x + 10*a)^2 + 9*b*sin(8*b*x + 8*a)^2 + 9*b*sin(6*b*x + 6*a)^2 + 9*b*sin(4*b*x + 4*a)^2 - 6*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + b*sin(2*b*x + 2*a)^2 + 2*(b*cos(12*b*x + 12*a) - 3*b*cos(10*b*x + 10*a) - 3*b*cos(8*b*x + 8*a) + 3*b*cos(6*b*x + 6*a) + 3*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) - b)*cos(14*b*x + 14*a) - 2*(3*b*cos(10*b*x + 10*a) + 3*b*cos(8*b*x + 8*a) - 3*b*cos(6*b*x + 6*a) - 3*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) + b)*cos(12*b*x + 12*a) + 6*(3*b*cos(8*b*x + 8*a) - 3*b*cos(6*b*x + 6*a) - 3*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) + b)*cos(10*b*x + 10*a) - 6*(3*b*cos(6*b*x + 6*a) + 3*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) - b)*cos(8*b*x + 8*a) + 6*(3*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) - 6*(b*cos(2*b*x + 2*a) + b)*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) + 2*(b*sin(12*b*x + 12*a) - 3*b*sin(10*b*x + 10*a) - 3*b*sin(8*b*x + 8*a) + 3*b*sin(6*b*x + 6*a) + 3*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - 2*(3*b*sin(10*b*x + 10*a) + 3*b*sin(8*b*x + 8*a) - 3*b*sin(6*b*x + 6*a) - 3*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + 6*(3*b*sin(8*b*x + 8*a) - 3*b*sin(6*b*x + 6*a) - 3*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 6*(3*b*sin(6*b*x + 6*a) + 3*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 6*(3*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
13,1,72,0,0.333426," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","\frac{5 \, \cos\left(12 \, b x + 12 \, a\right) - 12 \, \cos\left(10 \, b x + 10 \, a\right) - 30 \, \cos\left(8 \, b x + 8 \, a\right) + 100 \, \cos\left(6 \, b x + 6 \, a\right) + 75 \, \cos\left(4 \, b x + 4 \, a\right) - 600 \, \cos\left(2 \, b x + 2 \, a\right)}{3840 \, b}"," ",0,"1/3840*(5*cos(12*b*x + 12*a) - 12*cos(10*b*x + 10*a) - 30*cos(8*b*x + 8*a) + 100*cos(6*b*x + 6*a) + 75*cos(4*b*x + 4*a) - 600*cos(2*b*x + 2*a))/b","A",0
14,1,65,0,0.334847," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{120 \, b x - 2 \, \sin\left(10 \, b x + 10 \, a\right) + 5 \, \sin\left(8 \, b x + 8 \, a\right) + 10 \, \sin\left(6 \, b x + 6 \, a\right) - 40 \, \sin\left(4 \, b x + 4 \, a\right) - 20 \, \sin\left(2 \, b x + 2 \, a\right)}{640 \, b}"," ",0,"1/640*(120*b*x - 2*sin(10*b*x + 10*a) + 5*sin(8*b*x + 8*a) + 10*sin(6*b*x + 6*a) - 40*sin(4*b*x + 4*a) - 20*sin(2*b*x + 2*a))/b","A",0
15,1,50,0,0.326681," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","-\frac{3 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) - 12 \, \cos\left(4 \, b x + 4 \, a\right) + 72 \, \cos\left(2 \, b x + 2 \, a\right)}{384 \, b}"," ",0,"-1/384*(3*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) - 12*cos(4*b*x + 4*a) + 72*cos(2*b*x + 2*a))/b","A",0
16,1,41,0,0.329378," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","\frac{12 \, b x + \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)}{48 \, b}"," ",0,"1/48*(12*b*x + sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))/b","A",0
17,1,26,0,0.330062," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a),x, algorithm=""maxima"")","\frac{\cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(2 \, b x + 2 \, a\right)}{16 \, b}"," ",0,"1/16*(cos(4*b*x + 4*a) - 4*cos(2*b*x + 2*a))/b","A",0
18,1,55,0,0.332487," ","integrate(csc(2*b*x+2*a)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right)}{4 \, b}"," ",0,"-1/4*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2)/b","B",0
19,1,53,0,0.329672," ","integrate(csc(2*b*x+2*a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sin\left(2 \, b x + 2 \, a\right)}{2 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"1/2*sin(2*b*x + 2*a)/(b*cos(2*b*x + 2*a)^2 + b*sin(2*b*x + 2*a)^2 + 2*b*cos(2*b*x + 2*a) + b)","B",0
20,1,641,0,0.350685," ","integrate(csc(2*b*x+2*a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{4 \, \cos\left(4 \, b x + 4 \, a\right) \cos\left(2 \, b x + 2 \, a\right) + 8 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)}{16 \, {\left(b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"1/16*(4*cos(4*b*x + 4*a)*cos(2*b*x + 2*a) + 8*cos(2*b*x + 2*a)^2 - (2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2) + (2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + (2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 8*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a))/(b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(4*b*x + 4*a)^2 + 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 + 2*(2*b*cos(2*b*x + 2*a) + b)*cos(4*b*x + 4*a) + 4*b*cos(2*b*x + 2*a) + b)","B",0
21,1,308,0,0.349773," ","integrate(csc(2*b*x+2*a)^4*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(8 \, b x + 8 \, a\right) + 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) \sin\left(2 \, b x + 2 \, a\right)}{3 \, {\left(b \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} - 8 \, b \sin\left(6 \, b x + 6 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(6 \, b x + 6 \, a\right) + 4 \, b \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left(b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + b\right)}}"," ",0,"-1/3*((2*cos(2*b*x + 2*a) + 1)*sin(8*b*x + 8*a) + 2*(2*cos(2*b*x + 2*a) + 1)*sin(6*b*x + 6*a) - 2*cos(8*b*x + 8*a)*sin(2*b*x + 2*a) - 4*cos(6*b*x + 6*a)*sin(2*b*x + 2*a))/(b*cos(8*b*x + 8*a)^2 + 4*b*cos(6*b*x + 6*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(8*b*x + 8*a)^2 + 4*b*sin(6*b*x + 6*a)^2 - 8*b*sin(6*b*x + 6*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 + 2*(2*b*cos(6*b*x + 6*a) - 2*b*cos(2*b*x + 2*a) - b)*cos(8*b*x + 8*a) - 4*(2*b*cos(2*b*x + 2*a) + b)*cos(6*b*x + 6*a) + 4*b*cos(2*b*x + 2*a) + 4*(b*sin(6*b*x + 6*a) - b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + b)","B",0
22,1,3164,0,0.441331," ","integrate(csc(2*b*x+2*a)^5*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) + 6 \, \cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) + 6 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) + 4 \, {\left(9 \, \cos\left(8 \, b x + 8 \, a\right) - 16 \, \cos\left(6 \, b x + 6 \, a\right) + 9 \, \cos\left(4 \, b x + 4 \, a\right) + 12 \, \cos\left(2 \, b x + 2 \, a\right) + 3\right)} \cos\left(10 \, b x + 10 \, a\right) + 24 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(22 \, \cos\left(6 \, b x + 6 \, a\right) + 12 \, \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(2 \, b x + 2 \, a\right) - 6\right)} \cos\left(8 \, b x + 8 \, a\right) - 24 \, \cos\left(8 \, b x + 8 \, a\right)^{2} - 8 \, {\left(11 \, \cos\left(4 \, b x + 4 \, a\right) + 8 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) + 32 \, \cos\left(6 \, b x + 6 \, a\right)^{2} + 12 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) + 2\right)} \cos\left(4 \, b x + 4 \, a\right) - 24 \, \cos\left(4 \, b x + 4 \, a\right)^{2} + 24 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - 3 \, {\left(2 \, {\left(2 \, \cos\left(10 \, b x + 10 \, a\right) - \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(12 \, b x + 12 \, a\right) + \cos\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\cos\left(8 \, b x + 8 \, a\right) + 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) + 4 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(8 \, b x + 8 \, a\right) + \cos\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) + 16 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(10 \, b x + 10 \, a\right) - \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + \sin\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\sin\left(8 \, b x + 8 \, a\right) + 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 4 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + \sin\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 16 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(10 \, b x + 10 \, a\right) - \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(12 \, b x + 12 \, a\right) + \cos\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\cos\left(8 \, b x + 8 \, a\right) + 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) + 4 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(8 \, b x + 8 \, a\right) + \cos\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) + 16 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(10 \, b x + 10 \, a\right) - \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + \sin\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\sin\left(8 \, b x + 8 \, a\right) + 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 4 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + \sin\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 16 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 3 \, {\left(2 \, {\left(2 \, \cos\left(10 \, b x + 10 \, a\right) - \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(12 \, b x + 12 \, a\right) + \cos\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\cos\left(8 \, b x + 8 \, a\right) + 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) + 4 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(8 \, b x + 8 \, a\right) + \cos\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) + 16 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(10 \, b x + 10 \, a\right) - \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + \sin\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\sin\left(8 \, b x + 8 \, a\right) + 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 4 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + \sin\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 16 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) + 6 \, \sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) + 6 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 4 \, {\left(9 \, \sin\left(8 \, b x + 8 \, a\right) - 16 \, \sin\left(6 \, b x + 6 \, a\right) + 9 \, \sin\left(4 \, b x + 4 \, a\right) + 12 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 24 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(22 \, \sin\left(6 \, b x + 6 \, a\right) + 12 \, \sin\left(4 \, b x + 4 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 24 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 8 \, {\left(11 \, \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 32 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 24 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 36 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 24 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 12 \, \cos\left(2 \, b x + 2 \, a\right)}{64 \, {\left(b \cos\left(12 \, b x + 12 \, a\right)^{2} + 4 \, b \cos\left(10 \, b x + 10 \, a\right)^{2} + b \cos\left(8 \, b x + 8 \, a\right)^{2} + 16 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(12 \, b x + 12 \, a\right)^{2} + 4 \, b \sin\left(10 \, b x + 10 \, a\right)^{2} + b \sin\left(8 \, b x + 8 \, a\right)^{2} + 16 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, b \cos\left(10 \, b x + 10 \, a\right) - b \cos\left(8 \, b x + 8 \, a\right) - 4 \, b \cos\left(6 \, b x + 6 \, a\right) - b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(12 \, b x + 12 \, a\right) - 4 \, {\left(b \cos\left(8 \, b x + 8 \, a\right) + 4 \, b \cos\left(6 \, b x + 6 \, a\right) + b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(10 \, b x + 10 \, a\right) + 2 \, {\left(4 \, b \cos\left(6 \, b x + 6 \, a\right) + b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(8 \, b x + 8 \, a\right) + 8 \, {\left(b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) - 2 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, b \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(2 \, b \sin\left(10 \, b x + 10 \, a\right) - b \sin\left(8 \, b x + 8 \, a\right) - 4 \, b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 4 \, {\left(b \sin\left(8 \, b x + 8 \, a\right) + 4 \, b \sin\left(6 \, b x + 6 \, a\right) + b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 2 \, {\left(4 \, b \sin\left(6 \, b x + 6 \, a\right) + b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 8 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/64*(4*(3*cos(10*b*x + 10*a) + 6*cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) + 6*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a))*cos(12*b*x + 12*a) + 4*(9*cos(8*b*x + 8*a) - 16*cos(6*b*x + 6*a) + 9*cos(4*b*x + 4*a) + 12*cos(2*b*x + 2*a) + 3)*cos(10*b*x + 10*a) + 24*cos(10*b*x + 10*a)^2 - 4*(22*cos(6*b*x + 6*a) + 12*cos(4*b*x + 4*a) - 9*cos(2*b*x + 2*a) - 6)*cos(8*b*x + 8*a) - 24*cos(8*b*x + 8*a)^2 - 8*(11*cos(4*b*x + 4*a) + 8*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) + 32*cos(6*b*x + 6*a)^2 + 12*(3*cos(2*b*x + 2*a) + 2)*cos(4*b*x + 4*a) - 24*cos(4*b*x + 4*a)^2 + 24*cos(2*b*x + 2*a)^2 - 3*(2*(2*cos(10*b*x + 10*a) - cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) + 1)*cos(12*b*x + 12*a) + cos(12*b*x + 12*a)^2 - 4*(cos(8*b*x + 8*a) + 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) + 4*cos(10*b*x + 10*a)^2 + 2*(4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) - 1)*cos(8*b*x + 8*a) + cos(8*b*x + 8*a)^2 + 8*(cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) + 16*cos(6*b*x + 6*a)^2 - 2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(10*b*x + 10*a) - sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + sin(12*b*x + 12*a)^2 - 4*(sin(8*b*x + 8*a) + 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 4*sin(10*b*x + 10*a)^2 + 2*(4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + sin(8*b*x + 8*a)^2 + 8*(sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + 16*sin(6*b*x + 6*a)^2 + sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2) + 3*(2*(2*cos(10*b*x + 10*a) - cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) + 1)*cos(12*b*x + 12*a) + cos(12*b*x + 12*a)^2 - 4*(cos(8*b*x + 8*a) + 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) + 4*cos(10*b*x + 10*a)^2 + 2*(4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) - 1)*cos(8*b*x + 8*a) + cos(8*b*x + 8*a)^2 + 8*(cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) + 16*cos(6*b*x + 6*a)^2 - 2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(10*b*x + 10*a) - sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + sin(12*b*x + 12*a)^2 - 4*(sin(8*b*x + 8*a) + 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 4*sin(10*b*x + 10*a)^2 + 2*(4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + sin(8*b*x + 8*a)^2 + 8*(sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + 16*sin(6*b*x + 6*a)^2 + sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + 3*(2*(2*cos(10*b*x + 10*a) - cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) + 1)*cos(12*b*x + 12*a) + cos(12*b*x + 12*a)^2 - 4*(cos(8*b*x + 8*a) + 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) + 4*cos(10*b*x + 10*a)^2 + 2*(4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) - 1)*cos(8*b*x + 8*a) + cos(8*b*x + 8*a)^2 + 8*(cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) + 16*cos(6*b*x + 6*a)^2 - 2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(10*b*x + 10*a) - sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + sin(12*b*x + 12*a)^2 - 4*(sin(8*b*x + 8*a) + 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 4*sin(10*b*x + 10*a)^2 + 2*(4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + sin(8*b*x + 8*a)^2 + 8*(sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + 16*sin(6*b*x + 6*a)^2 + sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(3*sin(10*b*x + 10*a) + 6*sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) + 6*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + 4*(9*sin(8*b*x + 8*a) - 16*sin(6*b*x + 6*a) + 9*sin(4*b*x + 4*a) + 12*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 24*sin(10*b*x + 10*a)^2 - 4*(22*sin(6*b*x + 6*a) + 12*sin(4*b*x + 4*a) - 9*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 24*sin(8*b*x + 8*a)^2 - 8*(11*sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + 32*sin(6*b*x + 6*a)^2 - 24*sin(4*b*x + 4*a)^2 + 36*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 24*sin(2*b*x + 2*a)^2 + 12*cos(2*b*x + 2*a))/(b*cos(12*b*x + 12*a)^2 + 4*b*cos(10*b*x + 10*a)^2 + b*cos(8*b*x + 8*a)^2 + 16*b*cos(6*b*x + 6*a)^2 + b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(12*b*x + 12*a)^2 + 4*b*sin(10*b*x + 10*a)^2 + b*sin(8*b*x + 8*a)^2 + 16*b*sin(6*b*x + 6*a)^2 + b*sin(4*b*x + 4*a)^2 - 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 + 2*(2*b*cos(10*b*x + 10*a) - b*cos(8*b*x + 8*a) - 4*b*cos(6*b*x + 6*a) - b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) + b)*cos(12*b*x + 12*a) - 4*(b*cos(8*b*x + 8*a) + 4*b*cos(6*b*x + 6*a) + b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) - b)*cos(10*b*x + 10*a) + 2*(4*b*cos(6*b*x + 6*a) + b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) - b)*cos(8*b*x + 8*a) + 8*(b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) - 2*(2*b*cos(2*b*x + 2*a) + b)*cos(4*b*x + 4*a) + 4*b*cos(2*b*x + 2*a) + 2*(2*b*sin(10*b*x + 10*a) - b*sin(8*b*x + 8*a) - 4*b*sin(6*b*x + 6*a) - b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 4*(b*sin(8*b*x + 8*a) + 4*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 2*(4*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 8*(b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
23,1,80,0,0.351835," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","\frac{99 \, \sin\left(13 \, b x + 13 \, a\right) - 351 \, \sin\left(11 \, b x + 11 \, a\right) - 286 \, \sin\left(9 \, b x + 9 \, a\right) + 2574 \, \sin\left(7 \, b x + 7 \, a\right) - 1287 \, \sin\left(5 \, b x + 5 \, a\right) - 10725 \, \sin\left(3 \, b x + 3 \, a\right) + 25740 \, \sin\left(b x + a\right)}{164736 \, b}"," ",0,"1/164736*(99*sin(13*b*x + 13*a) - 351*sin(11*b*x + 11*a) - 286*sin(9*b*x + 9*a) + 2574*sin(7*b*x + 7*a) - 1287*sin(5*b*x + 5*a) - 10725*sin(3*b*x + 3*a) + 25740*sin(b*x + a))/b","A",0
24,1,69,0,0.344493," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{105 \, \cos\left(11 \, b x + 11 \, a\right) - 385 \, \cos\left(9 \, b x + 9 \, a\right) - 165 \, \cos\left(7 \, b x + 7 \, a\right) + 2541 \, \cos\left(5 \, b x + 5 \, a\right) - 2310 \, \cos\left(3 \, b x + 3 \, a\right) - 16170 \, \cos\left(b x + a\right)}{73920 \, b}"," ",0,"1/73920*(105*cos(11*b*x + 11*a) - 385*cos(9*b*x + 9*a) - 165*cos(7*b*x + 7*a) + 2541*cos(5*b*x + 5*a) - 2310*cos(3*b*x + 3*a) - 16170*cos(b*x + a))/b","A",0
25,1,47,0,0.345558," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","-\frac{7 \, \sin\left(9 \, b x + 9 \, a\right) - 27 \, \sin\left(7 \, b x + 7 \, a\right) + 168 \, \sin\left(3 \, b x + 3 \, a\right) - 378 \, \sin\left(b x + a\right)}{2016 \, b}"," ",0,"-1/2016*(7*sin(9*b*x + 9*a) - 27*sin(7*b*x + 7*a) + 168*sin(3*b*x + 3*a) - 378*sin(b*x + a))/b","A",0
26,1,47,0,0.339942," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","-\frac{15 \, \cos\left(7 \, b x + 7 \, a\right) - 63 \, \cos\left(5 \, b x + 5 \, a\right) + 35 \, \cos\left(3 \, b x + 3 \, a\right) + 525 \, \cos\left(b x + a\right)}{1680 \, b}"," ",0,"-1/1680*(15*cos(7*b*x + 7*a) - 63*cos(5*b*x + 5*a) + 35*cos(3*b*x + 3*a) + 525*cos(b*x + a))/b","A",0
27,1,34,0,0.330637," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a),x, algorithm=""maxima"")","\frac{\sin\left(5 \, b x + 5 \, a\right) - 5 \, \sin\left(3 \, b x + 3 \, a\right) + 10 \, \sin\left(b x + a\right)}{40 \, b}"," ",0,"1/40*(sin(5*b*x + 5*a) - 5*sin(3*b*x + 3*a) + 10*sin(b*x + a))/b","B",0
28,1,124,0,0.465302," ","integrate(csc(2*b*x+2*a)*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{\log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) + 2 \, \sin\left(b x + a\right)}{4 \, b}"," ",0,"-1/4*(log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) + 2*sin(b*x + a))/b","B",0
29,1,83,0,0.325830," ","integrate(csc(2*b*x+2*a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{\cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)}{2 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"1/2*(cos(2*b*x + 2*a)*cos(b*x + a) + sin(2*b*x + 2*a)*sin(b*x + a) + cos(b*x + a))/(b*cos(2*b*x + 2*a)^2 + b*sin(2*b*x + 2*a)^2 + 2*b*cos(2*b*x + 2*a) + b)","B",0
30,1,480,0,0.466873," ","integrate(csc(2*b*x+2*a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(\sin\left(3 \, b x + 3 \, a\right) - \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(\cos\left(3 \, b x + 3 \, a\right) - \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 4 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(3 \, b x + 3 \, a\right) - 8 \, \cos\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 8 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 8 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 4 \, \sin\left(b x + a\right)}{32 \, {\left(b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"1/32*(4*(sin(3*b*x + 3*a) - sin(b*x + a))*cos(4*b*x + 4*a) - (2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(cos(3*b*x + 3*a) - cos(b*x + a))*sin(4*b*x + 4*a) + 4*(2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a) - 8*cos(3*b*x + 3*a)*sin(2*b*x + 2*a) + 8*cos(b*x + a)*sin(2*b*x + 2*a) - 8*cos(2*b*x + 2*a)*sin(b*x + a) - 4*sin(b*x + a))/(b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(4*b*x + 4*a)^2 + 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 + 2*(2*b*cos(2*b*x + 2*a) + b)*cos(4*b*x + 4*a) + 4*b*cos(2*b*x + 2*a) + b)","B",0
31,1,987,0,0.359369," ","integrate(csc(2*b*x+2*a)^4*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \cos\left(5 \, b x + 5 \, a\right) + 10 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 12 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(5 \, b x + 5 \, a\right) + 12 \, {\left(10 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 40 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right) + 36 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) - 3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) + \cos\left(6 \, b x + 6 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} + 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 6 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + \sin\left(6 \, b x + 6 \, a\right)^{2} + 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 18 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) + \cos\left(6 \, b x + 6 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} + 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 6 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + \sin\left(6 \, b x + 6 \, a\right)^{2} + 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 18 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(3 \, \sin\left(5 \, b x + 5 \, a\right) + 10 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 36 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(5 \, b x + 5 \, a\right) + 12 \, {\left(10 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 120 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 36 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 12 \, \cos\left(b x + a\right)}{96 \, {\left(b \cos\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + 9 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} + 18 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(3 \, b \cos\left(4 \, b x + 4 \, a\right) + 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(6 \, b x + 6 \, a\right) + 6 \, {\left(3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(4 \, b x + 4 \, a\right) + 6 \, b \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/96*(4*(3*cos(5*b*x + 5*a) + 10*cos(3*b*x + 3*a) + 3*cos(b*x + a))*cos(6*b*x + 6*a) + 12*(3*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) + 1)*cos(5*b*x + 5*a) + 12*(10*cos(3*b*x + 3*a) + 3*cos(b*x + a))*cos(4*b*x + 4*a) + 40*(3*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a) + 36*cos(2*b*x + 2*a)*cos(b*x + a) - 3*(2*(3*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) + cos(6*b*x + 6*a)^2 + 6*(3*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 9*cos(4*b*x + 4*a)^2 + 9*cos(2*b*x + 2*a)^2 + 6*(sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + sin(6*b*x + 6*a)^2 + 9*sin(4*b*x + 4*a)^2 + 18*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) + 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + 3*(2*(3*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) + cos(6*b*x + 6*a)^2 + 6*(3*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 9*cos(4*b*x + 4*a)^2 + 9*cos(2*b*x + 2*a)^2 + 6*(sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + sin(6*b*x + 6*a)^2 + 9*sin(4*b*x + 4*a)^2 + 18*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) + 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(3*sin(5*b*x + 5*a) + 10*sin(3*b*x + 3*a) + 3*sin(b*x + a))*sin(6*b*x + 6*a) + 36*(sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(5*b*x + 5*a) + 12*(10*sin(3*b*x + 3*a) + 3*sin(b*x + a))*sin(4*b*x + 4*a) + 120*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) + 36*sin(2*b*x + 2*a)*sin(b*x + a) + 12*cos(b*x + a))/(b*cos(6*b*x + 6*a)^2 + 9*b*cos(4*b*x + 4*a)^2 + 9*b*cos(2*b*x + 2*a)^2 + b*sin(6*b*x + 6*a)^2 + 9*b*sin(4*b*x + 4*a)^2 + 18*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 9*b*sin(2*b*x + 2*a)^2 + 2*(3*b*cos(4*b*x + 4*a) + 3*b*cos(2*b*x + 2*a) + b)*cos(6*b*x + 6*a) + 6*(3*b*cos(2*b*x + 2*a) + b)*cos(4*b*x + 4*a) + 6*b*cos(2*b*x + 2*a) + 6*(b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
32,1,1805,0,0.523489," ","integrate(csc(2*b*x+2*a)^5*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(15 \, \sin\left(9 \, b x + 9 \, a\right) + 40 \, \sin\left(7 \, b x + 7 \, a\right) + 18 \, \sin\left(5 \, b x + 5 \, a\right) + 40 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) - 60 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) + 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(9 \, b x + 9 \, a\right) + 12 \, {\left(40 \, \sin\left(7 \, b x + 7 \, a\right) + 18 \, \sin\left(5 \, b x + 5 \, a\right) + 40 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) - 160 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(7 \, b x + 7 \, a\right) + 8 \, {\left(18 \, \sin\left(5 \, b x + 5 \, a\right) + 40 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 72 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(5 \, b x + 5 \, a\right) - 40 \, {\left(8 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) + 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) + \cos\left(10 \, b x + 10 \, a\right)^{2} + 6 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(8 \, b x + 8 \, a\right) + 9 \, \cos\left(8 \, b x + 8 \, a\right)^{2} - 4 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) + 4 \, \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, \cos\left(4 \, b x + 4 \, a\right)^{2} + 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) + 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + \sin\left(10 \, b x + 10 \, a\right)^{2} + 6 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 9 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 4 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 4 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 12 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(15 \, \cos\left(9 \, b x + 9 \, a\right) + 40 \, \cos\left(7 \, b x + 7 \, a\right) + 18 \, \cos\left(5 \, b x + 5 \, a\right) + 40 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 60 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) + 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(9 \, b x + 9 \, a\right) - 12 \, {\left(40 \, \cos\left(7 \, b x + 7 \, a\right) + 18 \, \cos\left(5 \, b x + 5 \, a\right) + 40 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 160 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(7 \, b x + 7 \, a\right) - 8 \, {\left(18 \, \cos\left(5 \, b x + 5 \, a\right) + 40 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 72 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(5 \, b x + 5 \, a\right) + 40 \, {\left(8 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) - 160 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 480 \, \cos\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 180 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 180 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 60 \, \sin\left(b x + a\right)}{512 \, {\left(b \cos\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + 9 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} + 12 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(3 \, b \cos\left(8 \, b x + 8 \, a\right) + 2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(10 \, b x + 10 \, a\right) + 6 \, {\left(2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, b \cos\left(4 \, b x + 4 \, a\right) + 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(6 \, b x + 6 \, a\right) + 4 \, {\left(3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(4 \, b x + 4 \, a\right) + 6 \, b \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(3 \, b \sin\left(8 \, b x + 8 \, a\right) + 2 \, b \sin\left(6 \, b x + 6 \, a\right) - 2 \, b \sin\left(4 \, b x + 4 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 6 \, {\left(2 \, b \sin\left(6 \, b x + 6 \, a\right) - 2 \, b \sin\left(4 \, b x + 4 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, b \sin\left(4 \, b x + 4 \, a\right) + 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/512*(4*(15*sin(9*b*x + 9*a) + 40*sin(7*b*x + 7*a) + 18*sin(5*b*x + 5*a) + 40*sin(3*b*x + 3*a) + 15*sin(b*x + a))*cos(10*b*x + 10*a) - 60*(3*sin(8*b*x + 8*a) + 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*cos(9*b*x + 9*a) + 12*(40*sin(7*b*x + 7*a) + 18*sin(5*b*x + 5*a) + 40*sin(3*b*x + 3*a) + 15*sin(b*x + a))*cos(8*b*x + 8*a) - 160*(2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*cos(7*b*x + 7*a) + 8*(18*sin(5*b*x + 5*a) + 40*sin(3*b*x + 3*a) + 15*sin(b*x + a))*cos(6*b*x + 6*a) + 72*(2*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*cos(5*b*x + 5*a) - 40*(8*sin(3*b*x + 3*a) + 3*sin(b*x + a))*cos(4*b*x + 4*a) - 15*(2*(3*cos(8*b*x + 8*a) + 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) + cos(10*b*x + 10*a)^2 + 6*(2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) - 1)*cos(8*b*x + 8*a) + 9*cos(8*b*x + 8*a)^2 - 4*(2*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) + 4*cos(6*b*x + 6*a)^2 + 4*(3*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 4*cos(4*b*x + 4*a)^2 + 9*cos(2*b*x + 2*a)^2 + 2*(3*sin(8*b*x + 8*a) + 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + sin(10*b*x + 10*a)^2 + 6*(2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 9*sin(8*b*x + 8*a)^2 - 4*(2*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + 4*sin(6*b*x + 6*a)^2 + 4*sin(4*b*x + 4*a)^2 + 12*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) + 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(15*cos(9*b*x + 9*a) + 40*cos(7*b*x + 7*a) + 18*cos(5*b*x + 5*a) + 40*cos(3*b*x + 3*a) + 15*cos(b*x + a))*sin(10*b*x + 10*a) + 60*(3*cos(8*b*x + 8*a) + 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) - 1)*sin(9*b*x + 9*a) - 12*(40*cos(7*b*x + 7*a) + 18*cos(5*b*x + 5*a) + 40*cos(3*b*x + 3*a) + 15*cos(b*x + a))*sin(8*b*x + 8*a) + 160*(2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) - 1)*sin(7*b*x + 7*a) - 8*(18*cos(5*b*x + 5*a) + 40*cos(3*b*x + 3*a) + 15*cos(b*x + a))*sin(6*b*x + 6*a) - 72*(2*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) + 1)*sin(5*b*x + 5*a) + 40*(8*cos(3*b*x + 3*a) + 3*cos(b*x + a))*sin(4*b*x + 4*a) - 160*(3*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a) + 480*cos(3*b*x + 3*a)*sin(2*b*x + 2*a) + 180*cos(b*x + a)*sin(2*b*x + 2*a) - 180*cos(2*b*x + 2*a)*sin(b*x + a) - 60*sin(b*x + a))/(b*cos(10*b*x + 10*a)^2 + 9*b*cos(8*b*x + 8*a)^2 + 4*b*cos(6*b*x + 6*a)^2 + 4*b*cos(4*b*x + 4*a)^2 + 9*b*cos(2*b*x + 2*a)^2 + b*sin(10*b*x + 10*a)^2 + 9*b*sin(8*b*x + 8*a)^2 + 4*b*sin(6*b*x + 6*a)^2 + 4*b*sin(4*b*x + 4*a)^2 + 12*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 9*b*sin(2*b*x + 2*a)^2 + 2*(3*b*cos(8*b*x + 8*a) + 2*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) - b)*cos(10*b*x + 10*a) + 6*(2*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) - b)*cos(8*b*x + 8*a) - 4*(2*b*cos(4*b*x + 4*a) + 3*b*cos(2*b*x + 2*a) + b)*cos(6*b*x + 6*a) + 4*(3*b*cos(2*b*x + 2*a) + b)*cos(4*b*x + 4*a) + 6*b*cos(2*b*x + 2*a) + 2*(3*b*sin(8*b*x + 8*a) + 2*b*sin(6*b*x + 6*a) - 2*b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 6*(2*b*sin(6*b*x + 6*a) - 2*b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 4*(2*b*sin(4*b*x + 4*a) + 3*b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
33,1,91,0,0.332275," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^8,x, algorithm=""maxima"")","\frac{429 \, \cos\left(15 \, b x + 15 \, a\right) + 495 \, \cos\left(13 \, b x + 13 \, a\right) - 4095 \, \cos\left(11 \, b x + 11 \, a\right) - 5005 \, \cos\left(9 \, b x + 9 \, a\right) + 19305 \, \cos\left(7 \, b x + 7 \, a\right) + 27027 \, \cos\left(5 \, b x + 5 \, a\right) - 75075 \, \cos\left(3 \, b x + 3 \, a\right) - 225225 \, \cos\left(b x + a\right)}{411840 \, b}"," ",0,"1/411840*(429*cos(15*b*x + 15*a) + 495*cos(13*b*x + 13*a) - 4095*cos(11*b*x + 11*a) - 5005*cos(9*b*x + 9*a) + 19305*cos(7*b*x + 7*a) + 27027*cos(5*b*x + 5*a) - 75075*cos(3*b*x + 3*a) - 225225*cos(b*x + a))/b","A",0
34,1,80,0,0.332281," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^7,x, algorithm=""maxima"")","-\frac{231 \, \sin\left(13 \, b x + 13 \, a\right) + 273 \, \sin\left(11 \, b x + 11 \, a\right) - 2002 \, \sin\left(9 \, b x + 9 \, a\right) - 2574 \, \sin\left(7 \, b x + 7 \, a\right) + 9009 \, \sin\left(5 \, b x + 5 \, a\right) + 15015 \, \sin\left(3 \, b x + 3 \, a\right) - 60060 \, \sin\left(b x + a\right)}{96096 \, b}"," ",0,"-1/96096*(231*sin(13*b*x + 13*a) + 273*sin(11*b*x + 11*a) - 2002*sin(9*b*x + 9*a) - 2574*sin(7*b*x + 7*a) + 9009*sin(5*b*x + 5*a) + 15015*sin(3*b*x + 3*a) - 60060*sin(b*x + a))/b","A",0
35,1,69,0,0.337202," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^6,x, algorithm=""maxima"")","-\frac{63 \, \cos\left(11 \, b x + 11 \, a\right) + 77 \, \cos\left(9 \, b x + 9 \, a\right) - 495 \, \cos\left(7 \, b x + 7 \, a\right) - 693 \, \cos\left(5 \, b x + 5 \, a\right) + 2310 \, \cos\left(3 \, b x + 3 \, a\right) + 6930 \, \cos\left(b x + a\right)}{11088 \, b}"," ",0,"-1/11088*(63*cos(11*b*x + 11*a) + 77*cos(9*b*x + 9*a) - 495*cos(7*b*x + 7*a) - 693*cos(5*b*x + 5*a) + 2310*cos(3*b*x + 3*a) + 6930*cos(b*x + a))/b","A",0
36,1,58,0,0.340195," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","\frac{35 \, \sin\left(9 \, b x + 9 \, a\right) + 45 \, \sin\left(7 \, b x + 7 \, a\right) - 252 \, \sin\left(5 \, b x + 5 \, a\right) - 420 \, \sin\left(3 \, b x + 3 \, a\right) + 1890 \, \sin\left(b x + a\right)}{2520 \, b}"," ",0,"1/2520*(35*sin(9*b*x + 9*a) + 45*sin(7*b*x + 7*a) - 252*sin(5*b*x + 5*a) - 420*sin(3*b*x + 3*a) + 1890*sin(b*x + a))/b","A",0
37,1,47,0,0.340728," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{5 \, \cos\left(7 \, b x + 7 \, a\right) + 7 \, \cos\left(5 \, b x + 5 \, a\right) - 35 \, \cos\left(3 \, b x + 3 \, a\right) - 105 \, \cos\left(b x + a\right)}{140 \, b}"," ",0,"1/140*(5*cos(7*b*x + 7*a) + 7*cos(5*b*x + 5*a) - 35*cos(3*b*x + 3*a) - 105*cos(b*x + a))/b","A",0
38,1,36,0,0.344905," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","-\frac{3 \, \sin\left(5 \, b x + 5 \, a\right) + 5 \, \sin\left(3 \, b x + 3 \, a\right) - 30 \, \sin\left(b x + a\right)}{30 \, b}"," ",0,"-1/30*(3*sin(5*b*x + 5*a) + 5*sin(3*b*x + 3*a) - 30*sin(b*x + a))/b","A",0
39,1,23,0,0.344305," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","-\frac{\cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)}{3 \, b}"," ",0,"-1/3*(cos(3*b*x + 3*a) + 3*cos(b*x + a))/b","A",0
40,1,11,0,0.343766," ","integrate(csc(b*x+a)*sin(2*b*x+2*a),x, algorithm=""maxima"")","\frac{2 \, \sin\left(b x + a\right)}{b}"," ",0,"2*sin(b*x + a)/b","A",0
41,1,233,0,0.476165," ","integrate(csc(b*x+a)*csc(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) + 4 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, \sin\left(b x + a\right)}{4 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"-1/4*((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) + 4*cos(b*x + a)*sin(2*b*x + 2*a) - 4*cos(2*b*x + 2*a)*sin(b*x + a) + 4*sin(b*x + a))/(b*cos(2*b*x + 2*a)^2 + b*sin(2*b*x + 2*a)^2 - 2*b*cos(2*b*x + 2*a) + b)","B",0
42,1,974,0,0.380790," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \cos\left(5 \, b x + 5 \, a\right) - 2 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(5 \, b x + 5 \, a\right) + 4 \, {\left(2 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 8 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 12 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 3 \, {\left(2 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 3 \, {\left(2 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(3 \, \sin\left(5 \, b x + 5 \, a\right) - 2 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 12 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(5 \, b x + 5 \, a\right) + 4 \, {\left(2 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 12 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 12 \, \cos\left(b x + a\right)}{16 \, {\left(b \cos\left(6 \, b x + 6 \, a\right)^{2} + b \cos\left(4 \, b x + 4 \, a\right)^{2} + b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(6 \, b x + 6 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 2 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/16*(4*(3*cos(5*b*x + 5*a) - 2*cos(3*b*x + 3*a) + 3*cos(b*x + a))*cos(6*b*x + 6*a) - 12*(cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(5*b*x + 5*a) + 4*(2*cos(3*b*x + 3*a) - 3*cos(b*x + a))*cos(4*b*x + 4*a) + 8*(cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a) - 12*cos(2*b*x + 2*a)*cos(b*x + a) + 3*(2*(cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - cos(6*b*x + 6*a)^2 - 2*(cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - cos(2*b*x + 2*a)^2 + 2*(sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 - 2*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - 3*(2*(cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - cos(6*b*x + 6*a)^2 - 2*(cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - cos(2*b*x + 2*a)^2 + 2*(sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 - 2*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(3*sin(5*b*x + 5*a) - 2*sin(3*b*x + 3*a) + 3*sin(b*x + a))*sin(6*b*x + 6*a) - 12*(sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(5*b*x + 5*a) + 4*(2*sin(3*b*x + 3*a) - 3*sin(b*x + a))*sin(4*b*x + 4*a) + 8*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) - 12*sin(2*b*x + 2*a)*sin(b*x + a) + 12*cos(b*x + a))/(b*cos(6*b*x + 6*a)^2 + b*cos(4*b*x + 4*a)^2 + b*cos(2*b*x + 2*a)^2 + b*sin(6*b*x + 6*a)^2 + b*sin(4*b*x + 4*a)^2 + 2*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + b*sin(2*b*x + 2*a)^2 - 2*(b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 2*(b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) - 2*(b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
43,1,1780,0,0.531708," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(15 \, \sin\left(9 \, b x + 9 \, a\right) - 20 \, \sin\left(7 \, b x + 7 \, a\right) - 22 \, \sin\left(5 \, b x + 5 \, a\right) - 20 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) + 60 \, {\left(\sin\left(8 \, b x + 8 \, a\right) + 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(9 \, b x + 9 \, a\right) + 4 \, {\left(20 \, \sin\left(7 \, b x + 7 \, a\right) + 22 \, \sin\left(5 \, b x + 5 \, a\right) + 20 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) - 80 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(7 \, b x + 7 \, a\right) + 8 \, {\left(22 \, \sin\left(5 \, b x + 5 \, a\right) + 20 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 88 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(5 \, b x + 5 \, a\right) - 40 \, {\left(4 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 15 \, {\left(2 \, {\left(\cos\left(8 \, b x + 8 \, a\right) + 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) - \cos\left(10 \, b x + 10 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 4 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(8 \, b x + 8 \, a\right) + 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - \sin\left(10 \, b x + 10 \, a\right)^{2} - 2 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(15 \, \cos\left(9 \, b x + 9 \, a\right) - 20 \, \cos\left(7 \, b x + 7 \, a\right) - 22 \, \cos\left(5 \, b x + 5 \, a\right) - 20 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 60 \, {\left(\cos\left(8 \, b x + 8 \, a\right) + 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(9 \, b x + 9 \, a\right) - 4 \, {\left(20 \, \cos\left(7 \, b x + 7 \, a\right) + 22 \, \cos\left(5 \, b x + 5 \, a\right) + 20 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 80 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(7 \, b x + 7 \, a\right) - 8 \, {\left(22 \, \cos\left(5 \, b x + 5 \, a\right) + 20 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 88 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(5 \, b x + 5 \, a\right) + 40 \, {\left(4 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) - 80 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 80 \, \cos\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 60 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) + 60 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 60 \, \sin\left(b x + a\right)}{96 \, {\left(b \cos\left(10 \, b x + 10 \, a\right)^{2} + b \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(10 \, b x + 10 \, a\right)^{2} + b \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b \cos\left(8 \, b x + 8 \, a\right) + 2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(10 \, b x + 10 \, a\right) + 2 \, {\left(2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 4 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b \sin\left(8 \, b x + 8 \, a\right) + 2 \, b \sin\left(6 \, b x + 6 \, a\right) - 2 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 2 \, {\left(2 \, b \sin\left(6 \, b x + 6 \, a\right) - 2 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/96*(4*(15*sin(9*b*x + 9*a) - 20*sin(7*b*x + 7*a) - 22*sin(5*b*x + 5*a) - 20*sin(3*b*x + 3*a) + 15*sin(b*x + a))*cos(10*b*x + 10*a) + 60*(sin(8*b*x + 8*a) + 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(9*b*x + 9*a) + 4*(20*sin(7*b*x + 7*a) + 22*sin(5*b*x + 5*a) + 20*sin(3*b*x + 3*a) - 15*sin(b*x + a))*cos(8*b*x + 8*a) - 80*(2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(7*b*x + 7*a) + 8*(22*sin(5*b*x + 5*a) + 20*sin(3*b*x + 3*a) - 15*sin(b*x + a))*cos(6*b*x + 6*a) + 88*(2*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*cos(5*b*x + 5*a) - 40*(4*sin(3*b*x + 3*a) - 3*sin(b*x + a))*cos(4*b*x + 4*a) + 15*(2*(cos(8*b*x + 8*a) + 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) - cos(10*b*x + 10*a)^2 - 2*(2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - cos(8*b*x + 8*a)^2 + 4*(2*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 4*cos(6*b*x + 6*a)^2 - 4*(cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 4*cos(4*b*x + 4*a)^2 - cos(2*b*x + 2*a)^2 + 2*(sin(8*b*x + 8*a) + 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - sin(10*b*x + 10*a)^2 - 2*(2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - sin(8*b*x + 8*a)^2 + 4*(2*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 4*sin(6*b*x + 6*a)^2 - 4*sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) - 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(15*cos(9*b*x + 9*a) - 20*cos(7*b*x + 7*a) - 22*cos(5*b*x + 5*a) - 20*cos(3*b*x + 3*a) + 15*cos(b*x + a))*sin(10*b*x + 10*a) - 60*(cos(8*b*x + 8*a) + 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*sin(9*b*x + 9*a) - 4*(20*cos(7*b*x + 7*a) + 22*cos(5*b*x + 5*a) + 20*cos(3*b*x + 3*a) - 15*cos(b*x + a))*sin(8*b*x + 8*a) + 80*(2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*sin(7*b*x + 7*a) - 8*(22*cos(5*b*x + 5*a) + 20*cos(3*b*x + 3*a) - 15*cos(b*x + a))*sin(6*b*x + 6*a) - 88*(2*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*sin(5*b*x + 5*a) + 40*(4*cos(3*b*x + 3*a) - 3*cos(b*x + a))*sin(4*b*x + 4*a) - 80*(cos(2*b*x + 2*a) - 1)*sin(3*b*x + 3*a) + 80*cos(3*b*x + 3*a)*sin(2*b*x + 2*a) - 60*cos(b*x + a)*sin(2*b*x + 2*a) + 60*cos(2*b*x + 2*a)*sin(b*x + a) - 60*sin(b*x + a))/(b*cos(10*b*x + 10*a)^2 + b*cos(8*b*x + 8*a)^2 + 4*b*cos(6*b*x + 6*a)^2 + 4*b*cos(4*b*x + 4*a)^2 + b*cos(2*b*x + 2*a)^2 + b*sin(10*b*x + 10*a)^2 + b*sin(8*b*x + 8*a)^2 + 4*b*sin(6*b*x + 6*a)^2 + 4*b*sin(4*b*x + 4*a)^2 + 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + b*sin(2*b*x + 2*a)^2 - 2*(b*cos(8*b*x + 8*a) + 2*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) + b)*cos(10*b*x + 10*a) + 2*(2*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 4*(2*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 4*(b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) - 2*(b*sin(8*b*x + 8*a) + 2*b*sin(6*b*x + 6*a) - 2*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 2*(2*b*sin(6*b*x + 6*a) - 2*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 4*(2*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
44,1,3846,0,0.504520," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(105 \, \cos\left(13 \, b x + 13 \, a\right) - 70 \, \cos\left(11 \, b x + 11 \, a\right) - 329 \, \cos\left(9 \, b x + 9 \, a\right) + 204 \, \cos\left(7 \, b x + 7 \, a\right) - 329 \, \cos\left(5 \, b x + 5 \, a\right) - 70 \, \cos\left(3 \, b x + 3 \, a\right) + 105 \, \cos\left(b x + a\right)\right)} \cos\left(14 \, b x + 14 \, a\right) - 420 \, {\left(\cos\left(12 \, b x + 12 \, a\right) + 3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(13 \, b x + 13 \, a\right) + 4 \, {\left(70 \, \cos\left(11 \, b x + 11 \, a\right) + 329 \, \cos\left(9 \, b x + 9 \, a\right) - 204 \, \cos\left(7 \, b x + 7 \, a\right) + 329 \, \cos\left(5 \, b x + 5 \, a\right) + 70 \, \cos\left(3 \, b x + 3 \, a\right) - 105 \, \cos\left(b x + a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) + 280 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(11 \, b x + 11 \, a\right) + 12 \, {\left(329 \, \cos\left(9 \, b x + 9 \, a\right) - 204 \, \cos\left(7 \, b x + 7 \, a\right) + 329 \, \cos\left(5 \, b x + 5 \, a\right) + 70 \, \cos\left(3 \, b x + 3 \, a\right) - 105 \, \cos\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) - 1316 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) + 3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(9 \, b x + 9 \, a\right) + 12 \, {\left(204 \, \cos\left(7 \, b x + 7 \, a\right) - 329 \, \cos\left(5 \, b x + 5 \, a\right) - 70 \, \cos\left(3 \, b x + 3 \, a\right) + 105 \, \cos\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) + 816 \, {\left(3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(7 \, b x + 7 \, a\right) - 84 \, {\left(47 \, \cos\left(5 \, b x + 5 \, a\right) + 10 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 1316 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(5 \, b x + 5 \, a\right) + 420 \, {\left(2 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 280 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 420 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 105 \, {\left(2 \, {\left(\cos\left(12 \, b x + 12 \, a\right) + 3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(14 \, b x + 14 \, a\right) - \cos\left(14 \, b x + 14 \, a\right)^{2} - 2 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - \cos\left(12 \, b x + 12 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) + 3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 9 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 6 \, {\left(3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 9 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 9 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 6 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(12 \, b x + 12 \, a\right) + 3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - \sin\left(14 \, b x + 14 \, a\right)^{2} - 2 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - \sin\left(12 \, b x + 12 \, a\right)^{2} + 6 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) + 3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 9 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 6 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 9 \, \sin\left(8 \, b x + 8 \, a\right)^{2} + 6 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 9 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 6 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 105 \, {\left(2 \, {\left(\cos\left(12 \, b x + 12 \, a\right) + 3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(14 \, b x + 14 \, a\right) - \cos\left(14 \, b x + 14 \, a\right)^{2} - 2 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - \cos\left(12 \, b x + 12 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) + 3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 9 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 6 \, {\left(3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 9 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 9 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 6 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(12 \, b x + 12 \, a\right) + 3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - \sin\left(14 \, b x + 14 \, a\right)^{2} - 2 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - \sin\left(12 \, b x + 12 \, a\right)^{2} + 6 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) + 3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 9 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 6 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 9 \, \sin\left(8 \, b x + 8 \, a\right)^{2} + 6 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 9 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 6 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(105 \, \sin\left(13 \, b x + 13 \, a\right) - 70 \, \sin\left(11 \, b x + 11 \, a\right) - 329 \, \sin\left(9 \, b x + 9 \, a\right) + 204 \, \sin\left(7 \, b x + 7 \, a\right) - 329 \, \sin\left(5 \, b x + 5 \, a\right) - 70 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 420 \, {\left(\sin\left(12 \, b x + 12 \, a\right) + 3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(13 \, b x + 13 \, a\right) + 4 \, {\left(70 \, \sin\left(11 \, b x + 11 \, a\right) + 329 \, \sin\left(9 \, b x + 9 \, a\right) - 204 \, \sin\left(7 \, b x + 7 \, a\right) + 329 \, \sin\left(5 \, b x + 5 \, a\right) + 70 \, \sin\left(3 \, b x + 3 \, a\right) - 105 \, \sin\left(b x + a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 280 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(11 \, b x + 11 \, a\right) + 12 \, {\left(329 \, \sin\left(9 \, b x + 9 \, a\right) - 204 \, \sin\left(7 \, b x + 7 \, a\right) + 329 \, \sin\left(5 \, b x + 5 \, a\right) + 70 \, \sin\left(3 \, b x + 3 \, a\right) - 105 \, \sin\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 1316 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) + 3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(9 \, b x + 9 \, a\right) + 12 \, {\left(204 \, \sin\left(7 \, b x + 7 \, a\right) - 329 \, \sin\left(5 \, b x + 5 \, a\right) - 70 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 816 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(7 \, b x + 7 \, a\right) - 84 \, {\left(47 \, \sin\left(5 \, b x + 5 \, a\right) + 10 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 1316 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(5 \, b x + 5 \, a\right) + 420 \, {\left(2 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 280 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 420 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 420 \, \cos\left(b x + a\right)}{768 \, {\left(b \cos\left(14 \, b x + 14 \, a\right)^{2} + b \cos\left(12 \, b x + 12 \, a\right)^{2} + 9 \, b \cos\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \cos\left(8 \, b x + 8 \, a\right)^{2} + 9 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(14 \, b x + 14 \, a\right)^{2} + b \sin\left(12 \, b x + 12 \, a\right)^{2} + 9 \, b \sin\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \sin\left(8 \, b x + 8 \, a\right)^{2} + 9 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} + 6 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b \cos\left(12 \, b x + 12 \, a\right) + 3 \, b \cos\left(10 \, b x + 10 \, a\right) - 3 \, b \cos\left(8 \, b x + 8 \, a\right) - 3 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(14 \, b x + 14 \, a\right) + 2 \, {\left(3 \, b \cos\left(10 \, b x + 10 \, a\right) - 3 \, b \cos\left(8 \, b x + 8 \, a\right) - 3 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(12 \, b x + 12 \, a\right) - 6 \, {\left(3 \, b \cos\left(8 \, b x + 8 \, a\right) + 3 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(10 \, b x + 10 \, a\right) + 6 \, {\left(3 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 6 \, {\left(3 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 6 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b \sin\left(12 \, b x + 12 \, a\right) + 3 \, b \sin\left(10 \, b x + 10 \, a\right) - 3 \, b \sin\left(8 \, b x + 8 \, a\right) - 3 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) + 2 \, {\left(3 \, b \sin\left(10 \, b x + 10 \, a\right) - 3 \, b \sin\left(8 \, b x + 8 \, a\right) - 3 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 6 \, {\left(3 \, b \sin\left(8 \, b x + 8 \, a\right) + 3 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 6 \, {\left(3 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 6 \, {\left(3 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/768*(4*(105*cos(13*b*x + 13*a) - 70*cos(11*b*x + 11*a) - 329*cos(9*b*x + 9*a) + 204*cos(7*b*x + 7*a) - 329*cos(5*b*x + 5*a) - 70*cos(3*b*x + 3*a) + 105*cos(b*x + a))*cos(14*b*x + 14*a) - 420*(cos(12*b*x + 12*a) + 3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(13*b*x + 13*a) + 4*(70*cos(11*b*x + 11*a) + 329*cos(9*b*x + 9*a) - 204*cos(7*b*x + 7*a) + 329*cos(5*b*x + 5*a) + 70*cos(3*b*x + 3*a) - 105*cos(b*x + a))*cos(12*b*x + 12*a) + 280*(3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(11*b*x + 11*a) + 12*(329*cos(9*b*x + 9*a) - 204*cos(7*b*x + 7*a) + 329*cos(5*b*x + 5*a) + 70*cos(3*b*x + 3*a) - 105*cos(b*x + a))*cos(10*b*x + 10*a) - 1316*(3*cos(8*b*x + 8*a) + 3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(9*b*x + 9*a) + 12*(204*cos(7*b*x + 7*a) - 329*cos(5*b*x + 5*a) - 70*cos(3*b*x + 3*a) + 105*cos(b*x + a))*cos(8*b*x + 8*a) + 816*(3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(7*b*x + 7*a) - 84*(47*cos(5*b*x + 5*a) + 10*cos(3*b*x + 3*a) - 15*cos(b*x + a))*cos(6*b*x + 6*a) + 1316*(3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(5*b*x + 5*a) + 420*(2*cos(3*b*x + 3*a) - 3*cos(b*x + a))*cos(4*b*x + 4*a) + 280*(cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a) - 420*cos(2*b*x + 2*a)*cos(b*x + a) + 105*(2*(cos(12*b*x + 12*a) + 3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(14*b*x + 14*a) - cos(14*b*x + 14*a)^2 - 2*(3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - cos(12*b*x + 12*a)^2 + 6*(3*cos(8*b*x + 8*a) + 3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) - 9*cos(10*b*x + 10*a)^2 - 6*(3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 9*cos(8*b*x + 8*a)^2 + 6*(3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 9*cos(6*b*x + 6*a)^2 - 6*(cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 9*cos(4*b*x + 4*a)^2 - cos(2*b*x + 2*a)^2 + 2*(sin(12*b*x + 12*a) + 3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - sin(14*b*x + 14*a)^2 - 2*(3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - sin(12*b*x + 12*a)^2 + 6*(3*sin(8*b*x + 8*a) + 3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 9*sin(10*b*x + 10*a)^2 - 6*(3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 9*sin(8*b*x + 8*a)^2 + 6*(3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 9*sin(6*b*x + 6*a)^2 - 9*sin(4*b*x + 4*a)^2 - 6*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - 105*(2*(cos(12*b*x + 12*a) + 3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(14*b*x + 14*a) - cos(14*b*x + 14*a)^2 - 2*(3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - cos(12*b*x + 12*a)^2 + 6*(3*cos(8*b*x + 8*a) + 3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) - 9*cos(10*b*x + 10*a)^2 - 6*(3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 9*cos(8*b*x + 8*a)^2 + 6*(3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 9*cos(6*b*x + 6*a)^2 - 6*(cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 9*cos(4*b*x + 4*a)^2 - cos(2*b*x + 2*a)^2 + 2*(sin(12*b*x + 12*a) + 3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - sin(14*b*x + 14*a)^2 - 2*(3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - sin(12*b*x + 12*a)^2 + 6*(3*sin(8*b*x + 8*a) + 3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 9*sin(10*b*x + 10*a)^2 - 6*(3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 9*sin(8*b*x + 8*a)^2 + 6*(3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 9*sin(6*b*x + 6*a)^2 - 9*sin(4*b*x + 4*a)^2 - 6*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(105*sin(13*b*x + 13*a) - 70*sin(11*b*x + 11*a) - 329*sin(9*b*x + 9*a) + 204*sin(7*b*x + 7*a) - 329*sin(5*b*x + 5*a) - 70*sin(3*b*x + 3*a) + 105*sin(b*x + a))*sin(14*b*x + 14*a) - 420*(sin(12*b*x + 12*a) + 3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(13*b*x + 13*a) + 4*(70*sin(11*b*x + 11*a) + 329*sin(9*b*x + 9*a) - 204*sin(7*b*x + 7*a) + 329*sin(5*b*x + 5*a) + 70*sin(3*b*x + 3*a) - 105*sin(b*x + a))*sin(12*b*x + 12*a) + 280*(3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(11*b*x + 11*a) + 12*(329*sin(9*b*x + 9*a) - 204*sin(7*b*x + 7*a) + 329*sin(5*b*x + 5*a) + 70*sin(3*b*x + 3*a) - 105*sin(b*x + a))*sin(10*b*x + 10*a) - 1316*(3*sin(8*b*x + 8*a) + 3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(9*b*x + 9*a) + 12*(204*sin(7*b*x + 7*a) - 329*sin(5*b*x + 5*a) - 70*sin(3*b*x + 3*a) + 105*sin(b*x + a))*sin(8*b*x + 8*a) + 816*(3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(7*b*x + 7*a) - 84*(47*sin(5*b*x + 5*a) + 10*sin(3*b*x + 3*a) - 15*sin(b*x + a))*sin(6*b*x + 6*a) + 1316*(3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(5*b*x + 5*a) + 420*(2*sin(3*b*x + 3*a) - 3*sin(b*x + a))*sin(4*b*x + 4*a) + 280*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) - 420*sin(2*b*x + 2*a)*sin(b*x + a) + 420*cos(b*x + a))/(b*cos(14*b*x + 14*a)^2 + b*cos(12*b*x + 12*a)^2 + 9*b*cos(10*b*x + 10*a)^2 + 9*b*cos(8*b*x + 8*a)^2 + 9*b*cos(6*b*x + 6*a)^2 + 9*b*cos(4*b*x + 4*a)^2 + b*cos(2*b*x + 2*a)^2 + b*sin(14*b*x + 14*a)^2 + b*sin(12*b*x + 12*a)^2 + 9*b*sin(10*b*x + 10*a)^2 + 9*b*sin(8*b*x + 8*a)^2 + 9*b*sin(6*b*x + 6*a)^2 + 9*b*sin(4*b*x + 4*a)^2 + 6*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + b*sin(2*b*x + 2*a)^2 - 2*(b*cos(12*b*x + 12*a) + 3*b*cos(10*b*x + 10*a) - 3*b*cos(8*b*x + 8*a) - 3*b*cos(6*b*x + 6*a) + 3*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) - b)*cos(14*b*x + 14*a) + 2*(3*b*cos(10*b*x + 10*a) - 3*b*cos(8*b*x + 8*a) - 3*b*cos(6*b*x + 6*a) + 3*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) - b)*cos(12*b*x + 12*a) - 6*(3*b*cos(8*b*x + 8*a) + 3*b*cos(6*b*x + 6*a) - 3*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) + b)*cos(10*b*x + 10*a) + 6*(3*b*cos(6*b*x + 6*a) - 3*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 6*(3*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 6*(b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) - 2*(b*sin(12*b*x + 12*a) + 3*b*sin(10*b*x + 10*a) - 3*b*sin(8*b*x + 8*a) - 3*b*sin(6*b*x + 6*a) + 3*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) + 2*(3*b*sin(10*b*x + 10*a) - 3*b*sin(8*b*x + 8*a) - 3*b*sin(6*b*x + 6*a) + 3*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 6*(3*b*sin(8*b*x + 8*a) + 3*b*sin(6*b*x + 6*a) - 3*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 6*(3*b*sin(6*b*x + 6*a) - 3*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 6*(3*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
45,1,87,0,0.358024," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^8,x, algorithm=""maxima"")","\frac{840 \, b x - 3 \, \sin\left(14 \, b x + 14 \, a\right) - 7 \, \sin\left(12 \, b x + 12 \, a\right) + 21 \, \sin\left(10 \, b x + 10 \, a\right) + 63 \, \sin\left(8 \, b x + 8 \, a\right) - 63 \, \sin\left(6 \, b x + 6 \, a\right) - 315 \, \sin\left(4 \, b x + 4 \, a\right) + 105 \, \sin\left(2 \, b x + 2 \, a\right)}{1344 \, b}"," ",0,"1/1344*(840*b*x - 3*sin(14*b*x + 14*a) - 7*sin(12*b*x + 12*a) + 21*sin(10*b*x + 10*a) + 63*sin(8*b*x + 8*a) - 63*sin(6*b*x + 6*a) - 315*sin(4*b*x + 4*a) + 105*sin(2*b*x + 2*a))/b","A",0
46,1,72,0,0.342772," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^7,x, algorithm=""maxima"")","-\frac{5 \, \cos\left(12 \, b x + 12 \, a\right) + 12 \, \cos\left(10 \, b x + 10 \, a\right) - 30 \, \cos\left(8 \, b x + 8 \, a\right) - 100 \, \cos\left(6 \, b x + 6 \, a\right) + 75 \, \cos\left(4 \, b x + 4 \, a\right) + 600 \, \cos\left(2 \, b x + 2 \, a\right)}{960 \, b}"," ",0,"-1/960*(5*cos(12*b*x + 12*a) + 12*cos(10*b*x + 10*a) - 30*cos(8*b*x + 8*a) - 100*cos(6*b*x + 6*a) + 75*cos(4*b*x + 4*a) + 600*cos(2*b*x + 2*a))/b","A",0
47,1,65,0,0.346634," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^6,x, algorithm=""maxima"")","\frac{120 \, b x + 2 \, \sin\left(10 \, b x + 10 \, a\right) + 5 \, \sin\left(8 \, b x + 8 \, a\right) - 10 \, \sin\left(6 \, b x + 6 \, a\right) - 40 \, \sin\left(4 \, b x + 4 \, a\right) + 20 \, \sin\left(2 \, b x + 2 \, a\right)}{160 \, b}"," ",0,"1/160*(120*b*x + 2*sin(10*b*x + 10*a) + 5*sin(8*b*x + 8*a) - 10*sin(6*b*x + 6*a) - 40*sin(4*b*x + 4*a) + 20*sin(2*b*x + 2*a))/b","A",0
48,1,50,0,0.350991," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","\frac{3 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 12 \, \cos\left(4 \, b x + 4 \, a\right) - 72 \, \cos\left(2 \, b x + 2 \, a\right)}{96 \, b}"," ",0,"1/96*(3*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 12*cos(4*b*x + 4*a) - 72*cos(2*b*x + 2*a))/b","A",0
49,1,43,0,0.355154," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{12 \, b x - \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)}{12 \, b}"," ",0,"1/12*(12*b*x - sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))/b","A",0
50,1,26,0,0.339604," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","-\frac{\cos\left(4 \, b x + 4 \, a\right) + 4 \, \cos\left(2 \, b x + 2 \, a\right)}{4 \, b}"," ",0,"-1/4*(cos(4*b*x + 4*a) + 4*cos(2*b*x + 2*a))/b","A",0
51,1,18,0,0.339778," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","\frac{2 \, b x + \sin\left(2 \, b x + 2 \, a\right)}{b}"," ",0,"(2*b*x + sin(2*b*x + 2*a))/b","A",0
52,1,81,0,0.351825," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)}{b}"," ",0,"(log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2))/b","B",0
53,1,656,0,0.371835," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a),x, algorithm=""maxima"")","\frac{4 \, \cos\left(4 \, b x + 4 \, a\right) \cos\left(2 \, b x + 2 \, a\right) - 8 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)}{4 \, {\left(b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"1/4*(4*cos(4*b*x + 4*a)*cos(2*b*x + 2*a) - 8*cos(2*b*x + 2*a)^2 + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2) - (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 8*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a))/(b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(4*b*x + 4*a)^2 - 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 - 2*(2*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 4*b*cos(2*b*x + 2*a) + b)","B",0
54,1,308,0,0.359659," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^2,x, algorithm=""maxima"")","\frac{4 \, {\left({\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(8 \, b x + 8 \, a\right) - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \cos\left(6 \, b x + 6 \, a\right) \sin\left(2 \, b x + 2 \, a\right)\right)}}{3 \, {\left(b \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} - 8 \, b \sin\left(6 \, b x + 6 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, b \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + b\right)}}"," ",0,"4/3*((2*cos(2*b*x + 2*a) - 1)*sin(8*b*x + 8*a) - 2*(2*cos(2*b*x + 2*a) - 1)*sin(6*b*x + 6*a) - 2*cos(8*b*x + 8*a)*sin(2*b*x + 2*a) + 4*cos(6*b*x + 6*a)*sin(2*b*x + 2*a))/(b*cos(8*b*x + 8*a)^2 + 4*b*cos(6*b*x + 6*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(8*b*x + 8*a)^2 + 4*b*sin(6*b*x + 6*a)^2 - 8*b*sin(6*b*x + 6*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 - 2*(2*b*cos(6*b*x + 6*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 4*(2*b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) - 4*b*cos(2*b*x + 2*a) - 4*(b*sin(6*b*x + 6*a) - b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + b)","B",0
55,1,3188,0,0.450454," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) - 6 \, \cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 6 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) + 4 \, {\left(9 \, \cos\left(8 \, b x + 8 \, a\right) + 16 \, \cos\left(6 \, b x + 6 \, a\right) + 9 \, \cos\left(4 \, b x + 4 \, a\right) - 12 \, \cos\left(2 \, b x + 2 \, a\right) + 3\right)} \cos\left(10 \, b x + 10 \, a\right) - 24 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(22 \, \cos\left(6 \, b x + 6 \, a\right) - 12 \, \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(2 \, b x + 2 \, a\right) + 6\right)} \cos\left(8 \, b x + 8 \, a\right) + 24 \, \cos\left(8 \, b x + 8 \, a\right)^{2} - 8 \, {\left(11 \, \cos\left(4 \, b x + 4 \, a\right) - 8 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 32 \, \cos\left(6 \, b x + 6 \, a\right)^{2} + 12 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 2\right)} \cos\left(4 \, b x + 4 \, a\right) + 24 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 24 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 3 \, {\left(2 \, {\left(2 \, \cos\left(10 \, b x + 10 \, a\right) + \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - \cos\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 4 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - \cos\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 16 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(10 \, b x + 10 \, a\right) + \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - \sin\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 4 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - \sin\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 16 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(10 \, b x + 10 \, a\right) + \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - \cos\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 4 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - \cos\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 16 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(10 \, b x + 10 \, a\right) + \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - \sin\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 4 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - \sin\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 16 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(10 \, b x + 10 \, a\right) + \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - \cos\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 4 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - \cos\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 16 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(10 \, b x + 10 \, a\right) + \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - \sin\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 4 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - \sin\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 16 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) - 6 \, \sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 6 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 4 \, {\left(9 \, \sin\left(8 \, b x + 8 \, a\right) + 16 \, \sin\left(6 \, b x + 6 \, a\right) + 9 \, \sin\left(4 \, b x + 4 \, a\right) - 12 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 24 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(22 \, \sin\left(6 \, b x + 6 \, a\right) - 12 \, \sin\left(4 \, b x + 4 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 24 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 8 \, {\left(11 \, \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 32 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + 24 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 36 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 24 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 12 \, \cos\left(2 \, b x + 2 \, a\right)}{16 \, {\left(b \cos\left(12 \, b x + 12 \, a\right)^{2} + 4 \, b \cos\left(10 \, b x + 10 \, a\right)^{2} + b \cos\left(8 \, b x + 8 \, a\right)^{2} + 16 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(12 \, b x + 12 \, a\right)^{2} + 4 \, b \sin\left(10 \, b x + 10 \, a\right)^{2} + b \sin\left(8 \, b x + 8 \, a\right)^{2} + 16 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(2 \, b \cos\left(10 \, b x + 10 \, a\right) + b \cos\left(8 \, b x + 8 \, a\right) - 4 \, b \cos\left(6 \, b x + 6 \, a\right) + b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(12 \, b x + 12 \, a\right) + 4 \, {\left(b \cos\left(8 \, b x + 8 \, a\right) - 4 \, b \cos\left(6 \, b x + 6 \, a\right) + b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(10 \, b x + 10 \, a\right) - 2 \, {\left(4 \, b \cos\left(6 \, b x + 6 \, a\right) - b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 8 \, {\left(b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 2 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(2 \, b \sin\left(10 \, b x + 10 \, a\right) + b \sin\left(8 \, b x + 8 \, a\right) - 4 \, b \sin\left(6 \, b x + 6 \, a\right) + b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 4 \, {\left(b \sin\left(8 \, b x + 8 \, a\right) - 4 \, b \sin\left(6 \, b x + 6 \, a\right) + b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 2 \, {\left(4 \, b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 8 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/16*(4*(3*cos(10*b*x + 10*a) - 6*cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 6*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a))*cos(12*b*x + 12*a) + 4*(9*cos(8*b*x + 8*a) + 16*cos(6*b*x + 6*a) + 9*cos(4*b*x + 4*a) - 12*cos(2*b*x + 2*a) + 3)*cos(10*b*x + 10*a) - 24*cos(10*b*x + 10*a)^2 - 4*(22*cos(6*b*x + 6*a) - 12*cos(4*b*x + 4*a) - 9*cos(2*b*x + 2*a) + 6)*cos(8*b*x + 8*a) + 24*cos(8*b*x + 8*a)^2 - 8*(11*cos(4*b*x + 4*a) - 8*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - 32*cos(6*b*x + 6*a)^2 + 12*(3*cos(2*b*x + 2*a) - 2)*cos(4*b*x + 4*a) + 24*cos(4*b*x + 4*a)^2 - 24*cos(2*b*x + 2*a)^2 + 3*(2*(2*cos(10*b*x + 10*a) + cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - cos(12*b*x + 12*a)^2 - 4*(cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - 4*cos(10*b*x + 10*a)^2 + 2*(4*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - cos(8*b*x + 8*a)^2 + 8*(cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 16*cos(6*b*x + 6*a)^2 - 2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(10*b*x + 10*a) + sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - sin(12*b*x + 12*a)^2 - 4*(sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 4*sin(10*b*x + 10*a)^2 + 2*(4*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - sin(8*b*x + 8*a)^2 + 8*(sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 16*sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2) - 3*(2*(2*cos(10*b*x + 10*a) + cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - cos(12*b*x + 12*a)^2 - 4*(cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - 4*cos(10*b*x + 10*a)^2 + 2*(4*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - cos(8*b*x + 8*a)^2 + 8*(cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 16*cos(6*b*x + 6*a)^2 - 2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(10*b*x + 10*a) + sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - sin(12*b*x + 12*a)^2 - 4*(sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 4*sin(10*b*x + 10*a)^2 + 2*(4*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - sin(8*b*x + 8*a)^2 + 8*(sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 16*sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - 3*(2*(2*cos(10*b*x + 10*a) + cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - cos(12*b*x + 12*a)^2 - 4*(cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - 4*cos(10*b*x + 10*a)^2 + 2*(4*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - cos(8*b*x + 8*a)^2 + 8*(cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 16*cos(6*b*x + 6*a)^2 - 2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(10*b*x + 10*a) + sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - sin(12*b*x + 12*a)^2 - 4*(sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 4*sin(10*b*x + 10*a)^2 + 2*(4*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - sin(8*b*x + 8*a)^2 + 8*(sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 16*sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(3*sin(10*b*x + 10*a) - 6*sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 6*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + 4*(9*sin(8*b*x + 8*a) + 16*sin(6*b*x + 6*a) + 9*sin(4*b*x + 4*a) - 12*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 24*sin(10*b*x + 10*a)^2 - 4*(22*sin(6*b*x + 6*a) - 12*sin(4*b*x + 4*a) - 9*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 24*sin(8*b*x + 8*a)^2 - 8*(11*sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 32*sin(6*b*x + 6*a)^2 + 24*sin(4*b*x + 4*a)^2 + 36*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 24*sin(2*b*x + 2*a)^2 + 12*cos(2*b*x + 2*a))/(b*cos(12*b*x + 12*a)^2 + 4*b*cos(10*b*x + 10*a)^2 + b*cos(8*b*x + 8*a)^2 + 16*b*cos(6*b*x + 6*a)^2 + b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(12*b*x + 12*a)^2 + 4*b*sin(10*b*x + 10*a)^2 + b*sin(8*b*x + 8*a)^2 + 16*b*sin(6*b*x + 6*a)^2 + b*sin(4*b*x + 4*a)^2 + 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 - 2*(2*b*cos(10*b*x + 10*a) + b*cos(8*b*x + 8*a) - 4*b*cos(6*b*x + 6*a) + b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(12*b*x + 12*a) + 4*(b*cos(8*b*x + 8*a) - 4*b*cos(6*b*x + 6*a) + b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(10*b*x + 10*a) - 2*(4*b*cos(6*b*x + 6*a) - b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 8*(b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 2*(2*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 4*b*cos(2*b*x + 2*a) - 2*(2*b*sin(10*b*x + 10*a) + b*sin(8*b*x + 8*a) - 4*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + 4*(b*sin(8*b*x + 8*a) - 4*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 2*(4*b*sin(6*b*x + 6*a) - b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 8*(b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
56,1,1227,0,0.368344," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{16 \, {\left(2 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(16 \, b x + 16 \, a\right) - 4 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(14 \, b x + 14 \, a\right) - 4 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) + 12 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) - {\left(6 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(16 \, b x + 16 \, a\right) + 2 \, {\left(6 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(14 \, b x + 14 \, a\right) + 2 \, {\left(6 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(12 \, b x + 12 \, a\right) - 6 \, {\left(6 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(10 \, b x + 10 \, a\right)\right)}}{15 \, {\left(b \cos\left(16 \, b x + 16 \, a\right)^{2} + 4 \, b \cos\left(14 \, b x + 14 \, a\right)^{2} + 4 \, b \cos\left(12 \, b x + 12 \, a\right)^{2} + 36 \, b \cos\left(10 \, b x + 10 \, a\right)^{2} + 36 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(16 \, b x + 16 \, a\right)^{2} + 4 \, b \sin\left(14 \, b x + 14 \, a\right)^{2} + 4 \, b \sin\left(12 \, b x + 12 \, a\right)^{2} + 36 \, b \sin\left(10 \, b x + 10 \, a\right)^{2} + 36 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} + 8 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(2 \, b \cos\left(14 \, b x + 14 \, a\right) + 2 \, b \cos\left(12 \, b x + 12 \, a\right) - 6 \, b \cos\left(10 \, b x + 10 \, a\right) + 6 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(16 \, b x + 16 \, a\right) + 4 \, {\left(2 \, b \cos\left(12 \, b x + 12 \, a\right) - 6 \, b \cos\left(10 \, b x + 10 \, a\right) + 6 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(14 \, b x + 14 \, a\right) - 4 \, {\left(6 \, b \cos\left(10 \, b x + 10 \, a\right) - 6 \, b \cos\left(6 \, b x + 6 \, a\right) + 2 \, b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(12 \, b x + 12 \, a\right) - 12 \, {\left(6 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(10 \, b x + 10 \, a\right) - 12 \, {\left(2 \, b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 4 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, b \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b \sin\left(14 \, b x + 14 \, a\right) + b \sin\left(12 \, b x + 12 \, a\right) - 3 \, b \sin\left(10 \, b x + 10 \, a\right) + 3 \, b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) + 8 \, {\left(b \sin\left(12 \, b x + 12 \, a\right) - 3 \, b \sin\left(10 \, b x + 10 \, a\right) + 3 \, b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 8 \, {\left(3 \, b \sin\left(10 \, b x + 10 \, a\right) - 3 \, b \sin\left(6 \, b x + 6 \, a\right) + b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 24 \, {\left(3 \, b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 24 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"16/15*(2*(3*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(16*b*x + 16*a) - 4*(3*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(14*b*x + 14*a) - 4*(3*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(12*b*x + 12*a) + 12*(3*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(10*b*x + 10*a) - (6*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*sin(16*b*x + 16*a) + 2*(6*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*sin(14*b*x + 14*a) + 2*(6*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*sin(12*b*x + 12*a) - 6*(6*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*sin(10*b*x + 10*a))/(b*cos(16*b*x + 16*a)^2 + 4*b*cos(14*b*x + 14*a)^2 + 4*b*cos(12*b*x + 12*a)^2 + 36*b*cos(10*b*x + 10*a)^2 + 36*b*cos(6*b*x + 6*a)^2 + 4*b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(16*b*x + 16*a)^2 + 4*b*sin(14*b*x + 14*a)^2 + 4*b*sin(12*b*x + 12*a)^2 + 36*b*sin(10*b*x + 10*a)^2 + 36*b*sin(6*b*x + 6*a)^2 + 4*b*sin(4*b*x + 4*a)^2 + 8*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 - 2*(2*b*cos(14*b*x + 14*a) + 2*b*cos(12*b*x + 12*a) - 6*b*cos(10*b*x + 10*a) + 6*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(16*b*x + 16*a) + 4*(2*b*cos(12*b*x + 12*a) - 6*b*cos(10*b*x + 10*a) + 6*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(14*b*x + 14*a) - 4*(6*b*cos(10*b*x + 10*a) - 6*b*cos(6*b*x + 6*a) + 2*b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(12*b*x + 12*a) - 12*(6*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(10*b*x + 10*a) - 12*(2*b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 4*(2*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 4*b*cos(2*b*x + 2*a) - 4*(b*sin(14*b*x + 14*a) + b*sin(12*b*x + 12*a) - 3*b*sin(10*b*x + 10*a) + 3*b*sin(6*b*x + 6*a) - b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(16*b*x + 16*a) + 8*(b*sin(12*b*x + 12*a) - 3*b*sin(10*b*x + 10*a) + 3*b*sin(6*b*x + 6*a) - b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - 8*(3*b*sin(10*b*x + 10*a) - 3*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 24*(3*b*sin(6*b*x + 6*a) - b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 24*(b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
57,1,7650,0,0.719732," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(15 \, \cos\left(18 \, b x + 18 \, a\right) - 30 \, \cos\left(16 \, b x + 16 \, a\right) - 40 \, \cos\left(14 \, b x + 14 \, a\right) + 110 \, \cos\left(12 \, b x + 12 \, a\right) + 18 \, \cos\left(10 \, b x + 10 \, a\right) + 110 \, \cos\left(8 \, b x + 8 \, a\right) - 40 \, \cos\left(6 \, b x + 6 \, a\right) - 30 \, \cos\left(4 \, b x + 4 \, a\right) + 15 \, \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(20 \, b x + 20 \, a\right) + 4 \, {\left(15 \, \cos\left(16 \, b x + 16 \, a\right) + 200 \, \cos\left(14 \, b x + 14 \, a\right) - 190 \, \cos\left(12 \, b x + 12 \, a\right) - 216 \, \cos\left(10 \, b x + 10 \, a\right) - 190 \, \cos\left(8 \, b x + 8 \, a\right) + 200 \, \cos\left(6 \, b x + 6 \, a\right) + 15 \, \cos\left(4 \, b x + 4 \, a\right) - 60 \, \cos\left(2 \, b x + 2 \, a\right) + 15\right)} \cos\left(18 \, b x + 18 \, a\right) - 120 \, \cos\left(18 \, b x + 18 \, a\right)^{2} - 12 \, {\left(40 \, \cos\left(14 \, b x + 14 \, a\right) + 130 \, \cos\left(12 \, b x + 12 \, a\right) - 102 \, \cos\left(10 \, b x + 10 \, a\right) + 130 \, \cos\left(8 \, b x + 8 \, a\right) + 40 \, \cos\left(6 \, b x + 6 \, a\right) - 60 \, \cos\left(4 \, b x + 4 \, a\right) - 5 \, \cos\left(2 \, b x + 2 \, a\right) + 10\right)} \cos\left(16 \, b x + 16 \, a\right) + 360 \, \cos\left(16 \, b x + 16 \, a\right)^{2} + 32 \, {\left(100 \, \cos\left(12 \, b x + 12 \, a\right) + 78 \, \cos\left(10 \, b x + 10 \, a\right) + 100 \, \cos\left(8 \, b x + 8 \, a\right) - 80 \, \cos\left(6 \, b x + 6 \, a\right) - 15 \, \cos\left(4 \, b x + 4 \, a\right) + 25 \, \cos\left(2 \, b x + 2 \, a\right) - 5\right)} \cos\left(14 \, b x + 14 \, a\right) - 1280 \, \cos\left(14 \, b x + 14 \, a\right)^{2} - 8 \, {\left(642 \, \cos\left(10 \, b x + 10 \, a\right) - 220 \, \cos\left(8 \, b x + 8 \, a\right) - 400 \, \cos\left(6 \, b x + 6 \, a\right) + 195 \, \cos\left(4 \, b x + 4 \, a\right) + 95 \, \cos\left(2 \, b x + 2 \, a\right) - 55\right)} \cos\left(12 \, b x + 12 \, a\right) + 880 \, \cos\left(12 \, b x + 12 \, a\right)^{2} - 24 \, {\left(214 \, \cos\left(8 \, b x + 8 \, a\right) - 104 \, \cos\left(6 \, b x + 6 \, a\right) - 51 \, \cos\left(4 \, b x + 4 \, a\right) + 36 \, \cos\left(2 \, b x + 2 \, a\right) - 3\right)} \cos\left(10 \, b x + 10 \, a\right) - 864 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 40 \, {\left(80 \, \cos\left(6 \, b x + 6 \, a\right) - 39 \, \cos\left(4 \, b x + 4 \, a\right) - 19 \, \cos\left(2 \, b x + 2 \, a\right) + 11\right)} \cos\left(8 \, b x + 8 \, a\right) + 880 \, \cos\left(8 \, b x + 8 \, a\right)^{2} - 160 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) - 5 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 1280 \, \cos\left(6 \, b x + 6 \, a\right)^{2} + 60 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 2\right)} \cos\left(4 \, b x + 4 \, a\right) + 360 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 120 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 15 \, {\left(2 \, {\left(2 \, \cos\left(18 \, b x + 18 \, a\right) + 3 \, \cos\left(16 \, b x + 16 \, a\right) - 8 \, \cos\left(14 \, b x + 14 \, a\right) - 2 \, \cos\left(12 \, b x + 12 \, a\right) + 12 \, \cos\left(10 \, b x + 10 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(20 \, b x + 20 \, a\right) - \cos\left(20 \, b x + 20 \, a\right)^{2} - 4 \, {\left(3 \, \cos\left(16 \, b x + 16 \, a\right) - 8 \, \cos\left(14 \, b x + 14 \, a\right) - 2 \, \cos\left(12 \, b x + 12 \, a\right) + 12 \, \cos\left(10 \, b x + 10 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(18 \, b x + 18 \, a\right) - 4 \, \cos\left(18 \, b x + 18 \, a\right)^{2} + 6 \, {\left(8 \, \cos\left(14 \, b x + 14 \, a\right) + 2 \, \cos\left(12 \, b x + 12 \, a\right) - 12 \, \cos\left(10 \, b x + 10 \, a\right) + 2 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(16 \, b x + 16 \, a\right) - 9 \, \cos\left(16 \, b x + 16 \, a\right)^{2} - 16 \, {\left(2 \, \cos\left(12 \, b x + 12 \, a\right) - 12 \, \cos\left(10 \, b x + 10 \, a\right) + 2 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(14 \, b x + 14 \, a\right) - 64 \, \cos\left(14 \, b x + 14 \, a\right)^{2} + 4 \, {\left(12 \, \cos\left(10 \, b x + 10 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - 4 \, \cos\left(12 \, b x + 12 \, a\right)^{2} + 24 \, {\left(2 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 144 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 16 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 64 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 6 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(18 \, b x + 18 \, a\right) + 3 \, \sin\left(16 \, b x + 16 \, a\right) - 8 \, \sin\left(14 \, b x + 14 \, a\right) - 2 \, \sin\left(12 \, b x + 12 \, a\right) + 12 \, \sin\left(10 \, b x + 10 \, a\right) - 2 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(20 \, b x + 20 \, a\right) - \sin\left(20 \, b x + 20 \, a\right)^{2} - 4 \, {\left(3 \, \sin\left(16 \, b x + 16 \, a\right) - 8 \, \sin\left(14 \, b x + 14 \, a\right) - 2 \, \sin\left(12 \, b x + 12 \, a\right) + 12 \, \sin\left(10 \, b x + 10 \, a\right) - 2 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(18 \, b x + 18 \, a\right) - 4 \, \sin\left(18 \, b x + 18 \, a\right)^{2} + 6 \, {\left(8 \, \sin\left(14 \, b x + 14 \, a\right) + 2 \, \sin\left(12 \, b x + 12 \, a\right) - 12 \, \sin\left(10 \, b x + 10 \, a\right) + 2 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) - 9 \, \sin\left(16 \, b x + 16 \, a\right)^{2} - 16 \, {\left(2 \, \sin\left(12 \, b x + 12 \, a\right) - 12 \, \sin\left(10 \, b x + 10 \, a\right) + 2 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 64 \, \sin\left(14 \, b x + 14 \, a\right)^{2} + 4 \, {\left(12 \, \sin\left(10 \, b x + 10 \, a\right) - 2 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 4 \, \sin\left(12 \, b x + 12 \, a\right)^{2} + 24 \, {\left(2 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 144 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(8 \, b x + 8 \, a\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 64 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 12 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) - 15 \, {\left(2 \, {\left(2 \, \cos\left(18 \, b x + 18 \, a\right) + 3 \, \cos\left(16 \, b x + 16 \, a\right) - 8 \, \cos\left(14 \, b x + 14 \, a\right) - 2 \, \cos\left(12 \, b x + 12 \, a\right) + 12 \, \cos\left(10 \, b x + 10 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(20 \, b x + 20 \, a\right) - \cos\left(20 \, b x + 20 \, a\right)^{2} - 4 \, {\left(3 \, \cos\left(16 \, b x + 16 \, a\right) - 8 \, \cos\left(14 \, b x + 14 \, a\right) - 2 \, \cos\left(12 \, b x + 12 \, a\right) + 12 \, \cos\left(10 \, b x + 10 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(18 \, b x + 18 \, a\right) - 4 \, \cos\left(18 \, b x + 18 \, a\right)^{2} + 6 \, {\left(8 \, \cos\left(14 \, b x + 14 \, a\right) + 2 \, \cos\left(12 \, b x + 12 \, a\right) - 12 \, \cos\left(10 \, b x + 10 \, a\right) + 2 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(16 \, b x + 16 \, a\right) - 9 \, \cos\left(16 \, b x + 16 \, a\right)^{2} - 16 \, {\left(2 \, \cos\left(12 \, b x + 12 \, a\right) - 12 \, \cos\left(10 \, b x + 10 \, a\right) + 2 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(14 \, b x + 14 \, a\right) - 64 \, \cos\left(14 \, b x + 14 \, a\right)^{2} + 4 \, {\left(12 \, \cos\left(10 \, b x + 10 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - 4 \, \cos\left(12 \, b x + 12 \, a\right)^{2} + 24 \, {\left(2 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 144 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 16 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 64 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 6 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(18 \, b x + 18 \, a\right) + 3 \, \sin\left(16 \, b x + 16 \, a\right) - 8 \, \sin\left(14 \, b x + 14 \, a\right) - 2 \, \sin\left(12 \, b x + 12 \, a\right) + 12 \, \sin\left(10 \, b x + 10 \, a\right) - 2 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(20 \, b x + 20 \, a\right) - \sin\left(20 \, b x + 20 \, a\right)^{2} - 4 \, {\left(3 \, \sin\left(16 \, b x + 16 \, a\right) - 8 \, \sin\left(14 \, b x + 14 \, a\right) - 2 \, \sin\left(12 \, b x + 12 \, a\right) + 12 \, \sin\left(10 \, b x + 10 \, a\right) - 2 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(18 \, b x + 18 \, a\right) - 4 \, \sin\left(18 \, b x + 18 \, a\right)^{2} + 6 \, {\left(8 \, \sin\left(14 \, b x + 14 \, a\right) + 2 \, \sin\left(12 \, b x + 12 \, a\right) - 12 \, \sin\left(10 \, b x + 10 \, a\right) + 2 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) - 9 \, \sin\left(16 \, b x + 16 \, a\right)^{2} - 16 \, {\left(2 \, \sin\left(12 \, b x + 12 \, a\right) - 12 \, \sin\left(10 \, b x + 10 \, a\right) + 2 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 64 \, \sin\left(14 \, b x + 14 \, a\right)^{2} + 4 \, {\left(12 \, \sin\left(10 \, b x + 10 \, a\right) - 2 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 4 \, \sin\left(12 \, b x + 12 \, a\right)^{2} + 24 \, {\left(2 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 144 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(8 \, b x + 8 \, a\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 64 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 12 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 15 \, {\left(2 \, {\left(2 \, \cos\left(18 \, b x + 18 \, a\right) + 3 \, \cos\left(16 \, b x + 16 \, a\right) - 8 \, \cos\left(14 \, b x + 14 \, a\right) - 2 \, \cos\left(12 \, b x + 12 \, a\right) + 12 \, \cos\left(10 \, b x + 10 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(20 \, b x + 20 \, a\right) - \cos\left(20 \, b x + 20 \, a\right)^{2} - 4 \, {\left(3 \, \cos\left(16 \, b x + 16 \, a\right) - 8 \, \cos\left(14 \, b x + 14 \, a\right) - 2 \, \cos\left(12 \, b x + 12 \, a\right) + 12 \, \cos\left(10 \, b x + 10 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(18 \, b x + 18 \, a\right) - 4 \, \cos\left(18 \, b x + 18 \, a\right)^{2} + 6 \, {\left(8 \, \cos\left(14 \, b x + 14 \, a\right) + 2 \, \cos\left(12 \, b x + 12 \, a\right) - 12 \, \cos\left(10 \, b x + 10 \, a\right) + 2 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(16 \, b x + 16 \, a\right) - 9 \, \cos\left(16 \, b x + 16 \, a\right)^{2} - 16 \, {\left(2 \, \cos\left(12 \, b x + 12 \, a\right) - 12 \, \cos\left(10 \, b x + 10 \, a\right) + 2 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(14 \, b x + 14 \, a\right) - 64 \, \cos\left(14 \, b x + 14 \, a\right)^{2} + 4 \, {\left(12 \, \cos\left(10 \, b x + 10 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - 4 \, \cos\left(12 \, b x + 12 \, a\right)^{2} + 24 \, {\left(2 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 144 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 16 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 64 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 6 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(18 \, b x + 18 \, a\right) + 3 \, \sin\left(16 \, b x + 16 \, a\right) - 8 \, \sin\left(14 \, b x + 14 \, a\right) - 2 \, \sin\left(12 \, b x + 12 \, a\right) + 12 \, \sin\left(10 \, b x + 10 \, a\right) - 2 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(20 \, b x + 20 \, a\right) - \sin\left(20 \, b x + 20 \, a\right)^{2} - 4 \, {\left(3 \, \sin\left(16 \, b x + 16 \, a\right) - 8 \, \sin\left(14 \, b x + 14 \, a\right) - 2 \, \sin\left(12 \, b x + 12 \, a\right) + 12 \, \sin\left(10 \, b x + 10 \, a\right) - 2 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(18 \, b x + 18 \, a\right) - 4 \, \sin\left(18 \, b x + 18 \, a\right)^{2} + 6 \, {\left(8 \, \sin\left(14 \, b x + 14 \, a\right) + 2 \, \sin\left(12 \, b x + 12 \, a\right) - 12 \, \sin\left(10 \, b x + 10 \, a\right) + 2 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) - 9 \, \sin\left(16 \, b x + 16 \, a\right)^{2} - 16 \, {\left(2 \, \sin\left(12 \, b x + 12 \, a\right) - 12 \, \sin\left(10 \, b x + 10 \, a\right) + 2 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 64 \, \sin\left(14 \, b x + 14 \, a\right)^{2} + 4 \, {\left(12 \, \sin\left(10 \, b x + 10 \, a\right) - 2 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 4 \, \sin\left(12 \, b x + 12 \, a\right)^{2} + 24 \, {\left(2 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 144 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(8 \, b x + 8 \, a\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 64 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 12 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(15 \, \sin\left(18 \, b x + 18 \, a\right) - 30 \, \sin\left(16 \, b x + 16 \, a\right) - 40 \, \sin\left(14 \, b x + 14 \, a\right) + 110 \, \sin\left(12 \, b x + 12 \, a\right) + 18 \, \sin\left(10 \, b x + 10 \, a\right) + 110 \, \sin\left(8 \, b x + 8 \, a\right) - 40 \, \sin\left(6 \, b x + 6 \, a\right) - 30 \, \sin\left(4 \, b x + 4 \, a\right) + 15 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(20 \, b x + 20 \, a\right) + 4 \, {\left(15 \, \sin\left(16 \, b x + 16 \, a\right) + 200 \, \sin\left(14 \, b x + 14 \, a\right) - 190 \, \sin\left(12 \, b x + 12 \, a\right) - 216 \, \sin\left(10 \, b x + 10 \, a\right) - 190 \, \sin\left(8 \, b x + 8 \, a\right) + 200 \, \sin\left(6 \, b x + 6 \, a\right) + 15 \, \sin\left(4 \, b x + 4 \, a\right) - 60 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(18 \, b x + 18 \, a\right) - 120 \, \sin\left(18 \, b x + 18 \, a\right)^{2} - 12 \, {\left(40 \, \sin\left(14 \, b x + 14 \, a\right) + 130 \, \sin\left(12 \, b x + 12 \, a\right) - 102 \, \sin\left(10 \, b x + 10 \, a\right) + 130 \, \sin\left(8 \, b x + 8 \, a\right) + 40 \, \sin\left(6 \, b x + 6 \, a\right) - 60 \, \sin\left(4 \, b x + 4 \, a\right) - 5 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) + 360 \, \sin\left(16 \, b x + 16 \, a\right)^{2} + 32 \, {\left(100 \, \sin\left(12 \, b x + 12 \, a\right) + 78 \, \sin\left(10 \, b x + 10 \, a\right) + 100 \, \sin\left(8 \, b x + 8 \, a\right) - 80 \, \sin\left(6 \, b x + 6 \, a\right) - 15 \, \sin\left(4 \, b x + 4 \, a\right) + 25 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 1280 \, \sin\left(14 \, b x + 14 \, a\right)^{2} - 8 \, {\left(642 \, \sin\left(10 \, b x + 10 \, a\right) - 220 \, \sin\left(8 \, b x + 8 \, a\right) - 400 \, \sin\left(6 \, b x + 6 \, a\right) + 195 \, \sin\left(4 \, b x + 4 \, a\right) + 95 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 880 \, \sin\left(12 \, b x + 12 \, a\right)^{2} - 24 \, {\left(214 \, \sin\left(8 \, b x + 8 \, a\right) - 104 \, \sin\left(6 \, b x + 6 \, a\right) - 51 \, \sin\left(4 \, b x + 4 \, a\right) + 36 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 864 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 40 \, {\left(80 \, \sin\left(6 \, b x + 6 \, a\right) - 39 \, \sin\left(4 \, b x + 4 \, a\right) - 19 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 880 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 160 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) - 5 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 1280 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + 360 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 60 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 120 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 60 \, \cos\left(2 \, b x + 2 \, a\right)}{96 \, {\left(b \cos\left(20 \, b x + 20 \, a\right)^{2} + 4 \, b \cos\left(18 \, b x + 18 \, a\right)^{2} + 9 \, b \cos\left(16 \, b x + 16 \, a\right)^{2} + 64 \, b \cos\left(14 \, b x + 14 \, a\right)^{2} + 4 \, b \cos\left(12 \, b x + 12 \, a\right)^{2} + 144 \, b \cos\left(10 \, b x + 10 \, a\right)^{2} + 4 \, b \cos\left(8 \, b x + 8 \, a\right)^{2} + 64 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(20 \, b x + 20 \, a\right)^{2} + 4 \, b \sin\left(18 \, b x + 18 \, a\right)^{2} + 9 \, b \sin\left(16 \, b x + 16 \, a\right)^{2} + 64 \, b \sin\left(14 \, b x + 14 \, a\right)^{2} + 4 \, b \sin\left(12 \, b x + 12 \, a\right)^{2} + 144 \, b \sin\left(10 \, b x + 10 \, a\right)^{2} + 4 \, b \sin\left(8 \, b x + 8 \, a\right)^{2} + 64 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} + 12 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(2 \, b \cos\left(18 \, b x + 18 \, a\right) + 3 \, b \cos\left(16 \, b x + 16 \, a\right) - 8 \, b \cos\left(14 \, b x + 14 \, a\right) - 2 \, b \cos\left(12 \, b x + 12 \, a\right) + 12 \, b \cos\left(10 \, b x + 10 \, a\right) - 2 \, b \cos\left(8 \, b x + 8 \, a\right) - 8 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(20 \, b x + 20 \, a\right) + 4 \, {\left(3 \, b \cos\left(16 \, b x + 16 \, a\right) - 8 \, b \cos\left(14 \, b x + 14 \, a\right) - 2 \, b \cos\left(12 \, b x + 12 \, a\right) + 12 \, b \cos\left(10 \, b x + 10 \, a\right) - 2 \, b \cos\left(8 \, b x + 8 \, a\right) - 8 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(18 \, b x + 18 \, a\right) - 6 \, {\left(8 \, b \cos\left(14 \, b x + 14 \, a\right) + 2 \, b \cos\left(12 \, b x + 12 \, a\right) - 12 \, b \cos\left(10 \, b x + 10 \, a\right) + 2 \, b \cos\left(8 \, b x + 8 \, a\right) + 8 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(16 \, b x + 16 \, a\right) + 16 \, {\left(2 \, b \cos\left(12 \, b x + 12 \, a\right) - 12 \, b \cos\left(10 \, b x + 10 \, a\right) + 2 \, b \cos\left(8 \, b x + 8 \, a\right) + 8 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(14 \, b x + 14 \, a\right) - 4 \, {\left(12 \, b \cos\left(10 \, b x + 10 \, a\right) - 2 \, b \cos\left(8 \, b x + 8 \, a\right) - 8 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(12 \, b x + 12 \, a\right) - 24 \, {\left(2 \, b \cos\left(8 \, b x + 8 \, a\right) + 8 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(10 \, b x + 10 \, a\right) + 4 \, {\left(8 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 16 \, {\left(3 \, b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 6 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(2 \, b \sin\left(18 \, b x + 18 \, a\right) + 3 \, b \sin\left(16 \, b x + 16 \, a\right) - 8 \, b \sin\left(14 \, b x + 14 \, a\right) - 2 \, b \sin\left(12 \, b x + 12 \, a\right) + 12 \, b \sin\left(10 \, b x + 10 \, a\right) - 2 \, b \sin\left(8 \, b x + 8 \, a\right) - 8 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(20 \, b x + 20 \, a\right) + 4 \, {\left(3 \, b \sin\left(16 \, b x + 16 \, a\right) - 8 \, b \sin\left(14 \, b x + 14 \, a\right) - 2 \, b \sin\left(12 \, b x + 12 \, a\right) + 12 \, b \sin\left(10 \, b x + 10 \, a\right) - 2 \, b \sin\left(8 \, b x + 8 \, a\right) - 8 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(18 \, b x + 18 \, a\right) - 6 \, {\left(8 \, b \sin\left(14 \, b x + 14 \, a\right) + 2 \, b \sin\left(12 \, b x + 12 \, a\right) - 12 \, b \sin\left(10 \, b x + 10 \, a\right) + 2 \, b \sin\left(8 \, b x + 8 \, a\right) + 8 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) + 16 \, {\left(2 \, b \sin\left(12 \, b x + 12 \, a\right) - 12 \, b \sin\left(10 \, b x + 10 \, a\right) + 2 \, b \sin\left(8 \, b x + 8 \, a\right) + 8 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 4 \, {\left(12 \, b \sin\left(10 \, b x + 10 \, a\right) - 2 \, b \sin\left(8 \, b x + 8 \, a\right) - 8 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 24 \, {\left(2 \, b \sin\left(8 \, b x + 8 \, a\right) + 8 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 4 \, {\left(8 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 16 \, {\left(3 \, b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/96*(4*(15*cos(18*b*x + 18*a) - 30*cos(16*b*x + 16*a) - 40*cos(14*b*x + 14*a) + 110*cos(12*b*x + 12*a) + 18*cos(10*b*x + 10*a) + 110*cos(8*b*x + 8*a) - 40*cos(6*b*x + 6*a) - 30*cos(4*b*x + 4*a) + 15*cos(2*b*x + 2*a))*cos(20*b*x + 20*a) + 4*(15*cos(16*b*x + 16*a) + 200*cos(14*b*x + 14*a) - 190*cos(12*b*x + 12*a) - 216*cos(10*b*x + 10*a) - 190*cos(8*b*x + 8*a) + 200*cos(6*b*x + 6*a) + 15*cos(4*b*x + 4*a) - 60*cos(2*b*x + 2*a) + 15)*cos(18*b*x + 18*a) - 120*cos(18*b*x + 18*a)^2 - 12*(40*cos(14*b*x + 14*a) + 130*cos(12*b*x + 12*a) - 102*cos(10*b*x + 10*a) + 130*cos(8*b*x + 8*a) + 40*cos(6*b*x + 6*a) - 60*cos(4*b*x + 4*a) - 5*cos(2*b*x + 2*a) + 10)*cos(16*b*x + 16*a) + 360*cos(16*b*x + 16*a)^2 + 32*(100*cos(12*b*x + 12*a) + 78*cos(10*b*x + 10*a) + 100*cos(8*b*x + 8*a) - 80*cos(6*b*x + 6*a) - 15*cos(4*b*x + 4*a) + 25*cos(2*b*x + 2*a) - 5)*cos(14*b*x + 14*a) - 1280*cos(14*b*x + 14*a)^2 - 8*(642*cos(10*b*x + 10*a) - 220*cos(8*b*x + 8*a) - 400*cos(6*b*x + 6*a) + 195*cos(4*b*x + 4*a) + 95*cos(2*b*x + 2*a) - 55)*cos(12*b*x + 12*a) + 880*cos(12*b*x + 12*a)^2 - 24*(214*cos(8*b*x + 8*a) - 104*cos(6*b*x + 6*a) - 51*cos(4*b*x + 4*a) + 36*cos(2*b*x + 2*a) - 3)*cos(10*b*x + 10*a) - 864*cos(10*b*x + 10*a)^2 + 40*(80*cos(6*b*x + 6*a) - 39*cos(4*b*x + 4*a) - 19*cos(2*b*x + 2*a) + 11)*cos(8*b*x + 8*a) + 880*cos(8*b*x + 8*a)^2 - 160*(3*cos(4*b*x + 4*a) - 5*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - 1280*cos(6*b*x + 6*a)^2 + 60*(cos(2*b*x + 2*a) - 2)*cos(4*b*x + 4*a) + 360*cos(4*b*x + 4*a)^2 - 120*cos(2*b*x + 2*a)^2 + 15*(2*(2*cos(18*b*x + 18*a) + 3*cos(16*b*x + 16*a) - 8*cos(14*b*x + 14*a) - 2*cos(12*b*x + 12*a) + 12*cos(10*b*x + 10*a) - 2*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(20*b*x + 20*a) - cos(20*b*x + 20*a)^2 - 4*(3*cos(16*b*x + 16*a) - 8*cos(14*b*x + 14*a) - 2*cos(12*b*x + 12*a) + 12*cos(10*b*x + 10*a) - 2*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(18*b*x + 18*a) - 4*cos(18*b*x + 18*a)^2 + 6*(8*cos(14*b*x + 14*a) + 2*cos(12*b*x + 12*a) - 12*cos(10*b*x + 10*a) + 2*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(16*b*x + 16*a) - 9*cos(16*b*x + 16*a)^2 - 16*(2*cos(12*b*x + 12*a) - 12*cos(10*b*x + 10*a) + 2*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(14*b*x + 14*a) - 64*cos(14*b*x + 14*a)^2 + 4*(12*cos(10*b*x + 10*a) - 2*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - 4*cos(12*b*x + 12*a)^2 + 24*(2*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) - 144*cos(10*b*x + 10*a)^2 - 4*(8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 4*cos(8*b*x + 8*a)^2 + 16*(3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 64*cos(6*b*x + 6*a)^2 - 6*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 9*cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(18*b*x + 18*a) + 3*sin(16*b*x + 16*a) - 8*sin(14*b*x + 14*a) - 2*sin(12*b*x + 12*a) + 12*sin(10*b*x + 10*a) - 2*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(20*b*x + 20*a) - sin(20*b*x + 20*a)^2 - 4*(3*sin(16*b*x + 16*a) - 8*sin(14*b*x + 14*a) - 2*sin(12*b*x + 12*a) + 12*sin(10*b*x + 10*a) - 2*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(18*b*x + 18*a) - 4*sin(18*b*x + 18*a)^2 + 6*(8*sin(14*b*x + 14*a) + 2*sin(12*b*x + 12*a) - 12*sin(10*b*x + 10*a) + 2*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(16*b*x + 16*a) - 9*sin(16*b*x + 16*a)^2 - 16*(2*sin(12*b*x + 12*a) - 12*sin(10*b*x + 10*a) + 2*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - 64*sin(14*b*x + 14*a)^2 + 4*(12*sin(10*b*x + 10*a) - 2*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 4*sin(12*b*x + 12*a)^2 + 24*(2*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 144*sin(10*b*x + 10*a)^2 - 4*(8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 4*sin(8*b*x + 8*a)^2 + 16*(3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 64*sin(6*b*x + 6*a)^2 - 9*sin(4*b*x + 4*a)^2 - 12*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2) - 15*(2*(2*cos(18*b*x + 18*a) + 3*cos(16*b*x + 16*a) - 8*cos(14*b*x + 14*a) - 2*cos(12*b*x + 12*a) + 12*cos(10*b*x + 10*a) - 2*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(20*b*x + 20*a) - cos(20*b*x + 20*a)^2 - 4*(3*cos(16*b*x + 16*a) - 8*cos(14*b*x + 14*a) - 2*cos(12*b*x + 12*a) + 12*cos(10*b*x + 10*a) - 2*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(18*b*x + 18*a) - 4*cos(18*b*x + 18*a)^2 + 6*(8*cos(14*b*x + 14*a) + 2*cos(12*b*x + 12*a) - 12*cos(10*b*x + 10*a) + 2*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(16*b*x + 16*a) - 9*cos(16*b*x + 16*a)^2 - 16*(2*cos(12*b*x + 12*a) - 12*cos(10*b*x + 10*a) + 2*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(14*b*x + 14*a) - 64*cos(14*b*x + 14*a)^2 + 4*(12*cos(10*b*x + 10*a) - 2*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - 4*cos(12*b*x + 12*a)^2 + 24*(2*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) - 144*cos(10*b*x + 10*a)^2 - 4*(8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 4*cos(8*b*x + 8*a)^2 + 16*(3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 64*cos(6*b*x + 6*a)^2 - 6*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 9*cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(18*b*x + 18*a) + 3*sin(16*b*x + 16*a) - 8*sin(14*b*x + 14*a) - 2*sin(12*b*x + 12*a) + 12*sin(10*b*x + 10*a) - 2*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(20*b*x + 20*a) - sin(20*b*x + 20*a)^2 - 4*(3*sin(16*b*x + 16*a) - 8*sin(14*b*x + 14*a) - 2*sin(12*b*x + 12*a) + 12*sin(10*b*x + 10*a) - 2*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(18*b*x + 18*a) - 4*sin(18*b*x + 18*a)^2 + 6*(8*sin(14*b*x + 14*a) + 2*sin(12*b*x + 12*a) - 12*sin(10*b*x + 10*a) + 2*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(16*b*x + 16*a) - 9*sin(16*b*x + 16*a)^2 - 16*(2*sin(12*b*x + 12*a) - 12*sin(10*b*x + 10*a) + 2*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - 64*sin(14*b*x + 14*a)^2 + 4*(12*sin(10*b*x + 10*a) - 2*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 4*sin(12*b*x + 12*a)^2 + 24*(2*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 144*sin(10*b*x + 10*a)^2 - 4*(8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 4*sin(8*b*x + 8*a)^2 + 16*(3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 64*sin(6*b*x + 6*a)^2 - 9*sin(4*b*x + 4*a)^2 - 12*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - 15*(2*(2*cos(18*b*x + 18*a) + 3*cos(16*b*x + 16*a) - 8*cos(14*b*x + 14*a) - 2*cos(12*b*x + 12*a) + 12*cos(10*b*x + 10*a) - 2*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(20*b*x + 20*a) - cos(20*b*x + 20*a)^2 - 4*(3*cos(16*b*x + 16*a) - 8*cos(14*b*x + 14*a) - 2*cos(12*b*x + 12*a) + 12*cos(10*b*x + 10*a) - 2*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(18*b*x + 18*a) - 4*cos(18*b*x + 18*a)^2 + 6*(8*cos(14*b*x + 14*a) + 2*cos(12*b*x + 12*a) - 12*cos(10*b*x + 10*a) + 2*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(16*b*x + 16*a) - 9*cos(16*b*x + 16*a)^2 - 16*(2*cos(12*b*x + 12*a) - 12*cos(10*b*x + 10*a) + 2*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(14*b*x + 14*a) - 64*cos(14*b*x + 14*a)^2 + 4*(12*cos(10*b*x + 10*a) - 2*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - 4*cos(12*b*x + 12*a)^2 + 24*(2*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) - 144*cos(10*b*x + 10*a)^2 - 4*(8*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 4*cos(8*b*x + 8*a)^2 + 16*(3*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 64*cos(6*b*x + 6*a)^2 - 6*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 9*cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(18*b*x + 18*a) + 3*sin(16*b*x + 16*a) - 8*sin(14*b*x + 14*a) - 2*sin(12*b*x + 12*a) + 12*sin(10*b*x + 10*a) - 2*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(20*b*x + 20*a) - sin(20*b*x + 20*a)^2 - 4*(3*sin(16*b*x + 16*a) - 8*sin(14*b*x + 14*a) - 2*sin(12*b*x + 12*a) + 12*sin(10*b*x + 10*a) - 2*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(18*b*x + 18*a) - 4*sin(18*b*x + 18*a)^2 + 6*(8*sin(14*b*x + 14*a) + 2*sin(12*b*x + 12*a) - 12*sin(10*b*x + 10*a) + 2*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(16*b*x + 16*a) - 9*sin(16*b*x + 16*a)^2 - 16*(2*sin(12*b*x + 12*a) - 12*sin(10*b*x + 10*a) + 2*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - 64*sin(14*b*x + 14*a)^2 + 4*(12*sin(10*b*x + 10*a) - 2*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 4*sin(12*b*x + 12*a)^2 + 24*(2*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 144*sin(10*b*x + 10*a)^2 - 4*(8*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 4*sin(8*b*x + 8*a)^2 + 16*(3*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 64*sin(6*b*x + 6*a)^2 - 9*sin(4*b*x + 4*a)^2 - 12*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(15*sin(18*b*x + 18*a) - 30*sin(16*b*x + 16*a) - 40*sin(14*b*x + 14*a) + 110*sin(12*b*x + 12*a) + 18*sin(10*b*x + 10*a) + 110*sin(8*b*x + 8*a) - 40*sin(6*b*x + 6*a) - 30*sin(4*b*x + 4*a) + 15*sin(2*b*x + 2*a))*sin(20*b*x + 20*a) + 4*(15*sin(16*b*x + 16*a) + 200*sin(14*b*x + 14*a) - 190*sin(12*b*x + 12*a) - 216*sin(10*b*x + 10*a) - 190*sin(8*b*x + 8*a) + 200*sin(6*b*x + 6*a) + 15*sin(4*b*x + 4*a) - 60*sin(2*b*x + 2*a))*sin(18*b*x + 18*a) - 120*sin(18*b*x + 18*a)^2 - 12*(40*sin(14*b*x + 14*a) + 130*sin(12*b*x + 12*a) - 102*sin(10*b*x + 10*a) + 130*sin(8*b*x + 8*a) + 40*sin(6*b*x + 6*a) - 60*sin(4*b*x + 4*a) - 5*sin(2*b*x + 2*a))*sin(16*b*x + 16*a) + 360*sin(16*b*x + 16*a)^2 + 32*(100*sin(12*b*x + 12*a) + 78*sin(10*b*x + 10*a) + 100*sin(8*b*x + 8*a) - 80*sin(6*b*x + 6*a) - 15*sin(4*b*x + 4*a) + 25*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - 1280*sin(14*b*x + 14*a)^2 - 8*(642*sin(10*b*x + 10*a) - 220*sin(8*b*x + 8*a) - 400*sin(6*b*x + 6*a) + 195*sin(4*b*x + 4*a) + 95*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + 880*sin(12*b*x + 12*a)^2 - 24*(214*sin(8*b*x + 8*a) - 104*sin(6*b*x + 6*a) - 51*sin(4*b*x + 4*a) + 36*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 864*sin(10*b*x + 10*a)^2 + 40*(80*sin(6*b*x + 6*a) - 39*sin(4*b*x + 4*a) - 19*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 880*sin(8*b*x + 8*a)^2 - 160*(3*sin(4*b*x + 4*a) - 5*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 1280*sin(6*b*x + 6*a)^2 + 360*sin(4*b*x + 4*a)^2 + 60*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 120*sin(2*b*x + 2*a)^2 + 60*cos(2*b*x + 2*a))/(b*cos(20*b*x + 20*a)^2 + 4*b*cos(18*b*x + 18*a)^2 + 9*b*cos(16*b*x + 16*a)^2 + 64*b*cos(14*b*x + 14*a)^2 + 4*b*cos(12*b*x + 12*a)^2 + 144*b*cos(10*b*x + 10*a)^2 + 4*b*cos(8*b*x + 8*a)^2 + 64*b*cos(6*b*x + 6*a)^2 + 9*b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(20*b*x + 20*a)^2 + 4*b*sin(18*b*x + 18*a)^2 + 9*b*sin(16*b*x + 16*a)^2 + 64*b*sin(14*b*x + 14*a)^2 + 4*b*sin(12*b*x + 12*a)^2 + 144*b*sin(10*b*x + 10*a)^2 + 4*b*sin(8*b*x + 8*a)^2 + 64*b*sin(6*b*x + 6*a)^2 + 9*b*sin(4*b*x + 4*a)^2 + 12*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 - 2*(2*b*cos(18*b*x + 18*a) + 3*b*cos(16*b*x + 16*a) - 8*b*cos(14*b*x + 14*a) - 2*b*cos(12*b*x + 12*a) + 12*b*cos(10*b*x + 10*a) - 2*b*cos(8*b*x + 8*a) - 8*b*cos(6*b*x + 6*a) + 3*b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(20*b*x + 20*a) + 4*(3*b*cos(16*b*x + 16*a) - 8*b*cos(14*b*x + 14*a) - 2*b*cos(12*b*x + 12*a) + 12*b*cos(10*b*x + 10*a) - 2*b*cos(8*b*x + 8*a) - 8*b*cos(6*b*x + 6*a) + 3*b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(18*b*x + 18*a) - 6*(8*b*cos(14*b*x + 14*a) + 2*b*cos(12*b*x + 12*a) - 12*b*cos(10*b*x + 10*a) + 2*b*cos(8*b*x + 8*a) + 8*b*cos(6*b*x + 6*a) - 3*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(16*b*x + 16*a) + 16*(2*b*cos(12*b*x + 12*a) - 12*b*cos(10*b*x + 10*a) + 2*b*cos(8*b*x + 8*a) + 8*b*cos(6*b*x + 6*a) - 3*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(14*b*x + 14*a) - 4*(12*b*cos(10*b*x + 10*a) - 2*b*cos(8*b*x + 8*a) - 8*b*cos(6*b*x + 6*a) + 3*b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(12*b*x + 12*a) - 24*(2*b*cos(8*b*x + 8*a) + 8*b*cos(6*b*x + 6*a) - 3*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(10*b*x + 10*a) + 4*(8*b*cos(6*b*x + 6*a) - 3*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 16*(3*b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 6*(2*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 4*b*cos(2*b*x + 2*a) - 2*(2*b*sin(18*b*x + 18*a) + 3*b*sin(16*b*x + 16*a) - 8*b*sin(14*b*x + 14*a) - 2*b*sin(12*b*x + 12*a) + 12*b*sin(10*b*x + 10*a) - 2*b*sin(8*b*x + 8*a) - 8*b*sin(6*b*x + 6*a) + 3*b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(20*b*x + 20*a) + 4*(3*b*sin(16*b*x + 16*a) - 8*b*sin(14*b*x + 14*a) - 2*b*sin(12*b*x + 12*a) + 12*b*sin(10*b*x + 10*a) - 2*b*sin(8*b*x + 8*a) - 8*b*sin(6*b*x + 6*a) + 3*b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(18*b*x + 18*a) - 6*(8*b*sin(14*b*x + 14*a) + 2*b*sin(12*b*x + 12*a) - 12*b*sin(10*b*x + 10*a) + 2*b*sin(8*b*x + 8*a) + 8*b*sin(6*b*x + 6*a) - 3*b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(16*b*x + 16*a) + 16*(2*b*sin(12*b*x + 12*a) - 12*b*sin(10*b*x + 10*a) + 2*b*sin(8*b*x + 8*a) + 8*b*sin(6*b*x + 6*a) - 3*b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - 4*(12*b*sin(10*b*x + 10*a) - 2*b*sin(8*b*x + 8*a) - 8*b*sin(6*b*x + 6*a) + 3*b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 24*(2*b*sin(8*b*x + 8*a) + 8*b*sin(6*b*x + 6*a) - 3*b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 4*(8*b*sin(6*b*x + 6*a) - 3*b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 16*(3*b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
58,1,2710,0,0.478731," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^6,x, algorithm=""maxima"")","-\frac{32 \, {\left({\left(20 \, \sin\left(10 \, b x + 10 \, a\right) - 5 \, \sin\left(8 \, b x + 8 \, a\right) - 10 \, \sin\left(6 \, b x + 6 \, a\right) + 4 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(24 \, b x + 24 \, a\right) - 2 \, {\left(20 \, \sin\left(10 \, b x + 10 \, a\right) - 5 \, \sin\left(8 \, b x + 8 \, a\right) - 10 \, \sin\left(6 \, b x + 6 \, a\right) + 4 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(22 \, b x + 22 \, a\right) - 4 \, {\left(20 \, \sin\left(10 \, b x + 10 \, a\right) - 5 \, \sin\left(8 \, b x + 8 \, a\right) - 10 \, \sin\left(6 \, b x + 6 \, a\right) + 4 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(20 \, b x + 20 \, a\right) + 10 \, {\left(20 \, \sin\left(10 \, b x + 10 \, a\right) - 5 \, \sin\left(8 \, b x + 8 \, a\right) - 10 \, \sin\left(6 \, b x + 6 \, a\right) + 4 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(18 \, b x + 18 \, a\right) + 5 \, {\left(20 \, \sin\left(10 \, b x + 10 \, a\right) - 5 \, \sin\left(8 \, b x + 8 \, a\right) - 10 \, \sin\left(6 \, b x + 6 \, a\right) + 4 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(16 \, b x + 16 \, a\right) - 20 \, {\left(20 \, \sin\left(10 \, b x + 10 \, a\right) - 5 \, \sin\left(8 \, b x + 8 \, a\right) - 10 \, \sin\left(6 \, b x + 6 \, a\right) + 4 \, \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(14 \, b x + 14 \, a\right) - {\left(20 \, \cos\left(10 \, b x + 10 \, a\right) - 5 \, \cos\left(8 \, b x + 8 \, a\right) - 10 \, \cos\left(6 \, b x + 6 \, a\right) + 4 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(24 \, b x + 24 \, a\right) + 2 \, {\left(20 \, \cos\left(10 \, b x + 10 \, a\right) - 5 \, \cos\left(8 \, b x + 8 \, a\right) - 10 \, \cos\left(6 \, b x + 6 \, a\right) + 4 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(22 \, b x + 22 \, a\right) + 4 \, {\left(20 \, \cos\left(10 \, b x + 10 \, a\right) - 5 \, \cos\left(8 \, b x + 8 \, a\right) - 10 \, \cos\left(6 \, b x + 6 \, a\right) + 4 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(20 \, b x + 20 \, a\right) - 10 \, {\left(20 \, \cos\left(10 \, b x + 10 \, a\right) - 5 \, \cos\left(8 \, b x + 8 \, a\right) - 10 \, \cos\left(6 \, b x + 6 \, a\right) + 4 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(18 \, b x + 18 \, a\right) - 5 \, {\left(20 \, \cos\left(10 \, b x + 10 \, a\right) - 5 \, \cos\left(8 \, b x + 8 \, a\right) - 10 \, \cos\left(6 \, b x + 6 \, a\right) + 4 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(16 \, b x + 16 \, a\right) + 20 \, {\left(20 \, \cos\left(10 \, b x + 10 \, a\right) - 5 \, \cos\left(8 \, b x + 8 \, a\right) - 10 \, \cos\left(6 \, b x + 6 \, a\right) + 4 \, \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(14 \, b x + 14 \, a\right)\right)}}{35 \, {\left(b \cos\left(24 \, b x + 24 \, a\right)^{2} + 4 \, b \cos\left(22 \, b x + 22 \, a\right)^{2} + 16 \, b \cos\left(20 \, b x + 20 \, a\right)^{2} + 100 \, b \cos\left(18 \, b x + 18 \, a\right)^{2} + 25 \, b \cos\left(16 \, b x + 16 \, a\right)^{2} + 400 \, b \cos\left(14 \, b x + 14 \, a\right)^{2} + 400 \, b \cos\left(10 \, b x + 10 \, a\right)^{2} + 25 \, b \cos\left(8 \, b x + 8 \, a\right)^{2} + 100 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 16 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(24 \, b x + 24 \, a\right)^{2} + 4 \, b \sin\left(22 \, b x + 22 \, a\right)^{2} + 16 \, b \sin\left(20 \, b x + 20 \, a\right)^{2} + 100 \, b \sin\left(18 \, b x + 18 \, a\right)^{2} + 25 \, b \sin\left(16 \, b x + 16 \, a\right)^{2} + 400 \, b \sin\left(14 \, b x + 14 \, a\right)^{2} + 400 \, b \sin\left(10 \, b x + 10 \, a\right)^{2} + 25 \, b \sin\left(8 \, b x + 8 \, a\right)^{2} + 100 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 16 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} + 16 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(2 \, b \cos\left(22 \, b x + 22 \, a\right) + 4 \, b \cos\left(20 \, b x + 20 \, a\right) - 10 \, b \cos\left(18 \, b x + 18 \, a\right) - 5 \, b \cos\left(16 \, b x + 16 \, a\right) + 20 \, b \cos\left(14 \, b x + 14 \, a\right) - 20 \, b \cos\left(10 \, b x + 10 \, a\right) + 5 \, b \cos\left(8 \, b x + 8 \, a\right) + 10 \, b \cos\left(6 \, b x + 6 \, a\right) - 4 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(24 \, b x + 24 \, a\right) + 4 \, {\left(4 \, b \cos\left(20 \, b x + 20 \, a\right) - 10 \, b \cos\left(18 \, b x + 18 \, a\right) - 5 \, b \cos\left(16 \, b x + 16 \, a\right) + 20 \, b \cos\left(14 \, b x + 14 \, a\right) - 20 \, b \cos\left(10 \, b x + 10 \, a\right) + 5 \, b \cos\left(8 \, b x + 8 \, a\right) + 10 \, b \cos\left(6 \, b x + 6 \, a\right) - 4 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(22 \, b x + 22 \, a\right) - 8 \, {\left(10 \, b \cos\left(18 \, b x + 18 \, a\right) + 5 \, b \cos\left(16 \, b x + 16 \, a\right) - 20 \, b \cos\left(14 \, b x + 14 \, a\right) + 20 \, b \cos\left(10 \, b x + 10 \, a\right) - 5 \, b \cos\left(8 \, b x + 8 \, a\right) - 10 \, b \cos\left(6 \, b x + 6 \, a\right) + 4 \, b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(20 \, b x + 20 \, a\right) + 20 \, {\left(5 \, b \cos\left(16 \, b x + 16 \, a\right) - 20 \, b \cos\left(14 \, b x + 14 \, a\right) + 20 \, b \cos\left(10 \, b x + 10 \, a\right) - 5 \, b \cos\left(8 \, b x + 8 \, a\right) - 10 \, b \cos\left(6 \, b x + 6 \, a\right) + 4 \, b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(18 \, b x + 18 \, a\right) - 10 \, {\left(20 \, b \cos\left(14 \, b x + 14 \, a\right) - 20 \, b \cos\left(10 \, b x + 10 \, a\right) + 5 \, b \cos\left(8 \, b x + 8 \, a\right) + 10 \, b \cos\left(6 \, b x + 6 \, a\right) - 4 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(16 \, b x + 16 \, a\right) - 40 \, {\left(20 \, b \cos\left(10 \, b x + 10 \, a\right) - 5 \, b \cos\left(8 \, b x + 8 \, a\right) - 10 \, b \cos\left(6 \, b x + 6 \, a\right) + 4 \, b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(14 \, b x + 14 \, a\right) - 40 \, {\left(5 \, b \cos\left(8 \, b x + 8 \, a\right) + 10 \, b \cos\left(6 \, b x + 6 \, a\right) - 4 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(10 \, b x + 10 \, a\right) + 10 \, {\left(10 \, b \cos\left(6 \, b x + 6 \, a\right) - 4 \, b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 20 \, {\left(4 \, b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 8 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(2 \, b \sin\left(22 \, b x + 22 \, a\right) + 4 \, b \sin\left(20 \, b x + 20 \, a\right) - 10 \, b \sin\left(18 \, b x + 18 \, a\right) - 5 \, b \sin\left(16 \, b x + 16 \, a\right) + 20 \, b \sin\left(14 \, b x + 14 \, a\right) - 20 \, b \sin\left(10 \, b x + 10 \, a\right) + 5 \, b \sin\left(8 \, b x + 8 \, a\right) + 10 \, b \sin\left(6 \, b x + 6 \, a\right) - 4 \, b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(24 \, b x + 24 \, a\right) + 4 \, {\left(4 \, b \sin\left(20 \, b x + 20 \, a\right) - 10 \, b \sin\left(18 \, b x + 18 \, a\right) - 5 \, b \sin\left(16 \, b x + 16 \, a\right) + 20 \, b \sin\left(14 \, b x + 14 \, a\right) - 20 \, b \sin\left(10 \, b x + 10 \, a\right) + 5 \, b \sin\left(8 \, b x + 8 \, a\right) + 10 \, b \sin\left(6 \, b x + 6 \, a\right) - 4 \, b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(22 \, b x + 22 \, a\right) - 8 \, {\left(10 \, b \sin\left(18 \, b x + 18 \, a\right) + 5 \, b \sin\left(16 \, b x + 16 \, a\right) - 20 \, b \sin\left(14 \, b x + 14 \, a\right) + 20 \, b \sin\left(10 \, b x + 10 \, a\right) - 5 \, b \sin\left(8 \, b x + 8 \, a\right) - 10 \, b \sin\left(6 \, b x + 6 \, a\right) + 4 \, b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(20 \, b x + 20 \, a\right) + 20 \, {\left(5 \, b \sin\left(16 \, b x + 16 \, a\right) - 20 \, b \sin\left(14 \, b x + 14 \, a\right) + 20 \, b \sin\left(10 \, b x + 10 \, a\right) - 5 \, b \sin\left(8 \, b x + 8 \, a\right) - 10 \, b \sin\left(6 \, b x + 6 \, a\right) + 4 \, b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(18 \, b x + 18 \, a\right) - 10 \, {\left(20 \, b \sin\left(14 \, b x + 14 \, a\right) - 20 \, b \sin\left(10 \, b x + 10 \, a\right) + 5 \, b \sin\left(8 \, b x + 8 \, a\right) + 10 \, b \sin\left(6 \, b x + 6 \, a\right) - 4 \, b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) - 40 \, {\left(20 \, b \sin\left(10 \, b x + 10 \, a\right) - 5 \, b \sin\left(8 \, b x + 8 \, a\right) - 10 \, b \sin\left(6 \, b x + 6 \, a\right) + 4 \, b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 40 \, {\left(5 \, b \sin\left(8 \, b x + 8 \, a\right) + 10 \, b \sin\left(6 \, b x + 6 \, a\right) - 4 \, b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 20 \, {\left(5 \, b \sin\left(6 \, b x + 6 \, a\right) - 2 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 40 \, {\left(2 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"-32/35*((20*sin(10*b*x + 10*a) - 5*sin(8*b*x + 8*a) - 10*sin(6*b*x + 6*a) + 4*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*cos(24*b*x + 24*a) - 2*(20*sin(10*b*x + 10*a) - 5*sin(8*b*x + 8*a) - 10*sin(6*b*x + 6*a) + 4*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*cos(22*b*x + 22*a) - 4*(20*sin(10*b*x + 10*a) - 5*sin(8*b*x + 8*a) - 10*sin(6*b*x + 6*a) + 4*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*cos(20*b*x + 20*a) + 10*(20*sin(10*b*x + 10*a) - 5*sin(8*b*x + 8*a) - 10*sin(6*b*x + 6*a) + 4*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*cos(18*b*x + 18*a) + 5*(20*sin(10*b*x + 10*a) - 5*sin(8*b*x + 8*a) - 10*sin(6*b*x + 6*a) + 4*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*cos(16*b*x + 16*a) - 20*(20*sin(10*b*x + 10*a) - 5*sin(8*b*x + 8*a) - 10*sin(6*b*x + 6*a) + 4*sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*cos(14*b*x + 14*a) - (20*cos(10*b*x + 10*a) - 5*cos(8*b*x + 8*a) - 10*cos(6*b*x + 6*a) + 4*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*sin(24*b*x + 24*a) + 2*(20*cos(10*b*x + 10*a) - 5*cos(8*b*x + 8*a) - 10*cos(6*b*x + 6*a) + 4*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*sin(22*b*x + 22*a) + 4*(20*cos(10*b*x + 10*a) - 5*cos(8*b*x + 8*a) - 10*cos(6*b*x + 6*a) + 4*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*sin(20*b*x + 20*a) - 10*(20*cos(10*b*x + 10*a) - 5*cos(8*b*x + 8*a) - 10*cos(6*b*x + 6*a) + 4*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*sin(18*b*x + 18*a) - 5*(20*cos(10*b*x + 10*a) - 5*cos(8*b*x + 8*a) - 10*cos(6*b*x + 6*a) + 4*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*sin(16*b*x + 16*a) + 20*(20*cos(10*b*x + 10*a) - 5*cos(8*b*x + 8*a) - 10*cos(6*b*x + 6*a) + 4*cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*sin(14*b*x + 14*a))/(b*cos(24*b*x + 24*a)^2 + 4*b*cos(22*b*x + 22*a)^2 + 16*b*cos(20*b*x + 20*a)^2 + 100*b*cos(18*b*x + 18*a)^2 + 25*b*cos(16*b*x + 16*a)^2 + 400*b*cos(14*b*x + 14*a)^2 + 400*b*cos(10*b*x + 10*a)^2 + 25*b*cos(8*b*x + 8*a)^2 + 100*b*cos(6*b*x + 6*a)^2 + 16*b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(24*b*x + 24*a)^2 + 4*b*sin(22*b*x + 22*a)^2 + 16*b*sin(20*b*x + 20*a)^2 + 100*b*sin(18*b*x + 18*a)^2 + 25*b*sin(16*b*x + 16*a)^2 + 400*b*sin(14*b*x + 14*a)^2 + 400*b*sin(10*b*x + 10*a)^2 + 25*b*sin(8*b*x + 8*a)^2 + 100*b*sin(6*b*x + 6*a)^2 + 16*b*sin(4*b*x + 4*a)^2 + 16*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 - 2*(2*b*cos(22*b*x + 22*a) + 4*b*cos(20*b*x + 20*a) - 10*b*cos(18*b*x + 18*a) - 5*b*cos(16*b*x + 16*a) + 20*b*cos(14*b*x + 14*a) - 20*b*cos(10*b*x + 10*a) + 5*b*cos(8*b*x + 8*a) + 10*b*cos(6*b*x + 6*a) - 4*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(24*b*x + 24*a) + 4*(4*b*cos(20*b*x + 20*a) - 10*b*cos(18*b*x + 18*a) - 5*b*cos(16*b*x + 16*a) + 20*b*cos(14*b*x + 14*a) - 20*b*cos(10*b*x + 10*a) + 5*b*cos(8*b*x + 8*a) + 10*b*cos(6*b*x + 6*a) - 4*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(22*b*x + 22*a) - 8*(10*b*cos(18*b*x + 18*a) + 5*b*cos(16*b*x + 16*a) - 20*b*cos(14*b*x + 14*a) + 20*b*cos(10*b*x + 10*a) - 5*b*cos(8*b*x + 8*a) - 10*b*cos(6*b*x + 6*a) + 4*b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(20*b*x + 20*a) + 20*(5*b*cos(16*b*x + 16*a) - 20*b*cos(14*b*x + 14*a) + 20*b*cos(10*b*x + 10*a) - 5*b*cos(8*b*x + 8*a) - 10*b*cos(6*b*x + 6*a) + 4*b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(18*b*x + 18*a) - 10*(20*b*cos(14*b*x + 14*a) - 20*b*cos(10*b*x + 10*a) + 5*b*cos(8*b*x + 8*a) + 10*b*cos(6*b*x + 6*a) - 4*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(16*b*x + 16*a) - 40*(20*b*cos(10*b*x + 10*a) - 5*b*cos(8*b*x + 8*a) - 10*b*cos(6*b*x + 6*a) + 4*b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(14*b*x + 14*a) - 40*(5*b*cos(8*b*x + 8*a) + 10*b*cos(6*b*x + 6*a) - 4*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(10*b*x + 10*a) + 10*(10*b*cos(6*b*x + 6*a) - 4*b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 20*(4*b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 8*(2*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 4*b*cos(2*b*x + 2*a) - 2*(2*b*sin(22*b*x + 22*a) + 4*b*sin(20*b*x + 20*a) - 10*b*sin(18*b*x + 18*a) - 5*b*sin(16*b*x + 16*a) + 20*b*sin(14*b*x + 14*a) - 20*b*sin(10*b*x + 10*a) + 5*b*sin(8*b*x + 8*a) + 10*b*sin(6*b*x + 6*a) - 4*b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(24*b*x + 24*a) + 4*(4*b*sin(20*b*x + 20*a) - 10*b*sin(18*b*x + 18*a) - 5*b*sin(16*b*x + 16*a) + 20*b*sin(14*b*x + 14*a) - 20*b*sin(10*b*x + 10*a) + 5*b*sin(8*b*x + 8*a) + 10*b*sin(6*b*x + 6*a) - 4*b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(22*b*x + 22*a) - 8*(10*b*sin(18*b*x + 18*a) + 5*b*sin(16*b*x + 16*a) - 20*b*sin(14*b*x + 14*a) + 20*b*sin(10*b*x + 10*a) - 5*b*sin(8*b*x + 8*a) - 10*b*sin(6*b*x + 6*a) + 4*b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(20*b*x + 20*a) + 20*(5*b*sin(16*b*x + 16*a) - 20*b*sin(14*b*x + 14*a) + 20*b*sin(10*b*x + 10*a) - 5*b*sin(8*b*x + 8*a) - 10*b*sin(6*b*x + 6*a) + 4*b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(18*b*x + 18*a) - 10*(20*b*sin(14*b*x + 14*a) - 20*b*sin(10*b*x + 10*a) + 5*b*sin(8*b*x + 8*a) + 10*b*sin(6*b*x + 6*a) - 4*b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(16*b*x + 16*a) - 40*(20*b*sin(10*b*x + 10*a) - 5*b*sin(8*b*x + 8*a) - 10*b*sin(6*b*x + 6*a) + 4*b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - 40*(5*b*sin(8*b*x + 8*a) + 10*b*sin(6*b*x + 6*a) - 4*b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 20*(5*b*sin(6*b*x + 6*a) - 2*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 40*(2*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
59,1,91,0,0.347206," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^10,x, algorithm=""maxima"")","\frac{715 \, \cos\left(17 \, b x + 17 \, a\right) + 2431 \, \cos\left(15 \, b x + 15 \, a\right) - 3740 \, \cos\left(13 \, b x + 13 \, a\right) - 22100 \, \cos\left(11 \, b x + 11 \, a\right) + 97240 \, \cos\left(7 \, b x + 7 \, a\right) + 68068 \, \cos\left(5 \, b x + 5 \, a\right) - 340340 \, \cos\left(3 \, b x + 3 \, a\right) - 850850 \, \cos\left(b x + a\right)}{777920 \, b}"," ",0,"1/777920*(715*cos(17*b*x + 17*a) + 2431*cos(15*b*x + 15*a) - 3740*cos(13*b*x + 13*a) - 22100*cos(11*b*x + 11*a) + 97240*cos(7*b*x + 7*a) + 68068*cos(5*b*x + 5*a) - 340340*cos(3*b*x + 3*a) - 850850*cos(b*x + a))/b","A",0
60,1,91,0,0.832767," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^9,x, algorithm=""maxima"")","-\frac{3003 \, \sin\left(15 \, b x + 15 \, a\right) + 10395 \, \sin\left(13 \, b x + 13 \, a\right) - 12285 \, \sin\left(11 \, b x + 11 \, a\right) - 85085 \, \sin\left(9 \, b x + 9 \, a\right) - 19305 \, \sin\left(7 \, b x + 7 \, a\right) + 351351 \, \sin\left(5 \, b x + 5 \, a\right) + 375375 \, \sin\left(3 \, b x + 3 \, a\right) - 2027025 \, \sin\left(b x + a\right)}{1441440 \, b}"," ",0,"-1/1441440*(3003*sin(15*b*x + 15*a) + 10395*sin(13*b*x + 13*a) - 12285*sin(11*b*x + 11*a) - 85085*sin(9*b*x + 9*a) - 19305*sin(7*b*x + 7*a) + 351351*sin(5*b*x + 5*a) + 375375*sin(3*b*x + 3*a) - 2027025*sin(b*x + a))/b","A",0
61,1,80,0,1.018394," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^8,x, algorithm=""maxima"")","-\frac{99 \, \cos\left(13 \, b x + 13 \, a\right) + 351 \, \cos\left(11 \, b x + 11 \, a\right) - 286 \, \cos\left(9 \, b x + 9 \, a\right) - 2574 \, \cos\left(7 \, b x + 7 \, a\right) - 1287 \, \cos\left(5 \, b x + 5 \, a\right) + 10725 \, \cos\left(3 \, b x + 3 \, a\right) + 25740 \, \cos\left(b x + a\right)}{20592 \, b}"," ",0,"-1/20592*(99*cos(13*b*x + 13*a) + 351*cos(11*b*x + 11*a) - 286*cos(9*b*x + 9*a) - 2574*cos(7*b*x + 7*a) - 1287*cos(5*b*x + 5*a) + 10725*cos(3*b*x + 3*a) + 25740*cos(b*x + a))/b","A",0
62,1,69,0,0.753804," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^7,x, algorithm=""maxima"")","\frac{105 \, \sin\left(11 \, b x + 11 \, a\right) + 385 \, \sin\left(9 \, b x + 9 \, a\right) - 165 \, \sin\left(7 \, b x + 7 \, a\right) - 2541 \, \sin\left(5 \, b x + 5 \, a\right) - 2310 \, \sin\left(3 \, b x + 3 \, a\right) + 16170 \, \sin\left(b x + a\right)}{9240 \, b}"," ",0,"1/9240*(105*sin(11*b*x + 11*a) + 385*sin(9*b*x + 9*a) - 165*sin(7*b*x + 7*a) - 2541*sin(5*b*x + 5*a) - 2310*sin(3*b*x + 3*a) + 16170*sin(b*x + a))/b","A",0
63,1,47,0,1.046087," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^6,x, algorithm=""maxima"")","\frac{7 \, \cos\left(9 \, b x + 9 \, a\right) + 27 \, \cos\left(7 \, b x + 7 \, a\right) - 168 \, \cos\left(3 \, b x + 3 \, a\right) - 378 \, \cos\left(b x + a\right)}{252 \, b}"," ",0,"1/252*(7*cos(9*b*x + 9*a) + 27*cos(7*b*x + 7*a) - 168*cos(3*b*x + 3*a) - 378*cos(b*x + a))/b","A",0
64,1,47,0,0.447171," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","-\frac{15 \, \sin\left(7 \, b x + 7 \, a\right) + 63 \, \sin\left(5 \, b x + 5 \, a\right) + 35 \, \sin\left(3 \, b x + 3 \, a\right) - 525 \, \sin\left(b x + a\right)}{210 \, b}"," ",0,"-1/210*(15*sin(7*b*x + 7*a) + 63*sin(5*b*x + 5*a) + 35*sin(3*b*x + 3*a) - 525*sin(b*x + a))/b","A",0
65,1,34,0,0.818766," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","-\frac{\cos\left(5 \, b x + 5 \, a\right) + 5 \, \cos\left(3 \, b x + 3 \, a\right) + 10 \, \cos\left(b x + a\right)}{5 \, b}"," ",0,"-1/5*(cos(5*b*x + 5*a) + 5*cos(3*b*x + 3*a) + 10*cos(b*x + a))/b","B",0
66,1,23,0,1.874550," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\sin\left(3 \, b x + 3 \, a\right) + 9 \, \sin\left(b x + a\right)\right)}}{3 \, b}"," ",0,"2/3*(sin(3*b*x + 3*a) + 9*sin(b*x + a))/b","A",0
67,1,92,0,0.991642," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, \cos\left(b x + a\right) - \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)\right)}}{b}"," ",0,"2*(2*cos(b*x + a) - log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2))/b","B",0
68,1,84,0,0.349101," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{4 \, {\left(\cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)}}{b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b}"," ",0,"-4*(cos(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))/(b*cos(2*b*x + 2*a)^2 + b*sin(2*b*x + 2*a)^2 - 2*b*cos(2*b*x + 2*a) + b)","B",0
69,1,834,0,1.144950," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a),x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \sin\left(5 \, b x + 5 \, a\right) - 10 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 36 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(5 \, b x + 5 \, a\right) + 12 \, {\left(10 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - \cos\left(6 \, b x + 6 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 6 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - \sin\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 18 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(3 \, \cos\left(5 \, b x + 5 \, a\right) - 10 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 12 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(5 \, b x + 5 \, a\right) - 12 \, {\left(10 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) - 40 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 120 \, \cos\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 36 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) + 36 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 12 \, \sin\left(b x + a\right)}{12 \, {\left(b \cos\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + 9 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} - 18 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(3 \, b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left(3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, b \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/12*(4*(3*sin(5*b*x + 5*a) - 10*sin(3*b*x + 3*a) + 3*sin(b*x + a))*cos(6*b*x + 6*a) + 36*(sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(5*b*x + 5*a) + 12*(10*sin(3*b*x + 3*a) - 3*sin(b*x + a))*cos(4*b*x + 4*a) + 3*(2*(3*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - cos(6*b*x + 6*a)^2 + 6*(3*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 9*cos(4*b*x + 4*a)^2 - 9*cos(2*b*x + 2*a)^2 + 6*(sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - sin(6*b*x + 6*a)^2 - 9*sin(4*b*x + 4*a)^2 + 18*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) - 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(3*cos(5*b*x + 5*a) - 10*cos(3*b*x + 3*a) + 3*cos(b*x + a))*sin(6*b*x + 6*a) - 12*(3*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*sin(5*b*x + 5*a) - 12*(10*cos(3*b*x + 3*a) - 3*cos(b*x + a))*sin(4*b*x + 4*a) - 40*(3*cos(2*b*x + 2*a) - 1)*sin(3*b*x + 3*a) + 120*cos(3*b*x + 3*a)*sin(2*b*x + 2*a) - 36*cos(b*x + a)*sin(2*b*x + 2*a) + 36*cos(2*b*x + 2*a)*sin(b*x + a) - 12*sin(b*x + a))/(b*cos(6*b*x + 6*a)^2 + 9*b*cos(4*b*x + 4*a)^2 + 9*b*cos(2*b*x + 2*a)^2 + b*sin(6*b*x + 6*a)^2 + 9*b*sin(4*b*x + 4*a)^2 - 18*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 9*b*sin(2*b*x + 2*a)^2 - 2*(3*b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(6*b*x + 6*a) - 6*(3*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 6*b*cos(2*b*x + 2*a) - 6*(b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
70,1,2237,0,0.589846," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(15 \, \cos\left(9 \, b x + 9 \, a\right) - 40 \, \cos\left(7 \, b x + 7 \, a\right) + 18 \, \cos\left(5 \, b x + 5 \, a\right) - 40 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) - 60 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(9 \, b x + 9 \, a\right) + 12 \, {\left(40 \, \cos\left(7 \, b x + 7 \, a\right) - 18 \, \cos\left(5 \, b x + 5 \, a\right) + 40 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) - 160 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(7 \, b x + 7 \, a\right) + 8 \, {\left(18 \, \cos\left(5 \, b x + 5 \, a\right) - 40 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 72 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(5 \, b x + 5 \, a\right) - 40 \, {\left(8 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 160 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 180 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - \cos\left(10 \, b x + 10 \, a\right)^{2} + 6 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 9 \, \cos\left(8 \, b x + 8 \, a\right)^{2} - 4 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - \sin\left(10 \, b x + 10 \, a\right)^{2} + 6 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) + 2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 9 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 4 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 12 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - \cos\left(10 \, b x + 10 \, a\right)^{2} + 6 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 9 \, \cos\left(8 \, b x + 8 \, a\right)^{2} - 4 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - \sin\left(10 \, b x + 10 \, a\right)^{2} + 6 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) + 2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 9 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 4 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 12 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(15 \, \sin\left(9 \, b x + 9 \, a\right) - 40 \, \sin\left(7 \, b x + 7 \, a\right) + 18 \, \sin\left(5 \, b x + 5 \, a\right) - 40 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 60 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(9 \, b x + 9 \, a\right) + 12 \, {\left(40 \, \sin\left(7 \, b x + 7 \, a\right) - 18 \, \sin\left(5 \, b x + 5 \, a\right) + 40 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 160 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) + 2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(7 \, b x + 7 \, a\right) + 8 \, {\left(18 \, \sin\left(5 \, b x + 5 \, a\right) - 40 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 72 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(5 \, b x + 5 \, a\right) - 40 \, {\left(8 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 480 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 180 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 60 \, \cos\left(b x + a\right)}{64 \, {\left(b \cos\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + 9 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} - 12 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(3 \, b \cos\left(8 \, b x + 8 \, a\right) - 2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) + 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(10 \, b x + 10 \, a\right) - 6 \, {\left(2 \, b \cos\left(6 \, b x + 6 \, a\right) + 2 \, b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) + 4 \, {\left(2 \, b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, {\left(3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(3 \, b \sin\left(8 \, b x + 8 \, a\right) - 2 \, b \sin\left(6 \, b x + 6 \, a\right) - 2 \, b \sin\left(4 \, b x + 4 \, a\right) + 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 6 \, {\left(2 \, b \sin\left(6 \, b x + 6 \, a\right) + 2 \, b \sin\left(4 \, b x + 4 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 4 \, {\left(2 \, b \sin\left(4 \, b x + 4 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/64*(4*(15*cos(9*b*x + 9*a) - 40*cos(7*b*x + 7*a) + 18*cos(5*b*x + 5*a) - 40*cos(3*b*x + 3*a) + 15*cos(b*x + a))*cos(10*b*x + 10*a) - 60*(3*cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*cos(9*b*x + 9*a) + 12*(40*cos(7*b*x + 7*a) - 18*cos(5*b*x + 5*a) + 40*cos(3*b*x + 3*a) - 15*cos(b*x + a))*cos(8*b*x + 8*a) - 160*(2*cos(6*b*x + 6*a) + 2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(7*b*x + 7*a) + 8*(18*cos(5*b*x + 5*a) - 40*cos(3*b*x + 3*a) + 15*cos(b*x + a))*cos(6*b*x + 6*a) + 72*(2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(5*b*x + 5*a) - 40*(8*cos(3*b*x + 3*a) - 3*cos(b*x + a))*cos(4*b*x + 4*a) + 160*(3*cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a) - 180*cos(2*b*x + 2*a)*cos(b*x + a) + 15*(2*(3*cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - cos(10*b*x + 10*a)^2 + 6*(2*cos(6*b*x + 6*a) + 2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 9*cos(8*b*x + 8*a)^2 - 4*(2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - 4*cos(6*b*x + 6*a)^2 + 4*(3*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 4*cos(4*b*x + 4*a)^2 - 9*cos(2*b*x + 2*a)^2 + 2*(3*sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - sin(10*b*x + 10*a)^2 + 6*(2*sin(6*b*x + 6*a) + 2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 9*sin(8*b*x + 8*a)^2 - 4*(2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 4*sin(6*b*x + 6*a)^2 - 4*sin(4*b*x + 4*a)^2 + 12*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - 15*(2*(3*cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - cos(10*b*x + 10*a)^2 + 6*(2*cos(6*b*x + 6*a) + 2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 9*cos(8*b*x + 8*a)^2 - 4*(2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - 4*cos(6*b*x + 6*a)^2 + 4*(3*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 4*cos(4*b*x + 4*a)^2 - 9*cos(2*b*x + 2*a)^2 + 2*(3*sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - sin(10*b*x + 10*a)^2 + 6*(2*sin(6*b*x + 6*a) + 2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 9*sin(8*b*x + 8*a)^2 - 4*(2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 4*sin(6*b*x + 6*a)^2 - 4*sin(4*b*x + 4*a)^2 + 12*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(15*sin(9*b*x + 9*a) - 40*sin(7*b*x + 7*a) + 18*sin(5*b*x + 5*a) - 40*sin(3*b*x + 3*a) + 15*sin(b*x + a))*sin(10*b*x + 10*a) - 60*(3*sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(9*b*x + 9*a) + 12*(40*sin(7*b*x + 7*a) - 18*sin(5*b*x + 5*a) + 40*sin(3*b*x + 3*a) - 15*sin(b*x + a))*sin(8*b*x + 8*a) - 160*(2*sin(6*b*x + 6*a) + 2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(7*b*x + 7*a) + 8*(18*sin(5*b*x + 5*a) - 40*sin(3*b*x + 3*a) + 15*sin(b*x + a))*sin(6*b*x + 6*a) + 72*(2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(5*b*x + 5*a) - 40*(8*sin(3*b*x + 3*a) - 3*sin(b*x + a))*sin(4*b*x + 4*a) + 480*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) - 180*sin(2*b*x + 2*a)*sin(b*x + a) + 60*cos(b*x + a))/(b*cos(10*b*x + 10*a)^2 + 9*b*cos(8*b*x + 8*a)^2 + 4*b*cos(6*b*x + 6*a)^2 + 4*b*cos(4*b*x + 4*a)^2 + 9*b*cos(2*b*x + 2*a)^2 + b*sin(10*b*x + 10*a)^2 + 9*b*sin(8*b*x + 8*a)^2 + 4*b*sin(6*b*x + 6*a)^2 + 4*b*sin(4*b*x + 4*a)^2 - 12*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 9*b*sin(2*b*x + 2*a)^2 - 2*(3*b*cos(8*b*x + 8*a) - 2*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) + 3*b*cos(2*b*x + 2*a) - b)*cos(10*b*x + 10*a) - 6*(2*b*cos(6*b*x + 6*a) + 2*b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) + 4*(2*b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(6*b*x + 6*a) - 4*(3*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 6*b*cos(2*b*x + 2*a) - 2*(3*b*sin(8*b*x + 8*a) - 2*b*sin(6*b*x + 6*a) - 2*b*sin(4*b*x + 4*a) + 3*b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 6*(2*b*sin(6*b*x + 6*a) + 2*b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 4*(2*b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
71,1,3095,0,1.051629," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(105 \, \sin\left(13 \, b x + 13 \, a\right) - 350 \, \sin\left(11 \, b x + 11 \, a\right) + 231 \, \sin\left(9 \, b x + 9 \, a\right) + 412 \, \sin\left(7 \, b x + 7 \, a\right) + 231 \, \sin\left(5 \, b x + 5 \, a\right) - 350 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)\right)} \cos\left(14 \, b x + 14 \, a\right) + 420 \, {\left(3 \, \sin\left(12 \, b x + 12 \, a\right) - \sin\left(10 \, b x + 10 \, a\right) - 5 \, \sin\left(8 \, b x + 8 \, a\right) + 5 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(13 \, b x + 13 \, a\right) + 12 \, {\left(350 \, \sin\left(11 \, b x + 11 \, a\right) - 231 \, \sin\left(9 \, b x + 9 \, a\right) - 412 \, \sin\left(7 \, b x + 7 \, a\right) - 231 \, \sin\left(5 \, b x + 5 \, a\right) + 350 \, \sin\left(3 \, b x + 3 \, a\right) - 105 \, \sin\left(b x + a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) + 1400 \, {\left(\sin\left(10 \, b x + 10 \, a\right) + 5 \, \sin\left(8 \, b x + 8 \, a\right) - 5 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(11 \, b x + 11 \, a\right) + 4 \, {\left(231 \, \sin\left(9 \, b x + 9 \, a\right) + 412 \, \sin\left(7 \, b x + 7 \, a\right) + 231 \, \sin\left(5 \, b x + 5 \, a\right) - 350 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) - 924 \, {\left(5 \, \sin\left(8 \, b x + 8 \, a\right) - 5 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(9 \, b x + 9 \, a\right) + 20 \, {\left(412 \, \sin\left(7 \, b x + 7 \, a\right) + 231 \, \sin\left(5 \, b x + 5 \, a\right) - 350 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) + 1648 \, {\left(5 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(7 \, b x + 7 \, a\right) - 140 \, {\left(33 \, \sin\left(5 \, b x + 5 \, a\right) - 50 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 924 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(5 \, b x + 5 \, a\right) + 140 \, {\left(10 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 105 \, {\left(2 \, {\left(3 \, \cos\left(12 \, b x + 12 \, a\right) - \cos\left(10 \, b x + 10 \, a\right) - 5 \, \cos\left(8 \, b x + 8 \, a\right) + 5 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(14 \, b x + 14 \, a\right) - \cos\left(14 \, b x + 14 \, a\right)^{2} + 6 \, {\left(\cos\left(10 \, b x + 10 \, a\right) + 5 \, \cos\left(8 \, b x + 8 \, a\right) - 5 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - 9 \, \cos\left(12 \, b x + 12 \, a\right)^{2} - 2 \, {\left(5 \, \cos\left(8 \, b x + 8 \, a\right) - 5 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - \cos\left(10 \, b x + 10 \, a\right)^{2} + 10 \, {\left(5 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 25 \, \cos\left(8 \, b x + 8 \, a\right)^{2} - 10 \, {\left(\cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 25 \, \cos\left(6 \, b x + 6 \, a\right)^{2} + 2 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(3 \, \sin\left(12 \, b x + 12 \, a\right) - \sin\left(10 \, b x + 10 \, a\right) - 5 \, \sin\left(8 \, b x + 8 \, a\right) + 5 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - \sin\left(14 \, b x + 14 \, a\right)^{2} + 6 \, {\left(\sin\left(10 \, b x + 10 \, a\right) + 5 \, \sin\left(8 \, b x + 8 \, a\right) - 5 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 9 \, \sin\left(12 \, b x + 12 \, a\right)^{2} - 2 \, {\left(5 \, \sin\left(8 \, b x + 8 \, a\right) - 5 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - \sin\left(10 \, b x + 10 \, a\right)^{2} + 10 \, {\left(5 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 25 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 10 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 25 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 6 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(105 \, \cos\left(13 \, b x + 13 \, a\right) - 350 \, \cos\left(11 \, b x + 11 \, a\right) + 231 \, \cos\left(9 \, b x + 9 \, a\right) + 412 \, \cos\left(7 \, b x + 7 \, a\right) + 231 \, \cos\left(5 \, b x + 5 \, a\right) - 350 \, \cos\left(3 \, b x + 3 \, a\right) + 105 \, \cos\left(b x + a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 420 \, {\left(3 \, \cos\left(12 \, b x + 12 \, a\right) - \cos\left(10 \, b x + 10 \, a\right) - 5 \, \cos\left(8 \, b x + 8 \, a\right) + 5 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(13 \, b x + 13 \, a\right) - 12 \, {\left(350 \, \cos\left(11 \, b x + 11 \, a\right) - 231 \, \cos\left(9 \, b x + 9 \, a\right) - 412 \, \cos\left(7 \, b x + 7 \, a\right) - 231 \, \cos\left(5 \, b x + 5 \, a\right) + 350 \, \cos\left(3 \, b x + 3 \, a\right) - 105 \, \cos\left(b x + a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 1400 \, {\left(\cos\left(10 \, b x + 10 \, a\right) + 5 \, \cos\left(8 \, b x + 8 \, a\right) - 5 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(11 \, b x + 11 \, a\right) - 4 \, {\left(231 \, \cos\left(9 \, b x + 9 \, a\right) + 412 \, \cos\left(7 \, b x + 7 \, a\right) + 231 \, \cos\left(5 \, b x + 5 \, a\right) - 350 \, \cos\left(3 \, b x + 3 \, a\right) + 105 \, \cos\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 924 \, {\left(5 \, \cos\left(8 \, b x + 8 \, a\right) - 5 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(9 \, b x + 9 \, a\right) - 20 \, {\left(412 \, \cos\left(7 \, b x + 7 \, a\right) + 231 \, \cos\left(5 \, b x + 5 \, a\right) - 350 \, \cos\left(3 \, b x + 3 \, a\right) + 105 \, \cos\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 1648 \, {\left(5 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(7 \, b x + 7 \, a\right) + 140 \, {\left(33 \, \cos\left(5 \, b x + 5 \, a\right) - 50 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 924 \, {\left(\cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(5 \, b x + 5 \, a\right) - 140 \, {\left(10 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) - 1400 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 4200 \, \cos\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 1260 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) + 1260 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 420 \, \sin\left(b x + a\right)}{480 \, {\left(b \cos\left(14 \, b x + 14 \, a\right)^{2} + 9 \, b \cos\left(12 \, b x + 12 \, a\right)^{2} + b \cos\left(10 \, b x + 10 \, a\right)^{2} + 25 \, b \cos\left(8 \, b x + 8 \, a\right)^{2} + 25 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + b \cos\left(4 \, b x + 4 \, a\right)^{2} + 9 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(14 \, b x + 14 \, a\right)^{2} + 9 \, b \sin\left(12 \, b x + 12 \, a\right)^{2} + b \sin\left(10 \, b x + 10 \, a\right)^{2} + 25 \, b \sin\left(8 \, b x + 8 \, a\right)^{2} + 25 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} - 6 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(3 \, b \cos\left(12 \, b x + 12 \, a\right) - b \cos\left(10 \, b x + 10 \, a\right) - 5 \, b \cos\left(8 \, b x + 8 \, a\right) + 5 \, b \cos\left(6 \, b x + 6 \, a\right) + b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(14 \, b x + 14 \, a\right) - 6 \, {\left(b \cos\left(10 \, b x + 10 \, a\right) + 5 \, b \cos\left(8 \, b x + 8 \, a\right) - 5 \, b \cos\left(6 \, b x + 6 \, a\right) - b \cos\left(4 \, b x + 4 \, a\right) + 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(12 \, b x + 12 \, a\right) + 2 \, {\left(5 \, b \cos\left(8 \, b x + 8 \, a\right) - 5 \, b \cos\left(6 \, b x + 6 \, a\right) - b \cos\left(4 \, b x + 4 \, a\right) + 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(10 \, b x + 10 \, a\right) - 10 \, {\left(5 \, b \cos\left(6 \, b x + 6 \, a\right) + b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) + 10 \, {\left(b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(6 \, b x + 6 \, a\right) - 2 \, {\left(3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(3 \, b \sin\left(12 \, b x + 12 \, a\right) - b \sin\left(10 \, b x + 10 \, a\right) - 5 \, b \sin\left(8 \, b x + 8 \, a\right) + 5 \, b \sin\left(6 \, b x + 6 \, a\right) + b \sin\left(4 \, b x + 4 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 6 \, {\left(b \sin\left(10 \, b x + 10 \, a\right) + 5 \, b \sin\left(8 \, b x + 8 \, a\right) - 5 \, b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(4 \, b x + 4 \, a\right) + 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 2 \, {\left(5 \, b \sin\left(8 \, b x + 8 \, a\right) - 5 \, b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(4 \, b x + 4 \, a\right) + 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 10 \, {\left(5 \, b \sin\left(6 \, b x + 6 \, a\right) + b \sin\left(4 \, b x + 4 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 10 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/480*(4*(105*sin(13*b*x + 13*a) - 350*sin(11*b*x + 11*a) + 231*sin(9*b*x + 9*a) + 412*sin(7*b*x + 7*a) + 231*sin(5*b*x + 5*a) - 350*sin(3*b*x + 3*a) + 105*sin(b*x + a))*cos(14*b*x + 14*a) + 420*(3*sin(12*b*x + 12*a) - sin(10*b*x + 10*a) - 5*sin(8*b*x + 8*a) + 5*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*cos(13*b*x + 13*a) + 12*(350*sin(11*b*x + 11*a) - 231*sin(9*b*x + 9*a) - 412*sin(7*b*x + 7*a) - 231*sin(5*b*x + 5*a) + 350*sin(3*b*x + 3*a) - 105*sin(b*x + a))*cos(12*b*x + 12*a) + 1400*(sin(10*b*x + 10*a) + 5*sin(8*b*x + 8*a) - 5*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*cos(11*b*x + 11*a) + 4*(231*sin(9*b*x + 9*a) + 412*sin(7*b*x + 7*a) + 231*sin(5*b*x + 5*a) - 350*sin(3*b*x + 3*a) + 105*sin(b*x + a))*cos(10*b*x + 10*a) - 924*(5*sin(8*b*x + 8*a) - 5*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*cos(9*b*x + 9*a) + 20*(412*sin(7*b*x + 7*a) + 231*sin(5*b*x + 5*a) - 350*sin(3*b*x + 3*a) + 105*sin(b*x + a))*cos(8*b*x + 8*a) + 1648*(5*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*cos(7*b*x + 7*a) - 140*(33*sin(5*b*x + 5*a) - 50*sin(3*b*x + 3*a) + 15*sin(b*x + a))*cos(6*b*x + 6*a) + 924*(sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*cos(5*b*x + 5*a) + 140*(10*sin(3*b*x + 3*a) - 3*sin(b*x + a))*cos(4*b*x + 4*a) + 105*(2*(3*cos(12*b*x + 12*a) - cos(10*b*x + 10*a) - 5*cos(8*b*x + 8*a) + 5*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(14*b*x + 14*a) - cos(14*b*x + 14*a)^2 + 6*(cos(10*b*x + 10*a) + 5*cos(8*b*x + 8*a) - 5*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - 9*cos(12*b*x + 12*a)^2 - 2*(5*cos(8*b*x + 8*a) - 5*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - cos(10*b*x + 10*a)^2 + 10*(5*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 25*cos(8*b*x + 8*a)^2 - 10*(cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - 25*cos(6*b*x + 6*a)^2 + 2*(3*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 9*cos(2*b*x + 2*a)^2 + 2*(3*sin(12*b*x + 12*a) - sin(10*b*x + 10*a) - 5*sin(8*b*x + 8*a) + 5*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - sin(14*b*x + 14*a)^2 + 6*(sin(10*b*x + 10*a) + 5*sin(8*b*x + 8*a) - 5*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 9*sin(12*b*x + 12*a)^2 - 2*(5*sin(8*b*x + 8*a) - 5*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - sin(10*b*x + 10*a)^2 + 10*(5*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 25*sin(8*b*x + 8*a)^2 - 10*(sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 25*sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 + 6*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) - 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(105*cos(13*b*x + 13*a) - 350*cos(11*b*x + 11*a) + 231*cos(9*b*x + 9*a) + 412*cos(7*b*x + 7*a) + 231*cos(5*b*x + 5*a) - 350*cos(3*b*x + 3*a) + 105*cos(b*x + a))*sin(14*b*x + 14*a) - 420*(3*cos(12*b*x + 12*a) - cos(10*b*x + 10*a) - 5*cos(8*b*x + 8*a) + 5*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*sin(13*b*x + 13*a) - 12*(350*cos(11*b*x + 11*a) - 231*cos(9*b*x + 9*a) - 412*cos(7*b*x + 7*a) - 231*cos(5*b*x + 5*a) + 350*cos(3*b*x + 3*a) - 105*cos(b*x + a))*sin(12*b*x + 12*a) - 1400*(cos(10*b*x + 10*a) + 5*cos(8*b*x + 8*a) - 5*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*sin(11*b*x + 11*a) - 4*(231*cos(9*b*x + 9*a) + 412*cos(7*b*x + 7*a) + 231*cos(5*b*x + 5*a) - 350*cos(3*b*x + 3*a) + 105*cos(b*x + a))*sin(10*b*x + 10*a) + 924*(5*cos(8*b*x + 8*a) - 5*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*sin(9*b*x + 9*a) - 20*(412*cos(7*b*x + 7*a) + 231*cos(5*b*x + 5*a) - 350*cos(3*b*x + 3*a) + 105*cos(b*x + a))*sin(8*b*x + 8*a) - 1648*(5*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*sin(7*b*x + 7*a) + 140*(33*cos(5*b*x + 5*a) - 50*cos(3*b*x + 3*a) + 15*cos(b*x + a))*sin(6*b*x + 6*a) - 924*(cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*sin(5*b*x + 5*a) - 140*(10*cos(3*b*x + 3*a) - 3*cos(b*x + a))*sin(4*b*x + 4*a) - 1400*(3*cos(2*b*x + 2*a) - 1)*sin(3*b*x + 3*a) + 4200*cos(3*b*x + 3*a)*sin(2*b*x + 2*a) - 1260*cos(b*x + a)*sin(2*b*x + 2*a) + 1260*cos(2*b*x + 2*a)*sin(b*x + a) - 420*sin(b*x + a))/(b*cos(14*b*x + 14*a)^2 + 9*b*cos(12*b*x + 12*a)^2 + b*cos(10*b*x + 10*a)^2 + 25*b*cos(8*b*x + 8*a)^2 + 25*b*cos(6*b*x + 6*a)^2 + b*cos(4*b*x + 4*a)^2 + 9*b*cos(2*b*x + 2*a)^2 + b*sin(14*b*x + 14*a)^2 + 9*b*sin(12*b*x + 12*a)^2 + b*sin(10*b*x + 10*a)^2 + 25*b*sin(8*b*x + 8*a)^2 + 25*b*sin(6*b*x + 6*a)^2 + b*sin(4*b*x + 4*a)^2 - 6*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 9*b*sin(2*b*x + 2*a)^2 - 2*(3*b*cos(12*b*x + 12*a) - b*cos(10*b*x + 10*a) - 5*b*cos(8*b*x + 8*a) + 5*b*cos(6*b*x + 6*a) + b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(14*b*x + 14*a) - 6*(b*cos(10*b*x + 10*a) + 5*b*cos(8*b*x + 8*a) - 5*b*cos(6*b*x + 6*a) - b*cos(4*b*x + 4*a) + 3*b*cos(2*b*x + 2*a) - b)*cos(12*b*x + 12*a) + 2*(5*b*cos(8*b*x + 8*a) - 5*b*cos(6*b*x + 6*a) - b*cos(4*b*x + 4*a) + 3*b*cos(2*b*x + 2*a) - b)*cos(10*b*x + 10*a) - 10*(5*b*cos(6*b*x + 6*a) + b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) + 10*(b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(6*b*x + 6*a) - 2*(3*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 6*b*cos(2*b*x + 2*a) - 2*(3*b*sin(12*b*x + 12*a) - b*sin(10*b*x + 10*a) - 5*b*sin(8*b*x + 8*a) + 5*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - 6*(b*sin(10*b*x + 10*a) + 5*b*sin(8*b*x + 8*a) - 5*b*sin(6*b*x + 6*a) - b*sin(4*b*x + 4*a) + 3*b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + 2*(5*b*sin(8*b*x + 8*a) - 5*b*sin(6*b*x + 6*a) - b*sin(4*b*x + 4*a) + 3*b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 10*(5*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 10*(b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
72,1,4268,0,1.565086," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(315 \, \cos\left(17 \, b x + 17 \, a\right) - 840 \, \cos\left(15 \, b x + 15 \, a\right) - 252 \, \cos\left(13 \, b x + 13 \, a\right) + 2376 \, \cos\left(11 \, b x + 11 \, a\right) - 1150 \, \cos\left(9 \, b x + 9 \, a\right) + 2376 \, \cos\left(7 \, b x + 7 \, a\right) - 252 \, \cos\left(5 \, b x + 5 \, a\right) - 840 \, \cos\left(3 \, b x + 3 \, a\right) + 315 \, \cos\left(b x + a\right)\right)} \cos\left(18 \, b x + 18 \, a\right) - 1260 \, {\left(3 \, \cos\left(16 \, b x + 16 \, a\right) - 8 \, \cos\left(12 \, b x + 12 \, a\right) + 6 \, \cos\left(10 \, b x + 10 \, a\right) + 6 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(17 \, b x + 17 \, a\right) + 12 \, {\left(840 \, \cos\left(15 \, b x + 15 \, a\right) + 252 \, \cos\left(13 \, b x + 13 \, a\right) - 2376 \, \cos\left(11 \, b x + 11 \, a\right) + 1150 \, \cos\left(9 \, b x + 9 \, a\right) - 2376 \, \cos\left(7 \, b x + 7 \, a\right) + 252 \, \cos\left(5 \, b x + 5 \, a\right) + 840 \, \cos\left(3 \, b x + 3 \, a\right) - 315 \, \cos\left(b x + a\right)\right)} \cos\left(16 \, b x + 16 \, a\right) - 3360 \, {\left(8 \, \cos\left(12 \, b x + 12 \, a\right) - 6 \, \cos\left(10 \, b x + 10 \, a\right) - 6 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(15 \, b x + 15 \, a\right) - 1008 \, {\left(8 \, \cos\left(12 \, b x + 12 \, a\right) - 6 \, \cos\left(10 \, b x + 10 \, a\right) - 6 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(13 \, b x + 13 \, a\right) + 32 \, {\left(2376 \, \cos\left(11 \, b x + 11 \, a\right) - 1150 \, \cos\left(9 \, b x + 9 \, a\right) + 2376 \, \cos\left(7 \, b x + 7 \, a\right) - 252 \, \cos\left(5 \, b x + 5 \, a\right) - 840 \, \cos\left(3 \, b x + 3 \, a\right) + 315 \, \cos\left(b x + a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) - 9504 \, {\left(6 \, \cos\left(10 \, b x + 10 \, a\right) + 6 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(11 \, b x + 11 \, a\right) + 24 \, {\left(1150 \, \cos\left(9 \, b x + 9 \, a\right) - 2376 \, \cos\left(7 \, b x + 7 \, a\right) + 252 \, \cos\left(5 \, b x + 5 \, a\right) + 840 \, \cos\left(3 \, b x + 3 \, a\right) - 315 \, \cos\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) + 4600 \, {\left(6 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(9 \, b x + 9 \, a\right) - 72 \, {\left(792 \, \cos\left(7 \, b x + 7 \, a\right) - 84 \, \cos\left(5 \, b x + 5 \, a\right) - 280 \, \cos\left(3 \, b x + 3 \, a\right) + 105 \, \cos\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) + 9504 \, {\left(8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(7 \, b x + 7 \, a\right) - 672 \, {\left(12 \, \cos\left(5 \, b x + 5 \, a\right) + 40 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 1008 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(5 \, b x + 5 \, a\right) + 3360 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 3780 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 315 \, {\left(2 \, {\left(3 \, \cos\left(16 \, b x + 16 \, a\right) - 8 \, \cos\left(12 \, b x + 12 \, a\right) + 6 \, \cos\left(10 \, b x + 10 \, a\right) + 6 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(18 \, b x + 18 \, a\right) - \cos\left(18 \, b x + 18 \, a\right)^{2} + 6 \, {\left(8 \, \cos\left(12 \, b x + 12 \, a\right) - 6 \, \cos\left(10 \, b x + 10 \, a\right) - 6 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(16 \, b x + 16 \, a\right) - 9 \, \cos\left(16 \, b x + 16 \, a\right)^{2} + 16 \, {\left(6 \, \cos\left(10 \, b x + 10 \, a\right) + 6 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - 64 \, \cos\left(12 \, b x + 12 \, a\right)^{2} - 12 \, {\left(6 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 36 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 12 \, {\left(8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 36 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 16 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 64 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(3 \, \sin\left(16 \, b x + 16 \, a\right) - 8 \, \sin\left(12 \, b x + 12 \, a\right) + 6 \, \sin\left(10 \, b x + 10 \, a\right) + 6 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(18 \, b x + 18 \, a\right) - \sin\left(18 \, b x + 18 \, a\right)^{2} + 6 \, {\left(8 \, \sin\left(12 \, b x + 12 \, a\right) - 6 \, \sin\left(10 \, b x + 10 \, a\right) - 6 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) - 9 \, \sin\left(16 \, b x + 16 \, a\right)^{2} + 16 \, {\left(6 \, \sin\left(10 \, b x + 10 \, a\right) + 6 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 64 \, \sin\left(12 \, b x + 12 \, a\right)^{2} - 12 \, {\left(6 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 36 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 12 \, {\left(8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 36 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 64 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + 48 \, \sin\left(6 \, b x + 6 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 315 \, {\left(2 \, {\left(3 \, \cos\left(16 \, b x + 16 \, a\right) - 8 \, \cos\left(12 \, b x + 12 \, a\right) + 6 \, \cos\left(10 \, b x + 10 \, a\right) + 6 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(18 \, b x + 18 \, a\right) - \cos\left(18 \, b x + 18 \, a\right)^{2} + 6 \, {\left(8 \, \cos\left(12 \, b x + 12 \, a\right) - 6 \, \cos\left(10 \, b x + 10 \, a\right) - 6 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(16 \, b x + 16 \, a\right) - 9 \, \cos\left(16 \, b x + 16 \, a\right)^{2} + 16 \, {\left(6 \, \cos\left(10 \, b x + 10 \, a\right) + 6 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - 64 \, \cos\left(12 \, b x + 12 \, a\right)^{2} - 12 \, {\left(6 \, \cos\left(8 \, b x + 8 \, a\right) - 8 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 36 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 12 \, {\left(8 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 36 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 16 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 64 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(3 \, \sin\left(16 \, b x + 16 \, a\right) - 8 \, \sin\left(12 \, b x + 12 \, a\right) + 6 \, \sin\left(10 \, b x + 10 \, a\right) + 6 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(18 \, b x + 18 \, a\right) - \sin\left(18 \, b x + 18 \, a\right)^{2} + 6 \, {\left(8 \, \sin\left(12 \, b x + 12 \, a\right) - 6 \, \sin\left(10 \, b x + 10 \, a\right) - 6 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) - 9 \, \sin\left(16 \, b x + 16 \, a\right)^{2} + 16 \, {\left(6 \, \sin\left(10 \, b x + 10 \, a\right) + 6 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 64 \, \sin\left(12 \, b x + 12 \, a\right)^{2} - 12 \, {\left(6 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 36 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 12 \, {\left(8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 36 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 64 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + 48 \, \sin\left(6 \, b x + 6 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(315 \, \sin\left(17 \, b x + 17 \, a\right) - 840 \, \sin\left(15 \, b x + 15 \, a\right) - 252 \, \sin\left(13 \, b x + 13 \, a\right) + 2376 \, \sin\left(11 \, b x + 11 \, a\right) - 1150 \, \sin\left(9 \, b x + 9 \, a\right) + 2376 \, \sin\left(7 \, b x + 7 \, a\right) - 252 \, \sin\left(5 \, b x + 5 \, a\right) - 840 \, \sin\left(3 \, b x + 3 \, a\right) + 315 \, \sin\left(b x + a\right)\right)} \sin\left(18 \, b x + 18 \, a\right) - 1260 \, {\left(3 \, \sin\left(16 \, b x + 16 \, a\right) - 8 \, \sin\left(12 \, b x + 12 \, a\right) + 6 \, \sin\left(10 \, b x + 10 \, a\right) + 6 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(17 \, b x + 17 \, a\right) + 12 \, {\left(840 \, \sin\left(15 \, b x + 15 \, a\right) + 252 \, \sin\left(13 \, b x + 13 \, a\right) - 2376 \, \sin\left(11 \, b x + 11 \, a\right) + 1150 \, \sin\left(9 \, b x + 9 \, a\right) - 2376 \, \sin\left(7 \, b x + 7 \, a\right) + 252 \, \sin\left(5 \, b x + 5 \, a\right) + 840 \, \sin\left(3 \, b x + 3 \, a\right) - 315 \, \sin\left(b x + a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) - 3360 \, {\left(8 \, \sin\left(12 \, b x + 12 \, a\right) - 6 \, \sin\left(10 \, b x + 10 \, a\right) - 6 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(15 \, b x + 15 \, a\right) - 1008 \, {\left(8 \, \sin\left(12 \, b x + 12 \, a\right) - 6 \, \sin\left(10 \, b x + 10 \, a\right) - 6 \, \sin\left(8 \, b x + 8 \, a\right) + 8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(13 \, b x + 13 \, a\right) + 32 \, {\left(2376 \, \sin\left(11 \, b x + 11 \, a\right) - 1150 \, \sin\left(9 \, b x + 9 \, a\right) + 2376 \, \sin\left(7 \, b x + 7 \, a\right) - 252 \, \sin\left(5 \, b x + 5 \, a\right) - 840 \, \sin\left(3 \, b x + 3 \, a\right) + 315 \, \sin\left(b x + a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 9504 \, {\left(6 \, \sin\left(10 \, b x + 10 \, a\right) + 6 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(11 \, b x + 11 \, a\right) + 24 \, {\left(1150 \, \sin\left(9 \, b x + 9 \, a\right) - 2376 \, \sin\left(7 \, b x + 7 \, a\right) + 252 \, \sin\left(5 \, b x + 5 \, a\right) + 840 \, \sin\left(3 \, b x + 3 \, a\right) - 315 \, \sin\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 4600 \, {\left(6 \, \sin\left(8 \, b x + 8 \, a\right) - 8 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(9 \, b x + 9 \, a\right) - 72 \, {\left(792 \, \sin\left(7 \, b x + 7 \, a\right) - 84 \, \sin\left(5 \, b x + 5 \, a\right) - 280 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 9504 \, {\left(8 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(7 \, b x + 7 \, a\right) - 672 \, {\left(12 \, \sin\left(5 \, b x + 5 \, a\right) + 40 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 3024 \, \sin\left(5 \, b x + 5 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 10080 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 3780 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 1260 \, \cos\left(b x + a\right)}{1536 \, {\left(b \cos\left(18 \, b x + 18 \, a\right)^{2} + 9 \, b \cos\left(16 \, b x + 16 \, a\right)^{2} + 64 \, b \cos\left(12 \, b x + 12 \, a\right)^{2} + 36 \, b \cos\left(10 \, b x + 10 \, a\right)^{2} + 36 \, b \cos\left(8 \, b x + 8 \, a\right)^{2} + 64 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(18 \, b x + 18 \, a\right)^{2} + 9 \, b \sin\left(16 \, b x + 16 \, a\right)^{2} + 64 \, b \sin\left(12 \, b x + 12 \, a\right)^{2} + 36 \, b \sin\left(10 \, b x + 10 \, a\right)^{2} + 36 \, b \sin\left(8 \, b x + 8 \, a\right)^{2} + 64 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} - 48 \, b \sin\left(6 \, b x + 6 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(3 \, b \cos\left(16 \, b x + 16 \, a\right) - 8 \, b \cos\left(12 \, b x + 12 \, a\right) + 6 \, b \cos\left(10 \, b x + 10 \, a\right) + 6 \, b \cos\left(8 \, b x + 8 \, a\right) - 8 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(18 \, b x + 18 \, a\right) - 6 \, {\left(8 \, b \cos\left(12 \, b x + 12 \, a\right) - 6 \, b \cos\left(10 \, b x + 10 \, a\right) - 6 \, b \cos\left(8 \, b x + 8 \, a\right) + 8 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(16 \, b x + 16 \, a\right) - 16 \, {\left(6 \, b \cos\left(10 \, b x + 10 \, a\right) + 6 \, b \cos\left(8 \, b x + 8 \, a\right) - 8 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(12 \, b x + 12 \, a\right) + 12 \, {\left(6 \, b \cos\left(8 \, b x + 8 \, a\right) - 8 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(10 \, b x + 10 \, a\right) - 12 \, {\left(8 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 16 \, {\left(3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(3 \, b \sin\left(16 \, b x + 16 \, a\right) - 8 \, b \sin\left(12 \, b x + 12 \, a\right) + 6 \, b \sin\left(10 \, b x + 10 \, a\right) + 6 \, b \sin\left(8 \, b x + 8 \, a\right) - 8 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(18 \, b x + 18 \, a\right) - 6 \, {\left(8 \, b \sin\left(12 \, b x + 12 \, a\right) - 6 \, b \sin\left(10 \, b x + 10 \, a\right) - 6 \, b \sin\left(8 \, b x + 8 \, a\right) + 8 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(16 \, b x + 16 \, a\right) - 16 \, {\left(6 \, b \sin\left(10 \, b x + 10 \, a\right) + 6 \, b \sin\left(8 \, b x + 8 \, a\right) - 8 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 12 \, {\left(6 \, b \sin\left(8 \, b x + 8 \, a\right) - 8 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 12 \, {\left(8 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + b\right)}}"," ",0,"1/1536*(4*(315*cos(17*b*x + 17*a) - 840*cos(15*b*x + 15*a) - 252*cos(13*b*x + 13*a) + 2376*cos(11*b*x + 11*a) - 1150*cos(9*b*x + 9*a) + 2376*cos(7*b*x + 7*a) - 252*cos(5*b*x + 5*a) - 840*cos(3*b*x + 3*a) + 315*cos(b*x + a))*cos(18*b*x + 18*a) - 1260*(3*cos(16*b*x + 16*a) - 8*cos(12*b*x + 12*a) + 6*cos(10*b*x + 10*a) + 6*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(2*b*x + 2*a) - 1)*cos(17*b*x + 17*a) + 12*(840*cos(15*b*x + 15*a) + 252*cos(13*b*x + 13*a) - 2376*cos(11*b*x + 11*a) + 1150*cos(9*b*x + 9*a) - 2376*cos(7*b*x + 7*a) + 252*cos(5*b*x + 5*a) + 840*cos(3*b*x + 3*a) - 315*cos(b*x + a))*cos(16*b*x + 16*a) - 3360*(8*cos(12*b*x + 12*a) - 6*cos(10*b*x + 10*a) - 6*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(2*b*x + 2*a) + 1)*cos(15*b*x + 15*a) - 1008*(8*cos(12*b*x + 12*a) - 6*cos(10*b*x + 10*a) - 6*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(2*b*x + 2*a) + 1)*cos(13*b*x + 13*a) + 32*(2376*cos(11*b*x + 11*a) - 1150*cos(9*b*x + 9*a) + 2376*cos(7*b*x + 7*a) - 252*cos(5*b*x + 5*a) - 840*cos(3*b*x + 3*a) + 315*cos(b*x + a))*cos(12*b*x + 12*a) - 9504*(6*cos(10*b*x + 10*a) + 6*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(2*b*x + 2*a) - 1)*cos(11*b*x + 11*a) + 24*(1150*cos(9*b*x + 9*a) - 2376*cos(7*b*x + 7*a) + 252*cos(5*b*x + 5*a) + 840*cos(3*b*x + 3*a) - 315*cos(b*x + a))*cos(10*b*x + 10*a) + 4600*(6*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(2*b*x + 2*a) - 1)*cos(9*b*x + 9*a) - 72*(792*cos(7*b*x + 7*a) - 84*cos(5*b*x + 5*a) - 280*cos(3*b*x + 3*a) + 105*cos(b*x + a))*cos(8*b*x + 8*a) + 9504*(8*cos(6*b*x + 6*a) - 3*cos(2*b*x + 2*a) + 1)*cos(7*b*x + 7*a) - 672*(12*cos(5*b*x + 5*a) + 40*cos(3*b*x + 3*a) - 15*cos(b*x + a))*cos(6*b*x + 6*a) + 1008*(3*cos(2*b*x + 2*a) - 1)*cos(5*b*x + 5*a) + 3360*(3*cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a) - 3780*cos(2*b*x + 2*a)*cos(b*x + a) + 315*(2*(3*cos(16*b*x + 16*a) - 8*cos(12*b*x + 12*a) + 6*cos(10*b*x + 10*a) + 6*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(2*b*x + 2*a) - 1)*cos(18*b*x + 18*a) - cos(18*b*x + 18*a)^2 + 6*(8*cos(12*b*x + 12*a) - 6*cos(10*b*x + 10*a) - 6*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(2*b*x + 2*a) + 1)*cos(16*b*x + 16*a) - 9*cos(16*b*x + 16*a)^2 + 16*(6*cos(10*b*x + 10*a) + 6*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - 64*cos(12*b*x + 12*a)^2 - 12*(6*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - 36*cos(10*b*x + 10*a)^2 + 12*(8*cos(6*b*x + 6*a) - 3*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 36*cos(8*b*x + 8*a)^2 + 16*(3*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 64*cos(6*b*x + 6*a)^2 - 9*cos(2*b*x + 2*a)^2 + 2*(3*sin(16*b*x + 16*a) - 8*sin(12*b*x + 12*a) + 6*sin(10*b*x + 10*a) + 6*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(2*b*x + 2*a))*sin(18*b*x + 18*a) - sin(18*b*x + 18*a)^2 + 6*(8*sin(12*b*x + 12*a) - 6*sin(10*b*x + 10*a) - 6*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(2*b*x + 2*a))*sin(16*b*x + 16*a) - 9*sin(16*b*x + 16*a)^2 + 16*(6*sin(10*b*x + 10*a) + 6*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 64*sin(12*b*x + 12*a)^2 - 12*(6*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 36*sin(10*b*x + 10*a)^2 + 12*(8*sin(6*b*x + 6*a) - 3*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 36*sin(8*b*x + 8*a)^2 - 64*sin(6*b*x + 6*a)^2 + 48*sin(6*b*x + 6*a)*sin(2*b*x + 2*a) - 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - 315*(2*(3*cos(16*b*x + 16*a) - 8*cos(12*b*x + 12*a) + 6*cos(10*b*x + 10*a) + 6*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(2*b*x + 2*a) - 1)*cos(18*b*x + 18*a) - cos(18*b*x + 18*a)^2 + 6*(8*cos(12*b*x + 12*a) - 6*cos(10*b*x + 10*a) - 6*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 3*cos(2*b*x + 2*a) + 1)*cos(16*b*x + 16*a) - 9*cos(16*b*x + 16*a)^2 + 16*(6*cos(10*b*x + 10*a) + 6*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - 64*cos(12*b*x + 12*a)^2 - 12*(6*cos(8*b*x + 8*a) - 8*cos(6*b*x + 6*a) + 3*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - 36*cos(10*b*x + 10*a)^2 + 12*(8*cos(6*b*x + 6*a) - 3*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 36*cos(8*b*x + 8*a)^2 + 16*(3*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 64*cos(6*b*x + 6*a)^2 - 9*cos(2*b*x + 2*a)^2 + 2*(3*sin(16*b*x + 16*a) - 8*sin(12*b*x + 12*a) + 6*sin(10*b*x + 10*a) + 6*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(2*b*x + 2*a))*sin(18*b*x + 18*a) - sin(18*b*x + 18*a)^2 + 6*(8*sin(12*b*x + 12*a) - 6*sin(10*b*x + 10*a) - 6*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(2*b*x + 2*a))*sin(16*b*x + 16*a) - 9*sin(16*b*x + 16*a)^2 + 16*(6*sin(10*b*x + 10*a) + 6*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 64*sin(12*b*x + 12*a)^2 - 12*(6*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 36*sin(10*b*x + 10*a)^2 + 12*(8*sin(6*b*x + 6*a) - 3*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 36*sin(8*b*x + 8*a)^2 - 64*sin(6*b*x + 6*a)^2 + 48*sin(6*b*x + 6*a)*sin(2*b*x + 2*a) - 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(315*sin(17*b*x + 17*a) - 840*sin(15*b*x + 15*a) - 252*sin(13*b*x + 13*a) + 2376*sin(11*b*x + 11*a) - 1150*sin(9*b*x + 9*a) + 2376*sin(7*b*x + 7*a) - 252*sin(5*b*x + 5*a) - 840*sin(3*b*x + 3*a) + 315*sin(b*x + a))*sin(18*b*x + 18*a) - 1260*(3*sin(16*b*x + 16*a) - 8*sin(12*b*x + 12*a) + 6*sin(10*b*x + 10*a) + 6*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(2*b*x + 2*a))*sin(17*b*x + 17*a) + 12*(840*sin(15*b*x + 15*a) + 252*sin(13*b*x + 13*a) - 2376*sin(11*b*x + 11*a) + 1150*sin(9*b*x + 9*a) - 2376*sin(7*b*x + 7*a) + 252*sin(5*b*x + 5*a) + 840*sin(3*b*x + 3*a) - 315*sin(b*x + a))*sin(16*b*x + 16*a) - 3360*(8*sin(12*b*x + 12*a) - 6*sin(10*b*x + 10*a) - 6*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(2*b*x + 2*a))*sin(15*b*x + 15*a) - 1008*(8*sin(12*b*x + 12*a) - 6*sin(10*b*x + 10*a) - 6*sin(8*b*x + 8*a) + 8*sin(6*b*x + 6*a) - 3*sin(2*b*x + 2*a))*sin(13*b*x + 13*a) + 32*(2376*sin(11*b*x + 11*a) - 1150*sin(9*b*x + 9*a) + 2376*sin(7*b*x + 7*a) - 252*sin(5*b*x + 5*a) - 840*sin(3*b*x + 3*a) + 315*sin(b*x + a))*sin(12*b*x + 12*a) - 9504*(6*sin(10*b*x + 10*a) + 6*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(2*b*x + 2*a))*sin(11*b*x + 11*a) + 24*(1150*sin(9*b*x + 9*a) - 2376*sin(7*b*x + 7*a) + 252*sin(5*b*x + 5*a) + 840*sin(3*b*x + 3*a) - 315*sin(b*x + a))*sin(10*b*x + 10*a) + 4600*(6*sin(8*b*x + 8*a) - 8*sin(6*b*x + 6*a) + 3*sin(2*b*x + 2*a))*sin(9*b*x + 9*a) - 72*(792*sin(7*b*x + 7*a) - 84*sin(5*b*x + 5*a) - 280*sin(3*b*x + 3*a) + 105*sin(b*x + a))*sin(8*b*x + 8*a) + 9504*(8*sin(6*b*x + 6*a) - 3*sin(2*b*x + 2*a))*sin(7*b*x + 7*a) - 672*(12*sin(5*b*x + 5*a) + 40*sin(3*b*x + 3*a) - 15*sin(b*x + a))*sin(6*b*x + 6*a) + 3024*sin(5*b*x + 5*a)*sin(2*b*x + 2*a) + 10080*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) - 3780*sin(2*b*x + 2*a)*sin(b*x + a) + 1260*cos(b*x + a))/(b*cos(18*b*x + 18*a)^2 + 9*b*cos(16*b*x + 16*a)^2 + 64*b*cos(12*b*x + 12*a)^2 + 36*b*cos(10*b*x + 10*a)^2 + 36*b*cos(8*b*x + 8*a)^2 + 64*b*cos(6*b*x + 6*a)^2 + 9*b*cos(2*b*x + 2*a)^2 + b*sin(18*b*x + 18*a)^2 + 9*b*sin(16*b*x + 16*a)^2 + 64*b*sin(12*b*x + 12*a)^2 + 36*b*sin(10*b*x + 10*a)^2 + 36*b*sin(8*b*x + 8*a)^2 + 64*b*sin(6*b*x + 6*a)^2 - 48*b*sin(6*b*x + 6*a)*sin(2*b*x + 2*a) + 9*b*sin(2*b*x + 2*a)^2 - 2*(3*b*cos(16*b*x + 16*a) - 8*b*cos(12*b*x + 12*a) + 6*b*cos(10*b*x + 10*a) + 6*b*cos(8*b*x + 8*a) - 8*b*cos(6*b*x + 6*a) + 3*b*cos(2*b*x + 2*a) - b)*cos(18*b*x + 18*a) - 6*(8*b*cos(12*b*x + 12*a) - 6*b*cos(10*b*x + 10*a) - 6*b*cos(8*b*x + 8*a) + 8*b*cos(6*b*x + 6*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(16*b*x + 16*a) - 16*(6*b*cos(10*b*x + 10*a) + 6*b*cos(8*b*x + 8*a) - 8*b*cos(6*b*x + 6*a) + 3*b*cos(2*b*x + 2*a) - b)*cos(12*b*x + 12*a) + 12*(6*b*cos(8*b*x + 8*a) - 8*b*cos(6*b*x + 6*a) + 3*b*cos(2*b*x + 2*a) - b)*cos(10*b*x + 10*a) - 12*(8*b*cos(6*b*x + 6*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 16*(3*b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) - 6*b*cos(2*b*x + 2*a) - 2*(3*b*sin(16*b*x + 16*a) - 8*b*sin(12*b*x + 12*a) + 6*b*sin(10*b*x + 10*a) + 6*b*sin(8*b*x + 8*a) - 8*b*sin(6*b*x + 6*a) + 3*b*sin(2*b*x + 2*a))*sin(18*b*x + 18*a) - 6*(8*b*sin(12*b*x + 12*a) - 6*b*sin(10*b*x + 10*a) - 6*b*sin(8*b*x + 8*a) + 8*b*sin(6*b*x + 6*a) - 3*b*sin(2*b*x + 2*a))*sin(16*b*x + 16*a) - 16*(6*b*sin(10*b*x + 10*a) + 6*b*sin(8*b*x + 8*a) - 8*b*sin(6*b*x + 6*a) + 3*b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + 12*(6*b*sin(8*b*x + 8*a) - 8*b*sin(6*b*x + 6*a) + 3*b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 12*(8*b*sin(6*b*x + 6*a) - 3*b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + b)","B",0
73,0,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^(5/2)*sin(b*x + a), x)","F",0
74,0,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^(3/2)*sin(b*x + a), x)","F",0
75,0,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\sin\left(2 \, b x + 2 \, a\right)} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(sqrt(sin(2*b*x + 2*a))*sin(b*x + a), x)","F",0
76,0,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(sin(b*x + a)/sqrt(sin(2*b*x + 2*a)), x)","F",0
77,0,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)/sin(2*b*x + 2*a)^(3/2), x)","F",0
78,0,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)/sin(2*b*x + 2*a)^(5/2), x)","F",0
79,0,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)/sin(2*b*x + 2*a)^(7/2), x)","F",0
80,0,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(9/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)/sin(2*b*x + 2*a)^(9/2), x)","F",0
81,0,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^(7/2)*sin(b*x + a)^2, x)","F",0
82,0,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^(5/2)*sin(b*x + a)^2, x)","F",0
83,0,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^(3/2)*sin(b*x + a)^2, x)","F",0
84,0,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\sin\left(2 \, b x + 2 \, a\right)} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sqrt(sin(2*b*x + 2*a))*sin(b*x + a)^2, x)","F",0
85,0,0,0,0.000000," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)^{2}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(sin(b*x + a)^2/sqrt(sin(2*b*x + 2*a)), x)","F",0
86,0,0,0,0.000000," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)^2/sin(2*b*x + 2*a)^(3/2), x)","F",0
87,0,0,0,0.000000," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)^2/sin(2*b*x + 2*a)^(5/2), x)","F",0
88,0,0,0,0.000000," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)^2/sin(2*b*x + 2*a)^(7/2), x)","F",0
89,0,0,0,0.000000," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^(3/2)*sin(b*x + a)^3, x)","F",0
90,0,0,0,0.000000," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\sin\left(2 \, b x + 2 \, a\right)} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sqrt(sin(2*b*x + 2*a))*sin(b*x + a)^3, x)","F",0
91,0,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)^{3}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(sin(b*x + a)^3/sqrt(sin(2*b*x + 2*a)), x)","F",0
92,0,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)^3/sin(2*b*x + 2*a)^(3/2), x)","F",0
93,0,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)^3/sin(2*b*x + 2*a)^(5/2), x)","F",0
94,0,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)^3/sin(2*b*x + 2*a)^(7/2), x)","F",0
95,0,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(9/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)^3/sin(2*b*x + 2*a)^(9/2), x)","F",0
96,0,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(11/2),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(sin(b*x + a)^3/sin(2*b*x + 2*a)^(11/2), x)","F",0
97,0,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)*sin(2*b*x + 2*a)^(7/2), x)","F",0
98,0,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)*sin(2*b*x + 2*a)^(5/2), x)","F",0
99,0,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)*sin(2*b*x + 2*a)^(3/2), x)","F",0
100,0,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right) \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(csc(b*x + a)*sqrt(sin(2*b*x + 2*a)), x)","F",0
101,0,0,0,0.000000," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(csc(b*x + a)/sqrt(sin(2*b*x + 2*a)), x)","F",0
102,0,0,0,0.000000," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)/sin(2*b*x + 2*a)^(3/2), x)","F",0
103,0,0,0,0.000000," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)/sin(2*b*x + 2*a)^(5/2), x)","F",0
104,0,0,0,0.000000," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)/sin(2*b*x + 2*a)^(7/2), x)","F",0
105,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(9/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2*sin(2*b*x + 2*a)^(9/2), x)","F",0
106,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2*sin(2*b*x + 2*a)^(7/2), x)","F",0
107,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2*sin(2*b*x + 2*a)^(5/2), x)","F",0
108,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2*sin(2*b*x + 2*a)^(3/2), x)","F",0
109,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(csc(b*x + a)^2*sqrt(sin(2*b*x + 2*a)), x)","F",0
110,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{2}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2/sqrt(sin(2*b*x + 2*a)), x)","F",0
111,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2/sin(2*b*x + 2*a)^(3/2), x)","F",0
112,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2/sin(2*b*x + 2*a)^(5/2), x)","F",0
113,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2/sin(2*b*x + 2*a)^(7/2), x)","F",0
114,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(9/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2/sin(2*b*x + 2*a)^(9/2), x)","F",0
115,0,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(9/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{3} \sin\left(2 \, b x + 2 \, a\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3*sin(2*b*x + 2*a)^(9/2), x)","F",0
116,0,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{3} \sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3*sin(2*b*x + 2*a)^(7/2), x)","F",0
117,0,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{3} \sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3*sin(2*b*x + 2*a)^(5/2), x)","F",0
118,0,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{3} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3*sin(2*b*x + 2*a)^(3/2), x)","F",0
119,0,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{3} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(csc(b*x + a)^3*sqrt(sin(2*b*x + 2*a)), x)","F",0
120,0,0,0,0.000000," ","integrate(csc(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{3}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3/sqrt(sin(2*b*x + 2*a)), x)","F",0
121,0,0,0,0.000000," ","integrate(csc(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3/sin(2*b*x + 2*a)^(3/2), x)","F",0
122,0,0,0,0.000000," ","integrate(csc(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3/sin(2*b*x + 2*a)^(5/2), x)","F",0
123,0,0,0,0.000000," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^m,x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*sin(b*x + a)^3, x)","F",0
124,0,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^m,x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*sin(b*x + a)^2, x)","F",0
125,0,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^m,x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*sin(b*x + a), x)","F",0
126,0,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^m,x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \csc\left(b x + a\right)\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*csc(b*x + a), x)","F",0
127,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^m,x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \csc\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*csc(b*x + a)^2, x)","F",0
128,0,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^m,x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \csc\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*csc(b*x + a)^3, x)","F",0
129,1,91,0,0.350156," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^7,x, algorithm=""maxima"")","\frac{429 \, \cos\left(15 \, b x + 15 \, a\right) + 495 \, \cos\left(13 \, b x + 13 \, a\right) - 4095 \, \cos\left(11 \, b x + 11 \, a\right) - 5005 \, \cos\left(9 \, b x + 9 \, a\right) + 19305 \, \cos\left(7 \, b x + 7 \, a\right) + 27027 \, \cos\left(5 \, b x + 5 \, a\right) - 75075 \, \cos\left(3 \, b x + 3 \, a\right) - 225225 \, \cos\left(b x + a\right)}{823680 \, b}"," ",0,"1/823680*(429*cos(15*b*x + 15*a) + 495*cos(13*b*x + 13*a) - 4095*cos(11*b*x + 11*a) - 5005*cos(9*b*x + 9*a) + 19305*cos(7*b*x + 7*a) + 27027*cos(5*b*x + 5*a) - 75075*cos(3*b*x + 3*a) - 225225*cos(b*x + a))/b","A",0
130,1,80,0,0.337541," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^6,x, algorithm=""maxima"")","-\frac{231 \, \sin\left(13 \, b x + 13 \, a\right) + 273 \, \sin\left(11 \, b x + 11 \, a\right) - 2002 \, \sin\left(9 \, b x + 9 \, a\right) - 2574 \, \sin\left(7 \, b x + 7 \, a\right) + 9009 \, \sin\left(5 \, b x + 5 \, a\right) + 15015 \, \sin\left(3 \, b x + 3 \, a\right) - 60060 \, \sin\left(b x + a\right)}{192192 \, b}"," ",0,"-1/192192*(231*sin(13*b*x + 13*a) + 273*sin(11*b*x + 11*a) - 2002*sin(9*b*x + 9*a) - 2574*sin(7*b*x + 7*a) + 9009*sin(5*b*x + 5*a) + 15015*sin(3*b*x + 3*a) - 60060*sin(b*x + a))/b","A",0
131,1,69,0,0.339041," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","-\frac{63 \, \cos\left(11 \, b x + 11 \, a\right) + 77 \, \cos\left(9 \, b x + 9 \, a\right) - 495 \, \cos\left(7 \, b x + 7 \, a\right) - 693 \, \cos\left(5 \, b x + 5 \, a\right) + 2310 \, \cos\left(3 \, b x + 3 \, a\right) + 6930 \, \cos\left(b x + a\right)}{22176 \, b}"," ",0,"-1/22176*(63*cos(11*b*x + 11*a) + 77*cos(9*b*x + 9*a) - 495*cos(7*b*x + 7*a) - 693*cos(5*b*x + 5*a) + 2310*cos(3*b*x + 3*a) + 6930*cos(b*x + a))/b","A",0
132,1,58,0,0.335784," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{35 \, \sin\left(9 \, b x + 9 \, a\right) + 45 \, \sin\left(7 \, b x + 7 \, a\right) - 252 \, \sin\left(5 \, b x + 5 \, a\right) - 420 \, \sin\left(3 \, b x + 3 \, a\right) + 1890 \, \sin\left(b x + a\right)}{5040 \, b}"," ",0,"1/5040*(35*sin(9*b*x + 9*a) + 45*sin(7*b*x + 7*a) - 252*sin(5*b*x + 5*a) - 420*sin(3*b*x + 3*a) + 1890*sin(b*x + a))/b","A",0
133,1,47,0,0.330119," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{5 \, \cos\left(7 \, b x + 7 \, a\right) + 7 \, \cos\left(5 \, b x + 5 \, a\right) - 35 \, \cos\left(3 \, b x + 3 \, a\right) - 105 \, \cos\left(b x + a\right)}{280 \, b}"," ",0,"1/280*(5*cos(7*b*x + 7*a) + 7*cos(5*b*x + 5*a) - 35*cos(3*b*x + 3*a) - 105*cos(b*x + a))/b","A",0
134,1,36,0,0.327650," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","-\frac{3 \, \sin\left(5 \, b x + 5 \, a\right) + 5 \, \sin\left(3 \, b x + 3 \, a\right) - 30 \, \sin\left(b x + a\right)}{60 \, b}"," ",0,"-1/60*(3*sin(5*b*x + 5*a) + 5*sin(3*b*x + 3*a) - 30*sin(b*x + a))/b","A",0
135,1,26,0,0.316902," ","integrate(cos(b*x+a)*sin(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{\cos\left(3 \, b x + 3 \, a\right)}{6 \, b} - \frac{\cos\left(b x + a\right)}{2 \, b}"," ",0,"-1/6*cos(3*b*x + 3*a)/b - 1/2*cos(b*x + a)/b","A",0
136,1,84,0,0.336570," ","integrate(cos(b*x+a)/sin(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{\log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)}{4 \, b}"," ",0,"-1/4*(log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2))/b","B",0
137,1,233,0,0.464898," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","-\frac{{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) + 4 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, \sin\left(b x + a\right)}{8 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"-1/8*((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) + 4*cos(b*x + a)*sin(2*b*x + 2*a) - 4*cos(2*b*x + 2*a)*sin(b*x + a) + 4*sin(b*x + a))/(b*cos(2*b*x + 2*a)^2 + b*sin(2*b*x + 2*a)^2 - 2*b*cos(2*b*x + 2*a) + b)","B",0
138,1,974,0,0.352452," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \cos\left(5 \, b x + 5 \, a\right) - 2 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(5 \, b x + 5 \, a\right) + 4 \, {\left(2 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 8 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 12 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 3 \, {\left(2 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 3 \, {\left(2 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(3 \, \sin\left(5 \, b x + 5 \, a\right) - 2 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 12 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(5 \, b x + 5 \, a\right) + 4 \, {\left(2 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 12 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 12 \, \cos\left(b x + a\right)}{32 \, {\left(b \cos\left(6 \, b x + 6 \, a\right)^{2} + b \cos\left(4 \, b x + 4 \, a\right)^{2} + b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(6 \, b x + 6 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 2 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/32*(4*(3*cos(5*b*x + 5*a) - 2*cos(3*b*x + 3*a) + 3*cos(b*x + a))*cos(6*b*x + 6*a) - 12*(cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(5*b*x + 5*a) + 4*(2*cos(3*b*x + 3*a) - 3*cos(b*x + a))*cos(4*b*x + 4*a) + 8*(cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a) - 12*cos(2*b*x + 2*a)*cos(b*x + a) + 3*(2*(cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - cos(6*b*x + 6*a)^2 - 2*(cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - cos(2*b*x + 2*a)^2 + 2*(sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 - 2*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - 3*(2*(cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - cos(6*b*x + 6*a)^2 - 2*(cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - cos(2*b*x + 2*a)^2 + 2*(sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 - 2*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(3*sin(5*b*x + 5*a) - 2*sin(3*b*x + 3*a) + 3*sin(b*x + a))*sin(6*b*x + 6*a) - 12*(sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(5*b*x + 5*a) + 4*(2*sin(3*b*x + 3*a) - 3*sin(b*x + a))*sin(4*b*x + 4*a) + 8*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) - 12*sin(2*b*x + 2*a)*sin(b*x + a) + 12*cos(b*x + a))/(b*cos(6*b*x + 6*a)^2 + b*cos(4*b*x + 4*a)^2 + b*cos(2*b*x + 2*a)^2 + b*sin(6*b*x + 6*a)^2 + b*sin(4*b*x + 4*a)^2 + 2*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + b*sin(2*b*x + 2*a)^2 - 2*(b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 2*(b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) - 2*(b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
139,1,1780,0,0.528307," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(15 \, \sin\left(9 \, b x + 9 \, a\right) - 20 \, \sin\left(7 \, b x + 7 \, a\right) - 22 \, \sin\left(5 \, b x + 5 \, a\right) - 20 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) + 60 \, {\left(\sin\left(8 \, b x + 8 \, a\right) + 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(9 \, b x + 9 \, a\right) + 4 \, {\left(20 \, \sin\left(7 \, b x + 7 \, a\right) + 22 \, \sin\left(5 \, b x + 5 \, a\right) + 20 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) - 80 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(7 \, b x + 7 \, a\right) + 8 \, {\left(22 \, \sin\left(5 \, b x + 5 \, a\right) + 20 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 88 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(5 \, b x + 5 \, a\right) - 40 \, {\left(4 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 15 \, {\left(2 \, {\left(\cos\left(8 \, b x + 8 \, a\right) + 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) - \cos\left(10 \, b x + 10 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 4 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(8 \, b x + 8 \, a\right) + 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - \sin\left(10 \, b x + 10 \, a\right)^{2} - 2 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(15 \, \cos\left(9 \, b x + 9 \, a\right) - 20 \, \cos\left(7 \, b x + 7 \, a\right) - 22 \, \cos\left(5 \, b x + 5 \, a\right) - 20 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 60 \, {\left(\cos\left(8 \, b x + 8 \, a\right) + 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(9 \, b x + 9 \, a\right) - 4 \, {\left(20 \, \cos\left(7 \, b x + 7 \, a\right) + 22 \, \cos\left(5 \, b x + 5 \, a\right) + 20 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 80 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(7 \, b x + 7 \, a\right) - 8 \, {\left(22 \, \cos\left(5 \, b x + 5 \, a\right) + 20 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 88 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(5 \, b x + 5 \, a\right) + 40 \, {\left(4 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) - 80 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 80 \, \cos\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 60 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) + 60 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 60 \, \sin\left(b x + a\right)}{192 \, {\left(b \cos\left(10 \, b x + 10 \, a\right)^{2} + b \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(10 \, b x + 10 \, a\right)^{2} + b \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b \cos\left(8 \, b x + 8 \, a\right) + 2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(10 \, b x + 10 \, a\right) + 2 \, {\left(2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 4 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b \sin\left(8 \, b x + 8 \, a\right) + 2 \, b \sin\left(6 \, b x + 6 \, a\right) - 2 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 2 \, {\left(2 \, b \sin\left(6 \, b x + 6 \, a\right) - 2 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/192*(4*(15*sin(9*b*x + 9*a) - 20*sin(7*b*x + 7*a) - 22*sin(5*b*x + 5*a) - 20*sin(3*b*x + 3*a) + 15*sin(b*x + a))*cos(10*b*x + 10*a) + 60*(sin(8*b*x + 8*a) + 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(9*b*x + 9*a) + 4*(20*sin(7*b*x + 7*a) + 22*sin(5*b*x + 5*a) + 20*sin(3*b*x + 3*a) - 15*sin(b*x + a))*cos(8*b*x + 8*a) - 80*(2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(7*b*x + 7*a) + 8*(22*sin(5*b*x + 5*a) + 20*sin(3*b*x + 3*a) - 15*sin(b*x + a))*cos(6*b*x + 6*a) + 88*(2*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*cos(5*b*x + 5*a) - 40*(4*sin(3*b*x + 3*a) - 3*sin(b*x + a))*cos(4*b*x + 4*a) + 15*(2*(cos(8*b*x + 8*a) + 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) - cos(10*b*x + 10*a)^2 - 2*(2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - cos(8*b*x + 8*a)^2 + 4*(2*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 4*cos(6*b*x + 6*a)^2 - 4*(cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 4*cos(4*b*x + 4*a)^2 - cos(2*b*x + 2*a)^2 + 2*(sin(8*b*x + 8*a) + 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - sin(10*b*x + 10*a)^2 - 2*(2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - sin(8*b*x + 8*a)^2 + 4*(2*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 4*sin(6*b*x + 6*a)^2 - 4*sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) - 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(15*cos(9*b*x + 9*a) - 20*cos(7*b*x + 7*a) - 22*cos(5*b*x + 5*a) - 20*cos(3*b*x + 3*a) + 15*cos(b*x + a))*sin(10*b*x + 10*a) - 60*(cos(8*b*x + 8*a) + 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*sin(9*b*x + 9*a) - 4*(20*cos(7*b*x + 7*a) + 22*cos(5*b*x + 5*a) + 20*cos(3*b*x + 3*a) - 15*cos(b*x + a))*sin(8*b*x + 8*a) + 80*(2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*sin(7*b*x + 7*a) - 8*(22*cos(5*b*x + 5*a) + 20*cos(3*b*x + 3*a) - 15*cos(b*x + a))*sin(6*b*x + 6*a) - 88*(2*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*sin(5*b*x + 5*a) + 40*(4*cos(3*b*x + 3*a) - 3*cos(b*x + a))*sin(4*b*x + 4*a) - 80*(cos(2*b*x + 2*a) - 1)*sin(3*b*x + 3*a) + 80*cos(3*b*x + 3*a)*sin(2*b*x + 2*a) - 60*cos(b*x + a)*sin(2*b*x + 2*a) + 60*cos(2*b*x + 2*a)*sin(b*x + a) - 60*sin(b*x + a))/(b*cos(10*b*x + 10*a)^2 + b*cos(8*b*x + 8*a)^2 + 4*b*cos(6*b*x + 6*a)^2 + 4*b*cos(4*b*x + 4*a)^2 + b*cos(2*b*x + 2*a)^2 + b*sin(10*b*x + 10*a)^2 + b*sin(8*b*x + 8*a)^2 + 4*b*sin(6*b*x + 6*a)^2 + 4*b*sin(4*b*x + 4*a)^2 + 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + b*sin(2*b*x + 2*a)^2 - 2*(b*cos(8*b*x + 8*a) + 2*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) + b)*cos(10*b*x + 10*a) + 2*(2*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 4*(2*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 4*(b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) - 2*(b*sin(8*b*x + 8*a) + 2*b*sin(6*b*x + 6*a) - 2*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 2*(2*b*sin(6*b*x + 6*a) - 2*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 4*(2*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
140,1,3846,0,0.502477," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(105 \, \cos\left(13 \, b x + 13 \, a\right) - 70 \, \cos\left(11 \, b x + 11 \, a\right) - 329 \, \cos\left(9 \, b x + 9 \, a\right) + 204 \, \cos\left(7 \, b x + 7 \, a\right) - 329 \, \cos\left(5 \, b x + 5 \, a\right) - 70 \, \cos\left(3 \, b x + 3 \, a\right) + 105 \, \cos\left(b x + a\right)\right)} \cos\left(14 \, b x + 14 \, a\right) - 420 \, {\left(\cos\left(12 \, b x + 12 \, a\right) + 3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(13 \, b x + 13 \, a\right) + 4 \, {\left(70 \, \cos\left(11 \, b x + 11 \, a\right) + 329 \, \cos\left(9 \, b x + 9 \, a\right) - 204 \, \cos\left(7 \, b x + 7 \, a\right) + 329 \, \cos\left(5 \, b x + 5 \, a\right) + 70 \, \cos\left(3 \, b x + 3 \, a\right) - 105 \, \cos\left(b x + a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) + 280 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(11 \, b x + 11 \, a\right) + 12 \, {\left(329 \, \cos\left(9 \, b x + 9 \, a\right) - 204 \, \cos\left(7 \, b x + 7 \, a\right) + 329 \, \cos\left(5 \, b x + 5 \, a\right) + 70 \, \cos\left(3 \, b x + 3 \, a\right) - 105 \, \cos\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) - 1316 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) + 3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(9 \, b x + 9 \, a\right) + 12 \, {\left(204 \, \cos\left(7 \, b x + 7 \, a\right) - 329 \, \cos\left(5 \, b x + 5 \, a\right) - 70 \, \cos\left(3 \, b x + 3 \, a\right) + 105 \, \cos\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) + 816 \, {\left(3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(7 \, b x + 7 \, a\right) - 84 \, {\left(47 \, \cos\left(5 \, b x + 5 \, a\right) + 10 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 1316 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(5 \, b x + 5 \, a\right) + 420 \, {\left(2 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 280 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 420 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 105 \, {\left(2 \, {\left(\cos\left(12 \, b x + 12 \, a\right) + 3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(14 \, b x + 14 \, a\right) - \cos\left(14 \, b x + 14 \, a\right)^{2} - 2 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - \cos\left(12 \, b x + 12 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) + 3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 9 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 6 \, {\left(3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 9 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 9 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 6 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(12 \, b x + 12 \, a\right) + 3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - \sin\left(14 \, b x + 14 \, a\right)^{2} - 2 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - \sin\left(12 \, b x + 12 \, a\right)^{2} + 6 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) + 3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 9 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 6 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 9 \, \sin\left(8 \, b x + 8 \, a\right)^{2} + 6 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 9 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 6 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 105 \, {\left(2 \, {\left(\cos\left(12 \, b x + 12 \, a\right) + 3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(14 \, b x + 14 \, a\right) - \cos\left(14 \, b x + 14 \, a\right)^{2} - 2 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) - 3 \, \cos\left(8 \, b x + 8 \, a\right) - 3 \, \cos\left(6 \, b x + 6 \, a\right) + 3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - \cos\left(12 \, b x + 12 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) + 3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 9 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 6 \, {\left(3 \, \cos\left(6 \, b x + 6 \, a\right) - 3 \, \cos\left(4 \, b x + 4 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 9 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 9 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 6 \, {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\sin\left(12 \, b x + 12 \, a\right) + 3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - \sin\left(14 \, b x + 14 \, a\right)^{2} - 2 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - \sin\left(12 \, b x + 12 \, a\right)^{2} + 6 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) + 3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 9 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 6 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 9 \, \sin\left(8 \, b x + 8 \, a\right)^{2} + 6 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 9 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} - 6 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(105 \, \sin\left(13 \, b x + 13 \, a\right) - 70 \, \sin\left(11 \, b x + 11 \, a\right) - 329 \, \sin\left(9 \, b x + 9 \, a\right) + 204 \, \sin\left(7 \, b x + 7 \, a\right) - 329 \, \sin\left(5 \, b x + 5 \, a\right) - 70 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) - 420 \, {\left(\sin\left(12 \, b x + 12 \, a\right) + 3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(13 \, b x + 13 \, a\right) + 4 \, {\left(70 \, \sin\left(11 \, b x + 11 \, a\right) + 329 \, \sin\left(9 \, b x + 9 \, a\right) - 204 \, \sin\left(7 \, b x + 7 \, a\right) + 329 \, \sin\left(5 \, b x + 5 \, a\right) + 70 \, \sin\left(3 \, b x + 3 \, a\right) - 105 \, \sin\left(b x + a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 280 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) - 3 \, \sin\left(8 \, b x + 8 \, a\right) - 3 \, \sin\left(6 \, b x + 6 \, a\right) + 3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(11 \, b x + 11 \, a\right) + 12 \, {\left(329 \, \sin\left(9 \, b x + 9 \, a\right) - 204 \, \sin\left(7 \, b x + 7 \, a\right) + 329 \, \sin\left(5 \, b x + 5 \, a\right) + 70 \, \sin\left(3 \, b x + 3 \, a\right) - 105 \, \sin\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 1316 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) + 3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(9 \, b x + 9 \, a\right) + 12 \, {\left(204 \, \sin\left(7 \, b x + 7 \, a\right) - 329 \, \sin\left(5 \, b x + 5 \, a\right) - 70 \, \sin\left(3 \, b x + 3 \, a\right) + 105 \, \sin\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 816 \, {\left(3 \, \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(7 \, b x + 7 \, a\right) - 84 \, {\left(47 \, \sin\left(5 \, b x + 5 \, a\right) + 10 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 1316 \, {\left(3 \, \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(5 \, b x + 5 \, a\right) + 420 \, {\left(2 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 280 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 420 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 420 \, \cos\left(b x + a\right)}{1536 \, {\left(b \cos\left(14 \, b x + 14 \, a\right)^{2} + b \cos\left(12 \, b x + 12 \, a\right)^{2} + 9 \, b \cos\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \cos\left(8 \, b x + 8 \, a\right)^{2} + 9 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(14 \, b x + 14 \, a\right)^{2} + b \sin\left(12 \, b x + 12 \, a\right)^{2} + 9 \, b \sin\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \sin\left(8 \, b x + 8 \, a\right)^{2} + 9 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} + 6 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b \cos\left(12 \, b x + 12 \, a\right) + 3 \, b \cos\left(10 \, b x + 10 \, a\right) - 3 \, b \cos\left(8 \, b x + 8 \, a\right) - 3 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(14 \, b x + 14 \, a\right) + 2 \, {\left(3 \, b \cos\left(10 \, b x + 10 \, a\right) - 3 \, b \cos\left(8 \, b x + 8 \, a\right) - 3 \, b \cos\left(6 \, b x + 6 \, a\right) + 3 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(12 \, b x + 12 \, a\right) - 6 \, {\left(3 \, b \cos\left(8 \, b x + 8 \, a\right) + 3 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(10 \, b x + 10 \, a\right) + 6 \, {\left(3 \, b \cos\left(6 \, b x + 6 \, a\right) - 3 \, b \cos\left(4 \, b x + 4 \, a\right) - b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 6 \, {\left(3 \, b \cos\left(4 \, b x + 4 \, a\right) + b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 6 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b \sin\left(12 \, b x + 12 \, a\right) + 3 \, b \sin\left(10 \, b x + 10 \, a\right) - 3 \, b \sin\left(8 \, b x + 8 \, a\right) - 3 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(14 \, b x + 14 \, a\right) + 2 \, {\left(3 \, b \sin\left(10 \, b x + 10 \, a\right) - 3 \, b \sin\left(8 \, b x + 8 \, a\right) - 3 \, b \sin\left(6 \, b x + 6 \, a\right) + 3 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - 6 \, {\left(3 \, b \sin\left(8 \, b x + 8 \, a\right) + 3 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) + 6 \, {\left(3 \, b \sin\left(6 \, b x + 6 \, a\right) - 3 \, b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 6 \, {\left(3 \, b \sin\left(4 \, b x + 4 \, a\right) + b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/1536*(4*(105*cos(13*b*x + 13*a) - 70*cos(11*b*x + 11*a) - 329*cos(9*b*x + 9*a) + 204*cos(7*b*x + 7*a) - 329*cos(5*b*x + 5*a) - 70*cos(3*b*x + 3*a) + 105*cos(b*x + a))*cos(14*b*x + 14*a) - 420*(cos(12*b*x + 12*a) + 3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(13*b*x + 13*a) + 4*(70*cos(11*b*x + 11*a) + 329*cos(9*b*x + 9*a) - 204*cos(7*b*x + 7*a) + 329*cos(5*b*x + 5*a) + 70*cos(3*b*x + 3*a) - 105*cos(b*x + a))*cos(12*b*x + 12*a) + 280*(3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(11*b*x + 11*a) + 12*(329*cos(9*b*x + 9*a) - 204*cos(7*b*x + 7*a) + 329*cos(5*b*x + 5*a) + 70*cos(3*b*x + 3*a) - 105*cos(b*x + a))*cos(10*b*x + 10*a) - 1316*(3*cos(8*b*x + 8*a) + 3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(9*b*x + 9*a) + 12*(204*cos(7*b*x + 7*a) - 329*cos(5*b*x + 5*a) - 70*cos(3*b*x + 3*a) + 105*cos(b*x + a))*cos(8*b*x + 8*a) + 816*(3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(7*b*x + 7*a) - 84*(47*cos(5*b*x + 5*a) + 10*cos(3*b*x + 3*a) - 15*cos(b*x + a))*cos(6*b*x + 6*a) + 1316*(3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(5*b*x + 5*a) + 420*(2*cos(3*b*x + 3*a) - 3*cos(b*x + a))*cos(4*b*x + 4*a) + 280*(cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a) - 420*cos(2*b*x + 2*a)*cos(b*x + a) + 105*(2*(cos(12*b*x + 12*a) + 3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(14*b*x + 14*a) - cos(14*b*x + 14*a)^2 - 2*(3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - cos(12*b*x + 12*a)^2 + 6*(3*cos(8*b*x + 8*a) + 3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) - 9*cos(10*b*x + 10*a)^2 - 6*(3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 9*cos(8*b*x + 8*a)^2 + 6*(3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 9*cos(6*b*x + 6*a)^2 - 6*(cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 9*cos(4*b*x + 4*a)^2 - cos(2*b*x + 2*a)^2 + 2*(sin(12*b*x + 12*a) + 3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - sin(14*b*x + 14*a)^2 - 2*(3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - sin(12*b*x + 12*a)^2 + 6*(3*sin(8*b*x + 8*a) + 3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 9*sin(10*b*x + 10*a)^2 - 6*(3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 9*sin(8*b*x + 8*a)^2 + 6*(3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 9*sin(6*b*x + 6*a)^2 - 9*sin(4*b*x + 4*a)^2 - 6*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - 105*(2*(cos(12*b*x + 12*a) + 3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(14*b*x + 14*a) - cos(14*b*x + 14*a)^2 - 2*(3*cos(10*b*x + 10*a) - 3*cos(8*b*x + 8*a) - 3*cos(6*b*x + 6*a) + 3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - cos(12*b*x + 12*a)^2 + 6*(3*cos(8*b*x + 8*a) + 3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(10*b*x + 10*a) - 9*cos(10*b*x + 10*a)^2 - 6*(3*cos(6*b*x + 6*a) - 3*cos(4*b*x + 4*a) - cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 9*cos(8*b*x + 8*a)^2 + 6*(3*cos(4*b*x + 4*a) + cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 9*cos(6*b*x + 6*a)^2 - 6*(cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 9*cos(4*b*x + 4*a)^2 - cos(2*b*x + 2*a)^2 + 2*(sin(12*b*x + 12*a) + 3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(14*b*x + 14*a) - sin(14*b*x + 14*a)^2 - 2*(3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - sin(12*b*x + 12*a)^2 + 6*(3*sin(8*b*x + 8*a) + 3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 9*sin(10*b*x + 10*a)^2 - 6*(3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 9*sin(8*b*x + 8*a)^2 + 6*(3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 9*sin(6*b*x + 6*a)^2 - 9*sin(4*b*x + 4*a)^2 - 6*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(105*sin(13*b*x + 13*a) - 70*sin(11*b*x + 11*a) - 329*sin(9*b*x + 9*a) + 204*sin(7*b*x + 7*a) - 329*sin(5*b*x + 5*a) - 70*sin(3*b*x + 3*a) + 105*sin(b*x + a))*sin(14*b*x + 14*a) - 420*(sin(12*b*x + 12*a) + 3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(13*b*x + 13*a) + 4*(70*sin(11*b*x + 11*a) + 329*sin(9*b*x + 9*a) - 204*sin(7*b*x + 7*a) + 329*sin(5*b*x + 5*a) + 70*sin(3*b*x + 3*a) - 105*sin(b*x + a))*sin(12*b*x + 12*a) + 280*(3*sin(10*b*x + 10*a) - 3*sin(8*b*x + 8*a) - 3*sin(6*b*x + 6*a) + 3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(11*b*x + 11*a) + 12*(329*sin(9*b*x + 9*a) - 204*sin(7*b*x + 7*a) + 329*sin(5*b*x + 5*a) + 70*sin(3*b*x + 3*a) - 105*sin(b*x + a))*sin(10*b*x + 10*a) - 1316*(3*sin(8*b*x + 8*a) + 3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(9*b*x + 9*a) + 12*(204*sin(7*b*x + 7*a) - 329*sin(5*b*x + 5*a) - 70*sin(3*b*x + 3*a) + 105*sin(b*x + a))*sin(8*b*x + 8*a) + 816*(3*sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(7*b*x + 7*a) - 84*(47*sin(5*b*x + 5*a) + 10*sin(3*b*x + 3*a) - 15*sin(b*x + a))*sin(6*b*x + 6*a) + 1316*(3*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*sin(5*b*x + 5*a) + 420*(2*sin(3*b*x + 3*a) - 3*sin(b*x + a))*sin(4*b*x + 4*a) + 280*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) - 420*sin(2*b*x + 2*a)*sin(b*x + a) + 420*cos(b*x + a))/(b*cos(14*b*x + 14*a)^2 + b*cos(12*b*x + 12*a)^2 + 9*b*cos(10*b*x + 10*a)^2 + 9*b*cos(8*b*x + 8*a)^2 + 9*b*cos(6*b*x + 6*a)^2 + 9*b*cos(4*b*x + 4*a)^2 + b*cos(2*b*x + 2*a)^2 + b*sin(14*b*x + 14*a)^2 + b*sin(12*b*x + 12*a)^2 + 9*b*sin(10*b*x + 10*a)^2 + 9*b*sin(8*b*x + 8*a)^2 + 9*b*sin(6*b*x + 6*a)^2 + 9*b*sin(4*b*x + 4*a)^2 + 6*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + b*sin(2*b*x + 2*a)^2 - 2*(b*cos(12*b*x + 12*a) + 3*b*cos(10*b*x + 10*a) - 3*b*cos(8*b*x + 8*a) - 3*b*cos(6*b*x + 6*a) + 3*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) - b)*cos(14*b*x + 14*a) + 2*(3*b*cos(10*b*x + 10*a) - 3*b*cos(8*b*x + 8*a) - 3*b*cos(6*b*x + 6*a) + 3*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) - b)*cos(12*b*x + 12*a) - 6*(3*b*cos(8*b*x + 8*a) + 3*b*cos(6*b*x + 6*a) - 3*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) + b)*cos(10*b*x + 10*a) + 6*(3*b*cos(6*b*x + 6*a) - 3*b*cos(4*b*x + 4*a) - b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 6*(3*b*cos(4*b*x + 4*a) + b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 6*(b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) - 2*(b*sin(12*b*x + 12*a) + 3*b*sin(10*b*x + 10*a) - 3*b*sin(8*b*x + 8*a) - 3*b*sin(6*b*x + 6*a) + 3*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(14*b*x + 14*a) + 2*(3*b*sin(10*b*x + 10*a) - 3*b*sin(8*b*x + 8*a) - 3*b*sin(6*b*x + 6*a) + 3*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - 6*(3*b*sin(8*b*x + 8*a) + 3*b*sin(6*b*x + 6*a) - 3*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) + 6*(3*b*sin(6*b*x + 6*a) - 3*b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 6*(3*b*sin(4*b*x + 4*a) + b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
141,1,72,0,0.338303," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","-\frac{5 \, \cos\left(12 \, b x + 12 \, a\right) + 12 \, \cos\left(10 \, b x + 10 \, a\right) - 30 \, \cos\left(8 \, b x + 8 \, a\right) - 100 \, \cos\left(6 \, b x + 6 \, a\right) + 75 \, \cos\left(4 \, b x + 4 \, a\right) + 600 \, \cos\left(2 \, b x + 2 \, a\right)}{3840 \, b}"," ",0,"-1/3840*(5*cos(12*b*x + 12*a) + 12*cos(10*b*x + 10*a) - 30*cos(8*b*x + 8*a) - 100*cos(6*b*x + 6*a) + 75*cos(4*b*x + 4*a) + 600*cos(2*b*x + 2*a))/b","A",0
142,1,65,0,0.340973," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{120 \, b x + 2 \, \sin\left(10 \, b x + 10 \, a\right) + 5 \, \sin\left(8 \, b x + 8 \, a\right) - 10 \, \sin\left(6 \, b x + 6 \, a\right) - 40 \, \sin\left(4 \, b x + 4 \, a\right) + 20 \, \sin\left(2 \, b x + 2 \, a\right)}{640 \, b}"," ",0,"1/640*(120*b*x + 2*sin(10*b*x + 10*a) + 5*sin(8*b*x + 8*a) - 10*sin(6*b*x + 6*a) - 40*sin(4*b*x + 4*a) + 20*sin(2*b*x + 2*a))/b","A",0
143,1,50,0,0.336991," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{3 \, \cos\left(8 \, b x + 8 \, a\right) + 8 \, \cos\left(6 \, b x + 6 \, a\right) - 12 \, \cos\left(4 \, b x + 4 \, a\right) - 72 \, \cos\left(2 \, b x + 2 \, a\right)}{384 \, b}"," ",0,"1/384*(3*cos(8*b*x + 8*a) + 8*cos(6*b*x + 6*a) - 12*cos(4*b*x + 4*a) - 72*cos(2*b*x + 2*a))/b","A",0
144,1,43,0,0.339482," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","\frac{12 \, b x - \sin\left(6 \, b x + 6 \, a\right) - 3 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)}{48 \, b}"," ",0,"1/48*(12*b*x - sin(6*b*x + 6*a) - 3*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))/b","A",0
145,1,26,0,0.334570," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{\cos\left(4 \, b x + 4 \, a\right) + 4 \, \cos\left(2 \, b x + 2 \, a\right)}{16 \, b}"," ",0,"-1/16*(cos(4*b*x + 4*a) + 4*cos(2*b*x + 2*a))/b","A",0
146,1,82,0,0.331608," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)}{4 \, b}"," ",0,"1/4*(log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2))/b","B",0
147,1,53,0,0.332993," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","-\frac{\sin\left(2 \, b x + 2 \, a\right)}{2 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"-1/2*sin(2*b*x + 2*a)/(b*cos(2*b*x + 2*a)^2 + b*sin(2*b*x + 2*a)^2 - 2*b*cos(2*b*x + 2*a) + b)","B",0
148,1,656,0,0.350912," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{4 \, \cos\left(4 \, b x + 4 \, a\right) \cos\left(2 \, b x + 2 \, a\right) - 8 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)}{16 \, {\left(b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"1/16*(4*cos(4*b*x + 4*a)*cos(2*b*x + 2*a) - 8*cos(2*b*x + 2*a)^2 + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2) - (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 8*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a))/(b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(4*b*x + 4*a)^2 - 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 - 2*(2*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 4*b*cos(2*b*x + 2*a) + b)","B",0
149,1,308,0,0.342985," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{{\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(8 \, b x + 8 \, a\right) - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \cos\left(6 \, b x + 6 \, a\right) \sin\left(2 \, b x + 2 \, a\right)}{3 \, {\left(b \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} - 8 \, b \sin\left(6 \, b x + 6 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, b \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + b\right)}}"," ",0,"1/3*((2*cos(2*b*x + 2*a) - 1)*sin(8*b*x + 8*a) - 2*(2*cos(2*b*x + 2*a) - 1)*sin(6*b*x + 6*a) - 2*cos(8*b*x + 8*a)*sin(2*b*x + 2*a) + 4*cos(6*b*x + 6*a)*sin(2*b*x + 2*a))/(b*cos(8*b*x + 8*a)^2 + 4*b*cos(6*b*x + 6*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(8*b*x + 8*a)^2 + 4*b*sin(6*b*x + 6*a)^2 - 8*b*sin(6*b*x + 6*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 - 2*(2*b*cos(6*b*x + 6*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 4*(2*b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) - 4*b*cos(2*b*x + 2*a) - 4*(b*sin(6*b*x + 6*a) - b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + b)","B",0
150,1,3188,0,0.437173," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \cos\left(10 \, b x + 10 \, a\right) - 6 \, \cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 6 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) + 4 \, {\left(9 \, \cos\left(8 \, b x + 8 \, a\right) + 16 \, \cos\left(6 \, b x + 6 \, a\right) + 9 \, \cos\left(4 \, b x + 4 \, a\right) - 12 \, \cos\left(2 \, b x + 2 \, a\right) + 3\right)} \cos\left(10 \, b x + 10 \, a\right) - 24 \, \cos\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(22 \, \cos\left(6 \, b x + 6 \, a\right) - 12 \, \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(2 \, b x + 2 \, a\right) + 6\right)} \cos\left(8 \, b x + 8 \, a\right) + 24 \, \cos\left(8 \, b x + 8 \, a\right)^{2} - 8 \, {\left(11 \, \cos\left(4 \, b x + 4 \, a\right) - 8 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 32 \, \cos\left(6 \, b x + 6 \, a\right)^{2} + 12 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 2\right)} \cos\left(4 \, b x + 4 \, a\right) + 24 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 24 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 3 \, {\left(2 \, {\left(2 \, \cos\left(10 \, b x + 10 \, a\right) + \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - \cos\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 4 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - \cos\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 16 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(10 \, b x + 10 \, a\right) + \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - \sin\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 4 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - \sin\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 16 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(10 \, b x + 10 \, a\right) + \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - \cos\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 4 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - \cos\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 16 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(10 \, b x + 10 \, a\right) + \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - \sin\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 4 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - \sin\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 16 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(10 \, b x + 10 \, a\right) + \cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(12 \, b x + 12 \, a\right) - \cos\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\cos\left(8 \, b x + 8 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right) + \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - 4 \, \cos\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) - \cos\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - \cos\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 16 \, \cos\left(6 \, b x + 6 \, a\right)^{2} - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(10 \, b x + 10 \, a\right) + \sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) - \sin\left(12 \, b x + 12 \, a\right)^{2} - 4 \, {\left(\sin\left(8 \, b x + 8 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right) + \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 4 \, \sin\left(10 \, b x + 10 \, a\right)^{2} + 2 \, {\left(4 \, \sin\left(6 \, b x + 6 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - \sin\left(8 \, b x + 8 \, a\right)^{2} + 8 \, {\left(\sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 16 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(3 \, \sin\left(10 \, b x + 10 \, a\right) - 6 \, \sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 6 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 4 \, {\left(9 \, \sin\left(8 \, b x + 8 \, a\right) + 16 \, \sin\left(6 \, b x + 6 \, a\right) + 9 \, \sin\left(4 \, b x + 4 \, a\right) - 12 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 24 \, \sin\left(10 \, b x + 10 \, a\right)^{2} - 4 \, {\left(22 \, \sin\left(6 \, b x + 6 \, a\right) - 12 \, \sin\left(4 \, b x + 4 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 24 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 8 \, {\left(11 \, \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 32 \, \sin\left(6 \, b x + 6 \, a\right)^{2} + 24 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 36 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 24 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 12 \, \cos\left(2 \, b x + 2 \, a\right)}{64 \, {\left(b \cos\left(12 \, b x + 12 \, a\right)^{2} + 4 \, b \cos\left(10 \, b x + 10 \, a\right)^{2} + b \cos\left(8 \, b x + 8 \, a\right)^{2} + 16 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(12 \, b x + 12 \, a\right)^{2} + 4 \, b \sin\left(10 \, b x + 10 \, a\right)^{2} + b \sin\left(8 \, b x + 8 \, a\right)^{2} + 16 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(2 \, b \cos\left(10 \, b x + 10 \, a\right) + b \cos\left(8 \, b x + 8 \, a\right) - 4 \, b \cos\left(6 \, b x + 6 \, a\right) + b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(12 \, b x + 12 \, a\right) + 4 \, {\left(b \cos\left(8 \, b x + 8 \, a\right) - 4 \, b \cos\left(6 \, b x + 6 \, a\right) + b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(10 \, b x + 10 \, a\right) - 2 \, {\left(4 \, b \cos\left(6 \, b x + 6 \, a\right) - b \cos\left(4 \, b x + 4 \, a\right) - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) - 8 \, {\left(b \cos\left(4 \, b x + 4 \, a\right) + 2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(6 \, b x + 6 \, a\right) + 2 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(2 \, b \sin\left(10 \, b x + 10 \, a\right) + b \sin\left(8 \, b x + 8 \, a\right) - 4 \, b \sin\left(6 \, b x + 6 \, a\right) + b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + 4 \, {\left(b \sin\left(8 \, b x + 8 \, a\right) - 4 \, b \sin\left(6 \, b x + 6 \, a\right) + b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 2 \, {\left(4 \, b \sin\left(6 \, b x + 6 \, a\right) - b \sin\left(4 \, b x + 4 \, a\right) - 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 8 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) + 2 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/64*(4*(3*cos(10*b*x + 10*a) - 6*cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 6*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a))*cos(12*b*x + 12*a) + 4*(9*cos(8*b*x + 8*a) + 16*cos(6*b*x + 6*a) + 9*cos(4*b*x + 4*a) - 12*cos(2*b*x + 2*a) + 3)*cos(10*b*x + 10*a) - 24*cos(10*b*x + 10*a)^2 - 4*(22*cos(6*b*x + 6*a) - 12*cos(4*b*x + 4*a) - 9*cos(2*b*x + 2*a) + 6)*cos(8*b*x + 8*a) + 24*cos(8*b*x + 8*a)^2 - 8*(11*cos(4*b*x + 4*a) - 8*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - 32*cos(6*b*x + 6*a)^2 + 12*(3*cos(2*b*x + 2*a) - 2)*cos(4*b*x + 4*a) + 24*cos(4*b*x + 4*a)^2 - 24*cos(2*b*x + 2*a)^2 + 3*(2*(2*cos(10*b*x + 10*a) + cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - cos(12*b*x + 12*a)^2 - 4*(cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - 4*cos(10*b*x + 10*a)^2 + 2*(4*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - cos(8*b*x + 8*a)^2 + 8*(cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 16*cos(6*b*x + 6*a)^2 - 2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(10*b*x + 10*a) + sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - sin(12*b*x + 12*a)^2 - 4*(sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 4*sin(10*b*x + 10*a)^2 + 2*(4*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - sin(8*b*x + 8*a)^2 + 8*(sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 16*sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2) - 3*(2*(2*cos(10*b*x + 10*a) + cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - cos(12*b*x + 12*a)^2 - 4*(cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - 4*cos(10*b*x + 10*a)^2 + 2*(4*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - cos(8*b*x + 8*a)^2 + 8*(cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 16*cos(6*b*x + 6*a)^2 - 2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(10*b*x + 10*a) + sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - sin(12*b*x + 12*a)^2 - 4*(sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 4*sin(10*b*x + 10*a)^2 + 2*(4*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - sin(8*b*x + 8*a)^2 + 8*(sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 16*sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - 3*(2*(2*cos(10*b*x + 10*a) + cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(12*b*x + 12*a) - cos(12*b*x + 12*a)^2 - 4*(cos(8*b*x + 8*a) - 4*cos(6*b*x + 6*a) + cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - 4*cos(10*b*x + 10*a)^2 + 2*(4*cos(6*b*x + 6*a) - cos(4*b*x + 4*a) - 2*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - cos(8*b*x + 8*a)^2 + 8*(cos(4*b*x + 4*a) + 2*cos(2*b*x + 2*a) - 1)*cos(6*b*x + 6*a) - 16*cos(6*b*x + 6*a)^2 - 2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 + 2*(2*sin(10*b*x + 10*a) + sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) - sin(12*b*x + 12*a)^2 - 4*(sin(8*b*x + 8*a) - 4*sin(6*b*x + 6*a) + sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 4*sin(10*b*x + 10*a)^2 + 2*(4*sin(6*b*x + 6*a) - sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - sin(8*b*x + 8*a)^2 + 8*(sin(4*b*x + 4*a) + 2*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 16*sin(6*b*x + 6*a)^2 - sin(4*b*x + 4*a)^2 - 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(3*sin(10*b*x + 10*a) - 6*sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 6*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + 4*(9*sin(8*b*x + 8*a) + 16*sin(6*b*x + 6*a) + 9*sin(4*b*x + 4*a) - 12*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 24*sin(10*b*x + 10*a)^2 - 4*(22*sin(6*b*x + 6*a) - 12*sin(4*b*x + 4*a) - 9*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 24*sin(8*b*x + 8*a)^2 - 8*(11*sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 32*sin(6*b*x + 6*a)^2 + 24*sin(4*b*x + 4*a)^2 + 36*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 24*sin(2*b*x + 2*a)^2 + 12*cos(2*b*x + 2*a))/(b*cos(12*b*x + 12*a)^2 + 4*b*cos(10*b*x + 10*a)^2 + b*cos(8*b*x + 8*a)^2 + 16*b*cos(6*b*x + 6*a)^2 + b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(12*b*x + 12*a)^2 + 4*b*sin(10*b*x + 10*a)^2 + b*sin(8*b*x + 8*a)^2 + 16*b*sin(6*b*x + 6*a)^2 + b*sin(4*b*x + 4*a)^2 + 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 - 2*(2*b*cos(10*b*x + 10*a) + b*cos(8*b*x + 8*a) - 4*b*cos(6*b*x + 6*a) + b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(12*b*x + 12*a) + 4*(b*cos(8*b*x + 8*a) - 4*b*cos(6*b*x + 6*a) + b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(10*b*x + 10*a) - 2*(4*b*cos(6*b*x + 6*a) - b*cos(4*b*x + 4*a) - 2*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) - 8*(b*cos(4*b*x + 4*a) + 2*b*cos(2*b*x + 2*a) - b)*cos(6*b*x + 6*a) + 2*(2*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 4*b*cos(2*b*x + 2*a) - 2*(2*b*sin(10*b*x + 10*a) + b*sin(8*b*x + 8*a) - 4*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(12*b*x + 12*a) + 4*(b*sin(8*b*x + 8*a) - 4*b*sin(6*b*x + 6*a) + b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 2*(4*b*sin(6*b*x + 6*a) - b*sin(4*b*x + 4*a) - 2*b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 8*(b*sin(4*b*x + 4*a) + 2*b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
151,1,80,0,0.336008," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","-\frac{99 \, \cos\left(13 \, b x + 13 \, a\right) + 351 \, \cos\left(11 \, b x + 11 \, a\right) - 286 \, \cos\left(9 \, b x + 9 \, a\right) - 2574 \, \cos\left(7 \, b x + 7 \, a\right) - 1287 \, \cos\left(5 \, b x + 5 \, a\right) + 10725 \, \cos\left(3 \, b x + 3 \, a\right) + 25740 \, \cos\left(b x + a\right)}{164736 \, b}"," ",0,"-1/164736*(99*cos(13*b*x + 13*a) + 351*cos(11*b*x + 11*a) - 286*cos(9*b*x + 9*a) - 2574*cos(7*b*x + 7*a) - 1287*cos(5*b*x + 5*a) + 10725*cos(3*b*x + 3*a) + 25740*cos(b*x + a))/b","A",0
152,1,69,0,0.340073," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{105 \, \sin\left(11 \, b x + 11 \, a\right) + 385 \, \sin\left(9 \, b x + 9 \, a\right) - 165 \, \sin\left(7 \, b x + 7 \, a\right) - 2541 \, \sin\left(5 \, b x + 5 \, a\right) - 2310 \, \sin\left(3 \, b x + 3 \, a\right) + 16170 \, \sin\left(b x + a\right)}{73920 \, b}"," ",0,"1/73920*(105*sin(11*b*x + 11*a) + 385*sin(9*b*x + 9*a) - 165*sin(7*b*x + 7*a) - 2541*sin(5*b*x + 5*a) - 2310*sin(3*b*x + 3*a) + 16170*sin(b*x + a))/b","A",0
153,1,47,0,0.329395," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{7 \, \cos\left(9 \, b x + 9 \, a\right) + 27 \, \cos\left(7 \, b x + 7 \, a\right) - 168 \, \cos\left(3 \, b x + 3 \, a\right) - 378 \, \cos\left(b x + a\right)}{2016 \, b}"," ",0,"1/2016*(7*cos(9*b*x + 9*a) + 27*cos(7*b*x + 7*a) - 168*cos(3*b*x + 3*a) - 378*cos(b*x + a))/b","A",0
154,1,47,0,0.330265," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","-\frac{15 \, \sin\left(7 \, b x + 7 \, a\right) + 63 \, \sin\left(5 \, b x + 5 \, a\right) + 35 \, \sin\left(3 \, b x + 3 \, a\right) - 525 \, \sin\left(b x + a\right)}{1680 \, b}"," ",0,"-1/1680*(15*sin(7*b*x + 7*a) + 63*sin(5*b*x + 5*a) + 35*sin(3*b*x + 3*a) - 525*sin(b*x + a))/b","A",0
155,1,34,0,0.326139," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{\cos\left(5 \, b x + 5 \, a\right) + 5 \, \cos\left(3 \, b x + 3 \, a\right) + 10 \, \cos\left(b x + a\right)}{40 \, b}"," ",0,"-1/40*(cos(5*b*x + 5*a) + 5*cos(3*b*x + 3*a) + 10*cos(b*x + a))/b","B",0
156,1,92,0,0.343021," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a),x, algorithm=""maxima"")","\frac{2 \, \cos\left(b x + a\right) - \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)}{4 \, b}"," ",0,"1/4*(2*cos(b*x + a) - log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2))/b","B",0
157,1,84,0,0.336728," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","-\frac{\cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)}{2 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"-1/2*(cos(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))/(b*cos(2*b*x + 2*a)^2 + b*sin(2*b*x + 2*a)^2 - 2*b*cos(2*b*x + 2*a) + b)","B",0
158,1,558,0,0.345294," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(\cos\left(3 \, b x + 3 \, a\right) + \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 8 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(\sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, \cos\left(b x + a\right)}{32 \, {\left(b \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(2 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"1/32*(4*(cos(3*b*x + 3*a) + cos(b*x + a))*cos(4*b*x + 4*a) - 4*(2*cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a) - 8*cos(2*b*x + 2*a)*cos(b*x + a) + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(sin(3*b*x + 3*a) + sin(b*x + a))*sin(4*b*x + 4*a) - 8*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) - 8*sin(2*b*x + 2*a)*sin(b*x + a) + 4*cos(b*x + a))/(b*cos(4*b*x + 4*a)^2 + 4*b*cos(2*b*x + 2*a)^2 + b*sin(4*b*x + 4*a)^2 - 4*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*b*sin(2*b*x + 2*a)^2 - 2*(2*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 4*b*cos(2*b*x + 2*a) + b)","B",0
159,1,834,0,0.656233," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, \sin\left(5 \, b x + 5 \, a\right) - 10 \, \sin\left(3 \, b x + 3 \, a\right) + 3 \, \sin\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 36 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(5 \, b x + 5 \, a\right) + 12 \, {\left(10 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - \cos\left(6 \, b x + 6 \, a\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 9 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 6 \, {\left(\sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - \sin\left(6 \, b x + 6 \, a\right)^{2} - 9 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 18 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(3 \, \cos\left(5 \, b x + 5 \, a\right) - 10 \, \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 12 \, {\left(3 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(5 \, b x + 5 \, a\right) - 12 \, {\left(10 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) - 40 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 120 \, \cos\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 36 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) + 36 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 12 \, \sin\left(b x + a\right)}{96 \, {\left(b \cos\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + 9 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(6 \, b x + 6 \, a\right)^{2} + 9 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} - 18 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(3 \, b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left(3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, b \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b \sin\left(4 \, b x + 4 \, a\right) - b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/96*(4*(3*sin(5*b*x + 5*a) - 10*sin(3*b*x + 3*a) + 3*sin(b*x + a))*cos(6*b*x + 6*a) + 36*(sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*cos(5*b*x + 5*a) + 12*(10*sin(3*b*x + 3*a) - 3*sin(b*x + a))*cos(4*b*x + 4*a) + 3*(2*(3*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - cos(6*b*x + 6*a)^2 + 6*(3*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 9*cos(4*b*x + 4*a)^2 - 9*cos(2*b*x + 2*a)^2 + 6*(sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - sin(6*b*x + 6*a)^2 - 9*sin(4*b*x + 4*a)^2 + 18*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) - 1)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(3*cos(5*b*x + 5*a) - 10*cos(3*b*x + 3*a) + 3*cos(b*x + a))*sin(6*b*x + 6*a) - 12*(3*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*sin(5*b*x + 5*a) - 12*(10*cos(3*b*x + 3*a) - 3*cos(b*x + a))*sin(4*b*x + 4*a) - 40*(3*cos(2*b*x + 2*a) - 1)*sin(3*b*x + 3*a) + 120*cos(3*b*x + 3*a)*sin(2*b*x + 2*a) - 36*cos(b*x + a)*sin(2*b*x + 2*a) + 36*cos(2*b*x + 2*a)*sin(b*x + a) - 12*sin(b*x + a))/(b*cos(6*b*x + 6*a)^2 + 9*b*cos(4*b*x + 4*a)^2 + 9*b*cos(2*b*x + 2*a)^2 + b*sin(6*b*x + 6*a)^2 + 9*b*sin(4*b*x + 4*a)^2 - 18*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 9*b*sin(2*b*x + 2*a)^2 - 2*(3*b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(6*b*x + 6*a) - 6*(3*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 6*b*cos(2*b*x + 2*a) - 6*(b*sin(4*b*x + 4*a) - b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
160,1,2237,0,0.414662," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(15 \, \cos\left(9 \, b x + 9 \, a\right) - 40 \, \cos\left(7 \, b x + 7 \, a\right) + 18 \, \cos\left(5 \, b x + 5 \, a\right) - 40 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \cos\left(10 \, b x + 10 \, a\right) - 60 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(9 \, b x + 9 \, a\right) + 12 \, {\left(40 \, \cos\left(7 \, b x + 7 \, a\right) - 18 \, \cos\left(5 \, b x + 5 \, a\right) + 40 \, \cos\left(3 \, b x + 3 \, a\right) - 15 \, \cos\left(b x + a\right)\right)} \cos\left(8 \, b x + 8 \, a\right) - 160 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(7 \, b x + 7 \, a\right) + 8 \, {\left(18 \, \cos\left(5 \, b x + 5 \, a\right) - 40 \, \cos\left(3 \, b x + 3 \, a\right) + 15 \, \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 6 \, a\right) + 72 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(5 \, b x + 5 \, a\right) - 40 \, {\left(8 \, \cos\left(3 \, b x + 3 \, a\right) - 3 \, \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 160 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 180 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 15 \, {\left(2 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - \cos\left(10 \, b x + 10 \, a\right)^{2} + 6 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 9 \, \cos\left(8 \, b x + 8 \, a\right)^{2} - 4 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - \sin\left(10 \, b x + 10 \, a\right)^{2} + 6 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) + 2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 9 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 4 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 12 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - 15 \, {\left(2 \, {\left(3 \, \cos\left(8 \, b x + 8 \, a\right) - 2 \, \cos\left(6 \, b x + 6 \, a\right) - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(10 \, b x + 10 \, a\right) - \cos\left(10 \, b x + 10 \, a\right)^{2} + 6 \, {\left(2 \, \cos\left(6 \, b x + 6 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(8 \, b x + 8 \, a\right) - 9 \, \cos\left(8 \, b x + 8 \, a\right)^{2} - 4 \, {\left(2 \, \cos\left(4 \, b x + 4 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(4 \, b x + 4 \, a\right)^{2} - 9 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - \sin\left(10 \, b x + 10 \, a\right)^{2} + 6 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) + 2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 9 \, \sin\left(8 \, b x + 8 \, a\right)^{2} - 4 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) - 4 \, \sin\left(6 \, b x + 6 \, a\right)^{2} - 4 \, \sin\left(4 \, b x + 4 \, a\right)^{2} + 12 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 9 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 6 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 4 \, {\left(15 \, \sin\left(9 \, b x + 9 \, a\right) - 40 \, \sin\left(7 \, b x + 7 \, a\right) + 18 \, \sin\left(5 \, b x + 5 \, a\right) - 40 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 60 \, {\left(3 \, \sin\left(8 \, b x + 8 \, a\right) - 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(9 \, b x + 9 \, a\right) + 12 \, {\left(40 \, \sin\left(7 \, b x + 7 \, a\right) - 18 \, \sin\left(5 \, b x + 5 \, a\right) + 40 \, \sin\left(3 \, b x + 3 \, a\right) - 15 \, \sin\left(b x + a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) - 160 \, {\left(2 \, \sin\left(6 \, b x + 6 \, a\right) + 2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(7 \, b x + 7 \, a\right) + 8 \, {\left(18 \, \sin\left(5 \, b x + 5 \, a\right) - 40 \, \sin\left(3 \, b x + 3 \, a\right) + 15 \, \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + 72 \, {\left(2 \, \sin\left(4 \, b x + 4 \, a\right) - 3 \, \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(5 \, b x + 5 \, a\right) - 40 \, {\left(8 \, \sin\left(3 \, b x + 3 \, a\right) - 3 \, \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 480 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 180 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 60 \, \cos\left(b x + a\right)}{512 \, {\left(b \cos\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \cos\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \cos\left(4 \, b x + 4 \, a\right)^{2} + 9 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(10 \, b x + 10 \, a\right)^{2} + 9 \, b \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, b \sin\left(6 \, b x + 6 \, a\right)^{2} + 4 \, b \sin\left(4 \, b x + 4 \, a\right)^{2} - 12 \, b \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 9 \, b \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(3 \, b \cos\left(8 \, b x + 8 \, a\right) - 2 \, b \cos\left(6 \, b x + 6 \, a\right) - 2 \, b \cos\left(4 \, b x + 4 \, a\right) + 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(10 \, b x + 10 \, a\right) - 6 \, {\left(2 \, b \cos\left(6 \, b x + 6 \, a\right) + 2 \, b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(8 \, b x + 8 \, a\right) + 4 \, {\left(2 \, b \cos\left(4 \, b x + 4 \, a\right) - 3 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \cos\left(6 \, b x + 6 \, a\right) - 4 \, {\left(3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, b \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(3 \, b \sin\left(8 \, b x + 8 \, a\right) - 2 \, b \sin\left(6 \, b x + 6 \, a\right) - 2 \, b \sin\left(4 \, b x + 4 \, a\right) + 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(10 \, b x + 10 \, a\right) - 6 \, {\left(2 \, b \sin\left(6 \, b x + 6 \, a\right) + 2 \, b \sin\left(4 \, b x + 4 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(8 \, b x + 8 \, a\right) + 4 \, {\left(2 \, b \sin\left(4 \, b x + 4 \, a\right) - 3 \, b \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(6 \, b x + 6 \, a\right) + b\right)}}"," ",0,"1/512*(4*(15*cos(9*b*x + 9*a) - 40*cos(7*b*x + 7*a) + 18*cos(5*b*x + 5*a) - 40*cos(3*b*x + 3*a) + 15*cos(b*x + a))*cos(10*b*x + 10*a) - 60*(3*cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*cos(9*b*x + 9*a) + 12*(40*cos(7*b*x + 7*a) - 18*cos(5*b*x + 5*a) + 40*cos(3*b*x + 3*a) - 15*cos(b*x + a))*cos(8*b*x + 8*a) - 160*(2*cos(6*b*x + 6*a) + 2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(7*b*x + 7*a) + 8*(18*cos(5*b*x + 5*a) - 40*cos(3*b*x + 3*a) + 15*cos(b*x + a))*cos(6*b*x + 6*a) + 72*(2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(5*b*x + 5*a) - 40*(8*cos(3*b*x + 3*a) - 3*cos(b*x + a))*cos(4*b*x + 4*a) + 160*(3*cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a) - 180*cos(2*b*x + 2*a)*cos(b*x + a) + 15*(2*(3*cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - cos(10*b*x + 10*a)^2 + 6*(2*cos(6*b*x + 6*a) + 2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 9*cos(8*b*x + 8*a)^2 - 4*(2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - 4*cos(6*b*x + 6*a)^2 + 4*(3*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 4*cos(4*b*x + 4*a)^2 - 9*cos(2*b*x + 2*a)^2 + 2*(3*sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - sin(10*b*x + 10*a)^2 + 6*(2*sin(6*b*x + 6*a) + 2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 9*sin(8*b*x + 8*a)^2 - 4*(2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 4*sin(6*b*x + 6*a)^2 - 4*sin(4*b*x + 4*a)^2 + 12*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - 15*(2*(3*cos(8*b*x + 8*a) - 2*cos(6*b*x + 6*a) - 2*cos(4*b*x + 4*a) + 3*cos(2*b*x + 2*a) - 1)*cos(10*b*x + 10*a) - cos(10*b*x + 10*a)^2 + 6*(2*cos(6*b*x + 6*a) + 2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(8*b*x + 8*a) - 9*cos(8*b*x + 8*a)^2 - 4*(2*cos(4*b*x + 4*a) - 3*cos(2*b*x + 2*a) + 1)*cos(6*b*x + 6*a) - 4*cos(6*b*x + 6*a)^2 + 4*(3*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - 4*cos(4*b*x + 4*a)^2 - 9*cos(2*b*x + 2*a)^2 + 2*(3*sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - sin(10*b*x + 10*a)^2 + 6*(2*sin(6*b*x + 6*a) + 2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) - 9*sin(8*b*x + 8*a)^2 - 4*(2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) - 4*sin(6*b*x + 6*a)^2 - 4*sin(4*b*x + 4*a)^2 + 12*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 9*sin(2*b*x + 2*a)^2 + 6*cos(2*b*x + 2*a) - 1)*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + 4*(15*sin(9*b*x + 9*a) - 40*sin(7*b*x + 7*a) + 18*sin(5*b*x + 5*a) - 40*sin(3*b*x + 3*a) + 15*sin(b*x + a))*sin(10*b*x + 10*a) - 60*(3*sin(8*b*x + 8*a) - 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) + 3*sin(2*b*x + 2*a))*sin(9*b*x + 9*a) + 12*(40*sin(7*b*x + 7*a) - 18*sin(5*b*x + 5*a) + 40*sin(3*b*x + 3*a) - 15*sin(b*x + a))*sin(8*b*x + 8*a) - 160*(2*sin(6*b*x + 6*a) + 2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(7*b*x + 7*a) + 8*(18*sin(5*b*x + 5*a) - 40*sin(3*b*x + 3*a) + 15*sin(b*x + a))*sin(6*b*x + 6*a) + 72*(2*sin(4*b*x + 4*a) - 3*sin(2*b*x + 2*a))*sin(5*b*x + 5*a) - 40*(8*sin(3*b*x + 3*a) - 3*sin(b*x + a))*sin(4*b*x + 4*a) + 480*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) - 180*sin(2*b*x + 2*a)*sin(b*x + a) + 60*cos(b*x + a))/(b*cos(10*b*x + 10*a)^2 + 9*b*cos(8*b*x + 8*a)^2 + 4*b*cos(6*b*x + 6*a)^2 + 4*b*cos(4*b*x + 4*a)^2 + 9*b*cos(2*b*x + 2*a)^2 + b*sin(10*b*x + 10*a)^2 + 9*b*sin(8*b*x + 8*a)^2 + 4*b*sin(6*b*x + 6*a)^2 + 4*b*sin(4*b*x + 4*a)^2 - 12*b*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 9*b*sin(2*b*x + 2*a)^2 - 2*(3*b*cos(8*b*x + 8*a) - 2*b*cos(6*b*x + 6*a) - 2*b*cos(4*b*x + 4*a) + 3*b*cos(2*b*x + 2*a) - b)*cos(10*b*x + 10*a) - 6*(2*b*cos(6*b*x + 6*a) + 2*b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(8*b*x + 8*a) + 4*(2*b*cos(4*b*x + 4*a) - 3*b*cos(2*b*x + 2*a) + b)*cos(6*b*x + 6*a) - 4*(3*b*cos(2*b*x + 2*a) - b)*cos(4*b*x + 4*a) - 6*b*cos(2*b*x + 2*a) - 2*(3*b*sin(8*b*x + 8*a) - 2*b*sin(6*b*x + 6*a) - 2*b*sin(4*b*x + 4*a) + 3*b*sin(2*b*x + 2*a))*sin(10*b*x + 10*a) - 6*(2*b*sin(6*b*x + 6*a) + 2*b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(8*b*x + 8*a) + 4*(2*b*sin(4*b*x + 4*a) - 3*b*sin(2*b*x + 2*a))*sin(6*b*x + 6*a) + b)","B",0
161,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)*sin(2*b*x + 2*a)^(5/2), x)","F",0
162,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)*sin(2*b*x + 2*a)^(3/2), x)","F",0
163,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right) \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(cos(b*x + a)*sqrt(sin(2*b*x + 2*a)), x)","F",0
164,0,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(cos(b*x + a)/sqrt(sin(2*b*x + 2*a)), x)","F",0
165,0,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/sin(2*b*x + 2*a)^(3/2), x)","F",0
166,0,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/sin(2*b*x + 2*a)^(5/2), x)","F",0
167,0,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/sin(2*b*x + 2*a)^(7/2), x)","F",0
168,0,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(9/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/sin(2*b*x + 2*a)^(9/2), x)","F",0
169,0,0,0,0.000000," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2*sin(2*b*x + 2*a)^(7/2), x)","F",0
170,0,0,0,0.000000," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2*sin(2*b*x + 2*a)^(5/2), x)","F",0
171,0,0,0,0.000000," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2*sin(2*b*x + 2*a)^(3/2), x)","F",0
172,0,0,0,0.000000," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(cos(b*x + a)^2*sqrt(sin(2*b*x + 2*a)), x)","F",0
173,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{2}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/sqrt(sin(2*b*x + 2*a)), x)","F",0
174,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/sin(2*b*x + 2*a)^(3/2), x)","F",0
175,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/sin(2*b*x + 2*a)^(5/2), x)","F",0
176,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/sin(2*b*x + 2*a)^(7/2), x)","F",0
177,0,0,0,0.000000," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{3} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3*sin(2*b*x + 2*a)^(3/2), x)","F",0
178,0,0,0,0.000000," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{3} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(cos(b*x + a)^3*sqrt(sin(2*b*x + 2*a)), x)","F",0
179,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sqrt(sin(2*b*x + 2*a)), x)","F",0
180,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sin(2*b*x + 2*a)^(3/2), x)","F",0
181,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sin(2*b*x + 2*a)^(5/2), x)","F",0
182,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(7/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sin(2*b*x + 2*a)^(7/2), x)","F",0
183,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(9/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sin(2*b*x + 2*a)^(9/2), x)","F",0
184,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(11/2),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sin(2*b*x + 2*a)^(11/2), x)","F",0
185,0,0,0,0.000000," ","integrate(cos(x)/sin(2*x)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(x\right)}{\sqrt{\sin\left(2 \, x\right)}}\,{d x}"," ",0,"integrate(cos(x)/sqrt(sin(2*x)), x)","F",0
186,0,0,0,0.000000," ","integrate(csc(x)*sin(2*x)^(1/2),x, algorithm=""maxima"")","\int \csc\left(x\right) \sqrt{\sin\left(2 \, x\right)}\,{d x}"," ",0,"integrate(csc(x)*sqrt(sin(2*x)), x)","F",0
187,0,0,0,0.000000," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^m,x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \cos\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*cos(b*x + a)^3, x)","F",0
188,0,0,0,0.000000," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^m,x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \cos\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*cos(b*x + a)^2, x)","F",0
189,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^m,x, algorithm=""maxima"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*cos(b*x + a), x)","F",0
190,1,58,0,0.341440," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""maxima"")","-\frac{35 \, \cos\left(9 \, b x + 9 \, a\right) - 45 \, \cos\left(7 \, b x + 7 \, a\right) - 252 \, \cos\left(5 \, b x + 5 \, a\right) + 420 \, \cos\left(3 \, b x + 3 \, a\right) + 1890 \, \cos\left(b x + a\right)}{20160 \, b}"," ",0,"-1/20160*(35*cos(9*b*x + 9*a) - 45*cos(7*b*x + 7*a) - 252*cos(5*b*x + 5*a) + 420*cos(3*b*x + 3*a) + 1890*cos(b*x + a))/b","A",0
191,0,0,0,0.000000," ","integrate(sin(b*x+a)*sin(d*x+c)^n,x, algorithm=""maxima"")","\int \sin\left(d x + c\right)^{n} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(sin(d*x + c)^n*sin(b*x + a), x)","F",0
192,1,916,0,0.413885," ","integrate(sin(b*x+a)*sin(d*x+c)^3,x, algorithm=""maxima"")","-\frac{{\left(b^{3} \sin\left(3 \, c\right) - 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) + 3 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) - {\left(b^{3} \sin\left(3 \, c\right) - 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) + 3 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a\right) - 3 \, {\left(b^{3} \sin\left(3 \, c\right) - b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) + 9 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a + 4 \, c\right) + 3 \, {\left(b^{3} \sin\left(3 \, c\right) - b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) + 9 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a - 2 \, c\right) - 3 \, {\left(b^{3} \sin\left(3 \, c\right) + b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) - 9 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a + 4 \, c\right) + 3 \, {\left(b^{3} \sin\left(3 \, c\right) + b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) - 9 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a - 2 \, c\right) + {\left(b^{3} \sin\left(3 \, c\right) + 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) - 3 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) - {\left(b^{3} \sin\left(3 \, c\right) + 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) - 3 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a\right) - {\left(b^{3} \cos\left(3 \, c\right) - 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) + 3 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) - {\left(b^{3} \cos\left(3 \, c\right) - 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) + 3 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a\right) + 3 \, {\left(b^{3} \cos\left(3 \, c\right) - b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) + 9 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a + 4 \, c\right) + 3 \, {\left(b^{3} \cos\left(3 \, c\right) - b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) + 9 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a - 2 \, c\right) + 3 \, {\left(b^{3} \cos\left(3 \, c\right) + b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) - 9 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a + 4 \, c\right) + 3 \, {\left(b^{3} \cos\left(3 \, c\right) + b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) - 9 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a - 2 \, c\right) - {\left(b^{3} \cos\left(3 \, c\right) + 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) - 3 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) - {\left(b^{3} \cos\left(3 \, c\right) + 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) - 3 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a\right)}{16 \, {\left(b^{4} \cos\left(3 \, c\right)^{2} + b^{4} \sin\left(3 \, c\right)^{2} + 9 \, {\left(\cos\left(3 \, c\right)^{2} + \sin\left(3 \, c\right)^{2}\right)} d^{4} - 10 \, {\left(b^{2} \cos\left(3 \, c\right)^{2} + b^{2} \sin\left(3 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"-1/16*((b^3*sin(3*c) - 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) + 3*d^3*sin(3*c))*cos((b + 3*d)*x + a + 6*c) - (b^3*sin(3*c) - 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) + 3*d^3*sin(3*c))*cos((b + 3*d)*x + a) - 3*(b^3*sin(3*c) - b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) + 9*d^3*sin(3*c))*cos((b + d)*x + a + 4*c) + 3*(b^3*sin(3*c) - b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) + 9*d^3*sin(3*c))*cos((b + d)*x + a - 2*c) - 3*(b^3*sin(3*c) + b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) - 9*d^3*sin(3*c))*cos(-(b - d)*x - a + 4*c) + 3*(b^3*sin(3*c) + b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) - 9*d^3*sin(3*c))*cos(-(b - d)*x - a - 2*c) + (b^3*sin(3*c) + 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) - 3*d^3*sin(3*c))*cos(-(b - 3*d)*x - a + 6*c) - (b^3*sin(3*c) + 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) - 3*d^3*sin(3*c))*cos(-(b - 3*d)*x - a) - (b^3*cos(3*c) - 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) + 3*d^3*cos(3*c))*sin((b + 3*d)*x + a + 6*c) - (b^3*cos(3*c) - 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) + 3*d^3*cos(3*c))*sin((b + 3*d)*x + a) + 3*(b^3*cos(3*c) - b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) + 9*d^3*cos(3*c))*sin((b + d)*x + a + 4*c) + 3*(b^3*cos(3*c) - b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) + 9*d^3*cos(3*c))*sin((b + d)*x + a - 2*c) + 3*(b^3*cos(3*c) + b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) - 9*d^3*cos(3*c))*sin(-(b - d)*x - a + 4*c) + 3*(b^3*cos(3*c) + b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) - 9*d^3*cos(3*c))*sin(-(b - d)*x - a - 2*c) - (b^3*cos(3*c) + 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) - 3*d^3*cos(3*c))*sin(-(b - 3*d)*x - a + 6*c) - (b^3*cos(3*c) + 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) - 3*d^3*cos(3*c))*sin(-(b - 3*d)*x - a))/(b^4*cos(3*c)^2 + b^4*sin(3*c)^2 + 9*(cos(3*c)^2 + sin(3*c)^2)*d^4 - 10*(b^2*cos(3*c)^2 + b^2*sin(3*c)^2)*d^2)","B",0
193,1,414,0,0.348488," ","integrate(sin(b*x+a)*sin(d*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} \cos\left(2 \, c\right) - 2 \, b d \cos\left(2 \, c\right)\right)} \cos\left({\left(b + 2 \, d\right)} x + a + 4 \, c\right) + {\left(b^{2} \cos\left(2 \, c\right) - 2 \, b d \cos\left(2 \, c\right)\right)} \cos\left({\left(b + 2 \, d\right)} x + a\right) + {\left(b^{2} \cos\left(2 \, c\right) + 2 \, b d \cos\left(2 \, c\right)\right)} \cos\left(-{\left(b - 2 \, d\right)} x - a + 4 \, c\right) + {\left(b^{2} \cos\left(2 \, c\right) + 2 \, b d \cos\left(2 \, c\right)\right)} \cos\left(-{\left(b - 2 \, d\right)} x - a\right) - 2 \, {\left(b^{2} \cos\left(2 \, c\right) - 4 \, d^{2} \cos\left(2 \, c\right)\right)} \cos\left(b x + a + 2 \, c\right) - 2 \, {\left(b^{2} \cos\left(2 \, c\right) - 4 \, d^{2} \cos\left(2 \, c\right)\right)} \cos\left(b x + a - 2 \, c\right) + {\left(b^{2} \sin\left(2 \, c\right) - 2 \, b d \sin\left(2 \, c\right)\right)} \sin\left({\left(b + 2 \, d\right)} x + a + 4 \, c\right) - {\left(b^{2} \sin\left(2 \, c\right) - 2 \, b d \sin\left(2 \, c\right)\right)} \sin\left({\left(b + 2 \, d\right)} x + a\right) + {\left(b^{2} \sin\left(2 \, c\right) + 2 \, b d \sin\left(2 \, c\right)\right)} \sin\left(-{\left(b - 2 \, d\right)} x - a + 4 \, c\right) - {\left(b^{2} \sin\left(2 \, c\right) + 2 \, b d \sin\left(2 \, c\right)\right)} \sin\left(-{\left(b - 2 \, d\right)} x - a\right) - 2 \, {\left(b^{2} \sin\left(2 \, c\right) - 4 \, d^{2} \sin\left(2 \, c\right)\right)} \sin\left(b x + a + 2 \, c\right) + 2 \, {\left(b^{2} \sin\left(2 \, c\right) - 4 \, d^{2} \sin\left(2 \, c\right)\right)} \sin\left(b x + a - 2 \, c\right)}{8 \, {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2} - 4 \, {\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"1/8*((b^2*cos(2*c) - 2*b*d*cos(2*c))*cos((b + 2*d)*x + a + 4*c) + (b^2*cos(2*c) - 2*b*d*cos(2*c))*cos((b + 2*d)*x + a) + (b^2*cos(2*c) + 2*b*d*cos(2*c))*cos(-(b - 2*d)*x - a + 4*c) + (b^2*cos(2*c) + 2*b*d*cos(2*c))*cos(-(b - 2*d)*x - a) - 2*(b^2*cos(2*c) - 4*d^2*cos(2*c))*cos(b*x + a + 2*c) - 2*(b^2*cos(2*c) - 4*d^2*cos(2*c))*cos(b*x + a - 2*c) + (b^2*sin(2*c) - 2*b*d*sin(2*c))*sin((b + 2*d)*x + a + 4*c) - (b^2*sin(2*c) - 2*b*d*sin(2*c))*sin((b + 2*d)*x + a) + (b^2*sin(2*c) + 2*b*d*sin(2*c))*sin(-(b - 2*d)*x - a + 4*c) - (b^2*sin(2*c) + 2*b*d*sin(2*c))*sin(-(b - 2*d)*x - a) - 2*(b^2*sin(2*c) - 4*d^2*sin(2*c))*sin(b*x + a + 2*c) + 2*(b^2*sin(2*c) - 4*d^2*sin(2*c))*sin(b*x + a - 2*c))/(b^3*cos(2*c)^2 + b^3*sin(2*c)^2 - 4*(b*cos(2*c)^2 + b*sin(2*c)^2)*d^2)","B",0
194,1,40,0,0.318580," ","integrate(sin(b*x+a)*sin(d*x+c),x, algorithm=""maxima"")","-\frac{\sin\left(b x + d x + a + c\right)}{2 \, {\left(b + d\right)}} - \frac{\sin\left(-b x + d x - a + c\right)}{2 \, {\left(b - d\right)}}"," ",0,"-1/2*sin(b*x + d*x + a + c)/(b + d) - 1/2*sin(-b*x + d*x - a + c)/(b - d)","A",0
195,1,108,0,0.396226," ","integrate(csc(b*x+c)*sin(b*x+a),x, algorithm=""maxima"")","\frac{2 \, b x \cos\left(-a + c\right) - \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) \sin\left(-a + c\right) - \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) \sin\left(-a + c\right)}{2 \, b}"," ",0,"1/2*(2*b*x*cos(-a + c) - log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2)*sin(-a + c) - log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2)*sin(-a + c))/b","B",0
196,1,454,0,0.363254," ","integrate(csc(b*x+c)^2*sin(b*x+a),x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(b x + 2 \, a\right) - \cos\left(b x + 2 \, c\right)\right)} \cos\left(2 \, b x + a + 2 \, c\right) - 2 \, \cos\left(b x + 2 \, a\right) \cos\left(a\right) + 2 \, \cos\left(b x + 2 \, c\right) \cos\left(a\right) + {\left(\cos\left(2 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) - 2 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right)^{2} - 2 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(-a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - {\left(\cos\left(2 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) - 2 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right)^{2} - 2 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(-a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + 2 \, {\left(\sin\left(b x + 2 \, a\right) - \sin\left(b x + 2 \, c\right)\right)} \sin\left(2 \, b x + a + 2 \, c\right) - 2 \, \sin\left(b x + 2 \, a\right) \sin\left(a\right) + 2 \, \sin\left(b x + 2 \, c\right) \sin\left(a\right)}{2 \, {\left(b \cos\left(2 \, b x + a + 2 \, c\right)^{2} - 2 \, b \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) + b \sin\left(2 \, b x + a + 2 \, c\right)^{2} - 2 \, b \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b\right)}}"," ",0,"-1/2*(2*(cos(b*x + 2*a) - cos(b*x + 2*c))*cos(2*b*x + a + 2*c) - 2*cos(b*x + 2*a)*cos(a) + 2*cos(b*x + 2*c)*cos(a) + (cos(2*b*x + a + 2*c)^2*cos(-a + c) - 2*cos(2*b*x + a + 2*c)*cos(a)*cos(-a + c) + cos(-a + c)*sin(2*b*x + a + 2*c)^2 - 2*cos(-a + c)*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*cos(-a + c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) - (cos(2*b*x + a + 2*c)^2*cos(-a + c) - 2*cos(2*b*x + a + 2*c)*cos(a)*cos(-a + c) + cos(-a + c)*sin(2*b*x + a + 2*c)^2 - 2*cos(-a + c)*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*cos(-a + c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2) + 2*(sin(b*x + 2*a) - sin(b*x + 2*c))*sin(2*b*x + a + 2*c) - 2*sin(b*x + 2*a)*sin(a) + 2*sin(b*x + 2*c)*sin(a))/(b*cos(2*b*x + a + 2*c)^2 - 2*b*cos(2*b*x + a + 2*c)*cos(a) + b*sin(2*b*x + a + 2*c)^2 - 2*b*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*b)","B",0
197,1,399,0,0.336069," ","integrate(csc(b*x+c)^3*sin(b*x+a),x, algorithm=""maxima"")","\frac{{\left(2 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - \sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) - 2 \, {\left(2 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - \sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \cos\left(2 \, b x + a + 3 \, c\right) - {\left(\sin\left(2 \, a\right) + \sin\left(2 \, c\right)\right)} \cos\left(a + c\right) - {\left(2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - \cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right) + 2 \, \cos\left(a + c\right) \sin\left(2 \, b x + 2 \, a + 2 \, c\right) + 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - \cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \sin\left(2 \, b x + a + 3 \, c\right) + {\left(\cos\left(2 \, a\right) + \cos\left(2 \, c\right)\right)} \sin\left(a + c\right) - 2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) \sin\left(a + c\right)}{b \cos\left(4 \, b x + a + 5 \, c\right)^{2} + 4 \, b \cos\left(2 \, b x + a + 3 \, c\right)^{2} - 4 \, b \cos\left(2 \, b x + a + 3 \, c\right) \cos\left(a + c\right) + b \cos\left(a + c\right)^{2} + b \sin\left(4 \, b x + a + 5 \, c\right)^{2} + 4 \, b \sin\left(2 \, b x + a + 3 \, c\right)^{2} - 4 \, b \sin\left(2 \, b x + a + 3 \, c\right) \sin\left(a + c\right) + b \sin\left(a + c\right)^{2} - 2 \, {\left(2 \, b \cos\left(2 \, b x + a + 3 \, c\right) - b \cos\left(a + c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) - 2 \, {\left(2 \, b \sin\left(2 \, b x + a + 3 \, c\right) - b \sin\left(a + c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right)}"," ",0,"((2*sin(2*b*x + 2*a + 2*c) - sin(2*a) - sin(2*c))*cos(4*b*x + a + 5*c) - 2*(2*sin(2*b*x + 2*a + 2*c) - sin(2*a) - sin(2*c))*cos(2*b*x + a + 3*c) - (sin(2*a) + sin(2*c))*cos(a + c) - (2*cos(2*b*x + 2*a + 2*c) - cos(2*a) - cos(2*c))*sin(4*b*x + a + 5*c) + 2*cos(a + c)*sin(2*b*x + 2*a + 2*c) + 2*(2*cos(2*b*x + 2*a + 2*c) - cos(2*a) - cos(2*c))*sin(2*b*x + a + 3*c) + (cos(2*a) + cos(2*c))*sin(a + c) - 2*cos(2*b*x + 2*a + 2*c)*sin(a + c))/(b*cos(4*b*x + a + 5*c)^2 + 4*b*cos(2*b*x + a + 3*c)^2 - 4*b*cos(2*b*x + a + 3*c)*cos(a + c) + b*cos(a + c)^2 + b*sin(4*b*x + a + 5*c)^2 + 4*b*sin(2*b*x + a + 3*c)^2 - 4*b*sin(2*b*x + a + 3*c)*sin(a + c) + b*sin(a + c)^2 - 2*(2*b*cos(2*b*x + a + 3*c) - b*cos(a + c))*cos(4*b*x + a + 5*c) - 2*(2*b*sin(2*b*x + a + 3*c) - b*sin(a + c))*sin(4*b*x + a + 5*c))","B",0
198,1,1773,0,0.423062," ","integrate(csc(b*x+c)^4*sin(b*x+a),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, \cos\left(5 \, b x + 2 \, a + 4 \, c\right) + 3 \, \cos\left(5 \, b x + 6 \, c\right) + 8 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) - 8 \, \cos\left(3 \, b x + 4 \, c\right) - 3 \, \cos\left(b x + 2 \, a\right) - 3 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) - 6 \, {\left(3 \, \cos\left(4 \, b x + a + 4 \, c\right) - 3 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(5 \, b x + 2 \, a + 4 \, c\right) - 6 \, {\left(3 \, \cos\left(4 \, b x + a + 4 \, c\right) - 3 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(5 \, b x + 6 \, c\right) - 6 \, {\left(8 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) - 8 \, \cos\left(3 \, b x + 4 \, c\right) - 3 \, \cos\left(b x + 2 \, a\right) - 3 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) + 16 \, {\left(3 \, \cos\left(2 \, b x + a + 2 \, c\right) - \cos\left(a\right)\right)} \cos\left(3 \, b x + 2 \, a + 2 \, c\right) - 16 \, {\left(3 \, \cos\left(2 \, b x + a + 2 \, c\right) - \cos\left(a\right)\right)} \cos\left(3 \, b x + 4 \, c\right) - 18 \, {\left(\cos\left(b x + 2 \, a\right) + \cos\left(b x + 2 \, c\right)\right)} \cos\left(2 \, b x + a + 2 \, c\right) + 6 \, \cos\left(b x + 2 \, a\right) \cos\left(a\right) + 6 \, \cos\left(b x + 2 \, c\right) \cos\left(a\right) - 3 \, {\left(\cos\left(6 \, b x + a + 6 \, c\right)^{2} \cos\left(-a + c\right) + 9 \, \cos\left(4 \, b x + a + 4 \, c\right)^{2} \cos\left(-a + c\right) + 9 \, \cos\left(2 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) - 6 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(6 \, b x + a + 6 \, c\right)^{2} + 9 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right)^{2} + 9 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right)^{2} - 6 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) - 2 \, {\left(3 \, \cos\left(4 \, b x + a + 4 \, c\right) \cos\left(-a + c\right) - 3 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) + \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) - 6 \, {\left(3 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) - \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(-a + c\right) - 2 \, {\left(3 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right) - 3 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) + \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) - 6 \, {\left(3 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) - \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + 3 \, {\left(\cos\left(6 \, b x + a + 6 \, c\right)^{2} \cos\left(-a + c\right) + 9 \, \cos\left(4 \, b x + a + 4 \, c\right)^{2} \cos\left(-a + c\right) + 9 \, \cos\left(2 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) - 6 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(6 \, b x + a + 6 \, c\right)^{2} + 9 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right)^{2} + 9 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right)^{2} - 6 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) - 2 \, {\left(3 \, \cos\left(4 \, b x + a + 4 \, c\right) \cos\left(-a + c\right) - 3 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) + \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) - 6 \, {\left(3 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) - \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(-a + c\right) - 2 \, {\left(3 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right) - 3 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) + \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) - 6 \, {\left(3 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) - \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + 2 \, {\left(3 \, \sin\left(5 \, b x + 2 \, a + 4 \, c\right) + 3 \, \sin\left(5 \, b x + 6 \, c\right) + 8 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) - 8 \, \sin\left(3 \, b x + 4 \, c\right) - 3 \, \sin\left(b x + 2 \, a\right) - 3 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) - 6 \, {\left(3 \, \sin\left(4 \, b x + a + 4 \, c\right) - 3 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(5 \, b x + 2 \, a + 4 \, c\right) - 6 \, {\left(3 \, \sin\left(4 \, b x + a + 4 \, c\right) - 3 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(5 \, b x + 6 \, c\right) - 6 \, {\left(8 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) - 8 \, \sin\left(3 \, b x + 4 \, c\right) - 3 \, \sin\left(b x + 2 \, a\right) - 3 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right) + 16 \, {\left(3 \, \sin\left(2 \, b x + a + 2 \, c\right) - \sin\left(a\right)\right)} \sin\left(3 \, b x + 2 \, a + 2 \, c\right) - 16 \, {\left(3 \, \sin\left(2 \, b x + a + 2 \, c\right) - \sin\left(a\right)\right)} \sin\left(3 \, b x + 4 \, c\right) - 18 \, {\left(\sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, c\right)\right)} \sin\left(2 \, b x + a + 2 \, c\right) + 6 \, \sin\left(b x + 2 \, a\right) \sin\left(a\right) + 6 \, \sin\left(b x + 2 \, c\right) \sin\left(a\right)}{12 \, {\left(b \cos\left(6 \, b x + a + 6 \, c\right)^{2} + 9 \, b \cos\left(4 \, b x + a + 4 \, c\right)^{2} + 9 \, b \cos\left(2 \, b x + a + 2 \, c\right)^{2} - 6 \, b \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) + b \sin\left(6 \, b x + a + 6 \, c\right)^{2} + 9 \, b \sin\left(4 \, b x + a + 4 \, c\right)^{2} + 9 \, b \sin\left(2 \, b x + a + 2 \, c\right)^{2} - 6 \, b \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b - 2 \, {\left(3 \, b \cos\left(4 \, b x + a + 4 \, c\right) - 3 \, b \cos\left(2 \, b x + a + 2 \, c\right) + b \cos\left(a\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) - 6 \, {\left(3 \, b \cos\left(2 \, b x + a + 2 \, c\right) - b \cos\left(a\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) - 2 \, {\left(3 \, b \sin\left(4 \, b x + a + 4 \, c\right) - 3 \, b \sin\left(2 \, b x + a + 2 \, c\right) + b \sin\left(a\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) - 6 \, {\left(3 \, b \sin\left(2 \, b x + a + 2 \, c\right) - b \sin\left(a\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right)\right)}}"," ",0,"1/12*(2*(3*cos(5*b*x + 2*a + 4*c) + 3*cos(5*b*x + 6*c) + 8*cos(3*b*x + 2*a + 2*c) - 8*cos(3*b*x + 4*c) - 3*cos(b*x + 2*a) - 3*cos(b*x + 2*c))*cos(6*b*x + a + 6*c) - 6*(3*cos(4*b*x + a + 4*c) - 3*cos(2*b*x + a + 2*c) + cos(a))*cos(5*b*x + 2*a + 4*c) - 6*(3*cos(4*b*x + a + 4*c) - 3*cos(2*b*x + a + 2*c) + cos(a))*cos(5*b*x + 6*c) - 6*(8*cos(3*b*x + 2*a + 2*c) - 8*cos(3*b*x + 4*c) - 3*cos(b*x + 2*a) - 3*cos(b*x + 2*c))*cos(4*b*x + a + 4*c) + 16*(3*cos(2*b*x + a + 2*c) - cos(a))*cos(3*b*x + 2*a + 2*c) - 16*(3*cos(2*b*x + a + 2*c) - cos(a))*cos(3*b*x + 4*c) - 18*(cos(b*x + 2*a) + cos(b*x + 2*c))*cos(2*b*x + a + 2*c) + 6*cos(b*x + 2*a)*cos(a) + 6*cos(b*x + 2*c)*cos(a) - 3*(cos(6*b*x + a + 6*c)^2*cos(-a + c) + 9*cos(4*b*x + a + 4*c)^2*cos(-a + c) + 9*cos(2*b*x + a + 2*c)^2*cos(-a + c) - 6*cos(2*b*x + a + 2*c)*cos(a)*cos(-a + c) + cos(-a + c)*sin(6*b*x + a + 6*c)^2 + 9*cos(-a + c)*sin(4*b*x + a + 4*c)^2 + 9*cos(-a + c)*sin(2*b*x + a + 2*c)^2 - 6*cos(-a + c)*sin(2*b*x + a + 2*c)*sin(a) - 2*(3*cos(4*b*x + a + 4*c)*cos(-a + c) - 3*cos(2*b*x + a + 2*c)*cos(-a + c) + cos(a)*cos(-a + c))*cos(6*b*x + a + 6*c) - 6*(3*cos(2*b*x + a + 2*c)*cos(-a + c) - cos(a)*cos(-a + c))*cos(4*b*x + a + 4*c) + (cos(a)^2 + sin(a)^2)*cos(-a + c) - 2*(3*cos(-a + c)*sin(4*b*x + a + 4*c) - 3*cos(-a + c)*sin(2*b*x + a + 2*c) + cos(-a + c)*sin(a))*sin(6*b*x + a + 6*c) - 6*(3*cos(-a + c)*sin(2*b*x + a + 2*c) - cos(-a + c)*sin(a))*sin(4*b*x + a + 4*c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) + 3*(cos(6*b*x + a + 6*c)^2*cos(-a + c) + 9*cos(4*b*x + a + 4*c)^2*cos(-a + c) + 9*cos(2*b*x + a + 2*c)^2*cos(-a + c) - 6*cos(2*b*x + a + 2*c)*cos(a)*cos(-a + c) + cos(-a + c)*sin(6*b*x + a + 6*c)^2 + 9*cos(-a + c)*sin(4*b*x + a + 4*c)^2 + 9*cos(-a + c)*sin(2*b*x + a + 2*c)^2 - 6*cos(-a + c)*sin(2*b*x + a + 2*c)*sin(a) - 2*(3*cos(4*b*x + a + 4*c)*cos(-a + c) - 3*cos(2*b*x + a + 2*c)*cos(-a + c) + cos(a)*cos(-a + c))*cos(6*b*x + a + 6*c) - 6*(3*cos(2*b*x + a + 2*c)*cos(-a + c) - cos(a)*cos(-a + c))*cos(4*b*x + a + 4*c) + (cos(a)^2 + sin(a)^2)*cos(-a + c) - 2*(3*cos(-a + c)*sin(4*b*x + a + 4*c) - 3*cos(-a + c)*sin(2*b*x + a + 2*c) + cos(-a + c)*sin(a))*sin(6*b*x + a + 6*c) - 6*(3*cos(-a + c)*sin(2*b*x + a + 2*c) - cos(-a + c)*sin(a))*sin(4*b*x + a + 4*c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2) + 2*(3*sin(5*b*x + 2*a + 4*c) + 3*sin(5*b*x + 6*c) + 8*sin(3*b*x + 2*a + 2*c) - 8*sin(3*b*x + 4*c) - 3*sin(b*x + 2*a) - 3*sin(b*x + 2*c))*sin(6*b*x + a + 6*c) - 6*(3*sin(4*b*x + a + 4*c) - 3*sin(2*b*x + a + 2*c) + sin(a))*sin(5*b*x + 2*a + 4*c) - 6*(3*sin(4*b*x + a + 4*c) - 3*sin(2*b*x + a + 2*c) + sin(a))*sin(5*b*x + 6*c) - 6*(8*sin(3*b*x + 2*a + 2*c) - 8*sin(3*b*x + 4*c) - 3*sin(b*x + 2*a) - 3*sin(b*x + 2*c))*sin(4*b*x + a + 4*c) + 16*(3*sin(2*b*x + a + 2*c) - sin(a))*sin(3*b*x + 2*a + 2*c) - 16*(3*sin(2*b*x + a + 2*c) - sin(a))*sin(3*b*x + 4*c) - 18*(sin(b*x + 2*a) + sin(b*x + 2*c))*sin(2*b*x + a + 2*c) + 6*sin(b*x + 2*a)*sin(a) + 6*sin(b*x + 2*c)*sin(a))/(b*cos(6*b*x + a + 6*c)^2 + 9*b*cos(4*b*x + a + 4*c)^2 + 9*b*cos(2*b*x + a + 2*c)^2 - 6*b*cos(2*b*x + a + 2*c)*cos(a) + b*sin(6*b*x + a + 6*c)^2 + 9*b*sin(4*b*x + a + 4*c)^2 + 9*b*sin(2*b*x + a + 2*c)^2 - 6*b*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*b - 2*(3*b*cos(4*b*x + a + 4*c) - 3*b*cos(2*b*x + a + 2*c) + b*cos(a))*cos(6*b*x + a + 6*c) - 6*(3*b*cos(2*b*x + a + 2*c) - b*cos(a))*cos(4*b*x + a + 4*c) - 2*(3*b*sin(4*b*x + a + 4*c) - 3*b*sin(2*b*x + a + 2*c) + b*sin(a))*sin(6*b*x + a + 6*c) - 6*(3*b*sin(2*b*x + a + 2*c) - b*sin(a))*sin(4*b*x + a + 4*c))","B",0
199,1,1076,0,0.349027," ","integrate(csc(b*x+c)^5*sin(b*x+a),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(6 \, \sin\left(4 \, b x + 2 \, a + 4 \, c\right) - 4 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \sin\left(2 \, b x + 4 \, c\right) + \sin\left(2 \, a\right) + \sin\left(2 \, c\right)\right)} \cos\left(8 \, b x + a + 9 \, c\right) - 4 \, {\left(6 \, \sin\left(4 \, b x + 2 \, a + 4 \, c\right) - 4 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \sin\left(2 \, b x + 4 \, c\right) + \sin\left(2 \, a\right) + \sin\left(2 \, c\right)\right)} \cos\left(6 \, b x + a + 7 \, c\right) + 6 \, {\left(4 \, \sin\left(2 \, b x + a + 3 \, c\right) - \sin\left(a + c\right)\right)} \cos\left(4 \, b x + 2 \, a + 4 \, c\right) + 6 \, {\left(6 \, \sin\left(4 \, b x + 2 \, a + 4 \, c\right) - 4 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \sin\left(2 \, b x + 4 \, c\right) + \sin\left(2 \, a\right) + \sin\left(2 \, c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) + 4 \, {\left(4 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - \sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \cos\left(2 \, b x + a + 3 \, c\right) - 4 \, {\left(4 \, \sin\left(2 \, b x + a + 3 \, c\right) - \sin\left(a + c\right)\right)} \cos\left(2 \, b x + 4 \, c\right) + {\left(\sin\left(2 \, a\right) + \sin\left(2 \, c\right)\right)} \cos\left(a + c\right) - {\left(6 \, \cos\left(4 \, b x + 2 \, a + 4 \, c\right) - 4 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \cos\left(2 \, b x + 4 \, c\right) + \cos\left(2 \, a\right) + \cos\left(2 \, c\right)\right)} \sin\left(8 \, b x + a + 9 \, c\right) + 4 \, {\left(6 \, \cos\left(4 \, b x + 2 \, a + 4 \, c\right) - 4 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \cos\left(2 \, b x + 4 \, c\right) + \cos\left(2 \, a\right) + \cos\left(2 \, c\right)\right)} \sin\left(6 \, b x + a + 7 \, c\right) - 6 \, {\left(4 \, \cos\left(2 \, b x + a + 3 \, c\right) - \cos\left(a + c\right)\right)} \sin\left(4 \, b x + 2 \, a + 4 \, c\right) - 6 \, {\left(6 \, \cos\left(4 \, b x + 2 \, a + 4 \, c\right) - 4 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \cos\left(2 \, b x + 4 \, c\right) + \cos\left(2 \, a\right) + \cos\left(2 \, c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right) - 4 \, \cos\left(a + c\right) \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, {\left(4 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - \cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \sin\left(2 \, b x + a + 3 \, c\right) + 4 \, {\left(4 \, \cos\left(2 \, b x + a + 3 \, c\right) - \cos\left(a + c\right)\right)} \sin\left(2 \, b x + 4 \, c\right) - {\left(\cos\left(2 \, a\right) + \cos\left(2 \, c\right)\right)} \sin\left(a + c\right) + 4 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) \sin\left(a + c\right)\right)}}{3 \, {\left(b \cos\left(8 \, b x + a + 9 \, c\right)^{2} + 16 \, b \cos\left(6 \, b x + a + 7 \, c\right)^{2} + 36 \, b \cos\left(4 \, b x + a + 5 \, c\right)^{2} + 16 \, b \cos\left(2 \, b x + a + 3 \, c\right)^{2} - 8 \, b \cos\left(2 \, b x + a + 3 \, c\right) \cos\left(a + c\right) + b \cos\left(a + c\right)^{2} + b \sin\left(8 \, b x + a + 9 \, c\right)^{2} + 16 \, b \sin\left(6 \, b x + a + 7 \, c\right)^{2} + 36 \, b \sin\left(4 \, b x + a + 5 \, c\right)^{2} + 16 \, b \sin\left(2 \, b x + a + 3 \, c\right)^{2} - 8 \, b \sin\left(2 \, b x + a + 3 \, c\right) \sin\left(a + c\right) + b \sin\left(a + c\right)^{2} - 2 \, {\left(4 \, b \cos\left(6 \, b x + a + 7 \, c\right) - 6 \, b \cos\left(4 \, b x + a + 5 \, c\right) + 4 \, b \cos\left(2 \, b x + a + 3 \, c\right) - b \cos\left(a + c\right)\right)} \cos\left(8 \, b x + a + 9 \, c\right) - 8 \, {\left(6 \, b \cos\left(4 \, b x + a + 5 \, c\right) - 4 \, b \cos\left(2 \, b x + a + 3 \, c\right) + b \cos\left(a + c\right)\right)} \cos\left(6 \, b x + a + 7 \, c\right) - 12 \, {\left(4 \, b \cos\left(2 \, b x + a + 3 \, c\right) - b \cos\left(a + c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) - 2 \, {\left(4 \, b \sin\left(6 \, b x + a + 7 \, c\right) - 6 \, b \sin\left(4 \, b x + a + 5 \, c\right) + 4 \, b \sin\left(2 \, b x + a + 3 \, c\right) - b \sin\left(a + c\right)\right)} \sin\left(8 \, b x + a + 9 \, c\right) - 8 \, {\left(6 \, b \sin\left(4 \, b x + a + 5 \, c\right) - 4 \, b \sin\left(2 \, b x + a + 3 \, c\right) + b \sin\left(a + c\right)\right)} \sin\left(6 \, b x + a + 7 \, c\right) - 12 \, {\left(4 \, b \sin\left(2 \, b x + a + 3 \, c\right) - b \sin\left(a + c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right)\right)}}"," ",0,"-2/3*((6*sin(4*b*x + 2*a + 4*c) - 4*sin(2*b*x + 2*a + 2*c) - 4*sin(2*b*x + 4*c) + sin(2*a) + sin(2*c))*cos(8*b*x + a + 9*c) - 4*(6*sin(4*b*x + 2*a + 4*c) - 4*sin(2*b*x + 2*a + 2*c) - 4*sin(2*b*x + 4*c) + sin(2*a) + sin(2*c))*cos(6*b*x + a + 7*c) + 6*(4*sin(2*b*x + a + 3*c) - sin(a + c))*cos(4*b*x + 2*a + 4*c) + 6*(6*sin(4*b*x + 2*a + 4*c) - 4*sin(2*b*x + 2*a + 2*c) - 4*sin(2*b*x + 4*c) + sin(2*a) + sin(2*c))*cos(4*b*x + a + 5*c) + 4*(4*sin(2*b*x + 2*a + 2*c) - sin(2*a) - sin(2*c))*cos(2*b*x + a + 3*c) - 4*(4*sin(2*b*x + a + 3*c) - sin(a + c))*cos(2*b*x + 4*c) + (sin(2*a) + sin(2*c))*cos(a + c) - (6*cos(4*b*x + 2*a + 4*c) - 4*cos(2*b*x + 2*a + 2*c) - 4*cos(2*b*x + 4*c) + cos(2*a) + cos(2*c))*sin(8*b*x + a + 9*c) + 4*(6*cos(4*b*x + 2*a + 4*c) - 4*cos(2*b*x + 2*a + 2*c) - 4*cos(2*b*x + 4*c) + cos(2*a) + cos(2*c))*sin(6*b*x + a + 7*c) - 6*(4*cos(2*b*x + a + 3*c) - cos(a + c))*sin(4*b*x + 2*a + 4*c) - 6*(6*cos(4*b*x + 2*a + 4*c) - 4*cos(2*b*x + 2*a + 2*c) - 4*cos(2*b*x + 4*c) + cos(2*a) + cos(2*c))*sin(4*b*x + a + 5*c) - 4*cos(a + c)*sin(2*b*x + 2*a + 2*c) - 4*(4*cos(2*b*x + 2*a + 2*c) - cos(2*a) - cos(2*c))*sin(2*b*x + a + 3*c) + 4*(4*cos(2*b*x + a + 3*c) - cos(a + c))*sin(2*b*x + 4*c) - (cos(2*a) + cos(2*c))*sin(a + c) + 4*cos(2*b*x + 2*a + 2*c)*sin(a + c))/(b*cos(8*b*x + a + 9*c)^2 + 16*b*cos(6*b*x + a + 7*c)^2 + 36*b*cos(4*b*x + a + 5*c)^2 + 16*b*cos(2*b*x + a + 3*c)^2 - 8*b*cos(2*b*x + a + 3*c)*cos(a + c) + b*cos(a + c)^2 + b*sin(8*b*x + a + 9*c)^2 + 16*b*sin(6*b*x + a + 7*c)^2 + 36*b*sin(4*b*x + a + 5*c)^2 + 16*b*sin(2*b*x + a + 3*c)^2 - 8*b*sin(2*b*x + a + 3*c)*sin(a + c) + b*sin(a + c)^2 - 2*(4*b*cos(6*b*x + a + 7*c) - 6*b*cos(4*b*x + a + 5*c) + 4*b*cos(2*b*x + a + 3*c) - b*cos(a + c))*cos(8*b*x + a + 9*c) - 8*(6*b*cos(4*b*x + a + 5*c) - 4*b*cos(2*b*x + a + 3*c) + b*cos(a + c))*cos(6*b*x + a + 7*c) - 12*(4*b*cos(2*b*x + a + 3*c) - b*cos(a + c))*cos(4*b*x + a + 5*c) - 2*(4*b*sin(6*b*x + a + 7*c) - 6*b*sin(4*b*x + a + 5*c) + 4*b*sin(2*b*x + a + 3*c) - b*sin(a + c))*sin(8*b*x + a + 9*c) - 8*(6*b*sin(4*b*x + a + 5*c) - 4*b*sin(2*b*x + a + 3*c) + b*sin(a + c))*sin(6*b*x + a + 7*c) - 12*(4*b*sin(2*b*x + a + 3*c) - b*sin(a + c))*sin(4*b*x + a + 5*c))","B",0
200,1,3879,0,0.569430," ","integrate(csc(b*x+c)^6*sin(b*x+a),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, \cos\left(9 \, b x + 2 \, a + 8 \, c\right) + 15 \, \cos\left(9 \, b x + 10 \, c\right) - 70 \, \cos\left(7 \, b x + 2 \, a + 6 \, c\right) - 70 \, \cos\left(7 \, b x + 8 \, c\right) - 128 \, \cos\left(5 \, b x + 2 \, a + 4 \, c\right) + 128 \, \cos\left(5 \, b x + 6 \, c\right) + 70 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) + 70 \, \cos\left(3 \, b x + 4 \, c\right) - 15 \, \cos\left(b x + 2 \, a\right) - 15 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(10 \, b x + a + 10 \, c\right) - 30 \, {\left(5 \, \cos\left(8 \, b x + a + 8 \, c\right) - 10 \, \cos\left(6 \, b x + a + 6 \, c\right) + 10 \, \cos\left(4 \, b x + a + 4 \, c\right) - 5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(9 \, b x + 2 \, a + 8 \, c\right) - 30 \, {\left(5 \, \cos\left(8 \, b x + a + 8 \, c\right) - 10 \, \cos\left(6 \, b x + a + 6 \, c\right) + 10 \, \cos\left(4 \, b x + a + 4 \, c\right) - 5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(9 \, b x + 10 \, c\right) + 10 \, {\left(70 \, \cos\left(7 \, b x + 2 \, a + 6 \, c\right) + 70 \, \cos\left(7 \, b x + 8 \, c\right) + 128 \, \cos\left(5 \, b x + 2 \, a + 4 \, c\right) - 128 \, \cos\left(5 \, b x + 6 \, c\right) - 70 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) - 70 \, \cos\left(3 \, b x + 4 \, c\right) + 15 \, \cos\left(b x + 2 \, a\right) + 15 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(8 \, b x + a + 8 \, c\right) - 140 \, {\left(10 \, \cos\left(6 \, b x + a + 6 \, c\right) - 10 \, \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) - \cos\left(a\right)\right)} \cos\left(7 \, b x + 2 \, a + 6 \, c\right) - 140 \, {\left(10 \, \cos\left(6 \, b x + a + 6 \, c\right) - 10 \, \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) - \cos\left(a\right)\right)} \cos\left(7 \, b x + 8 \, c\right) - 20 \, {\left(128 \, \cos\left(5 \, b x + 2 \, a + 4 \, c\right) - 128 \, \cos\left(5 \, b x + 6 \, c\right) - 70 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) - 70 \, \cos\left(3 \, b x + 4 \, c\right) + 15 \, \cos\left(b x + 2 \, a\right) + 15 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) + 256 \, {\left(10 \, \cos\left(4 \, b x + a + 4 \, c\right) - 5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(5 \, b x + 2 \, a + 4 \, c\right) - 256 \, {\left(10 \, \cos\left(4 \, b x + a + 4 \, c\right) - 5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(5 \, b x + 6 \, c\right) - 100 \, {\left(14 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) + 14 \, \cos\left(3 \, b x + 4 \, c\right) - 3 \, \cos\left(b x + 2 \, a\right) - 3 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) + 140 \, {\left(5 \, \cos\left(2 \, b x + a + 2 \, c\right) - \cos\left(a\right)\right)} \cos\left(3 \, b x + 2 \, a + 2 \, c\right) + 140 \, {\left(5 \, \cos\left(2 \, b x + a + 2 \, c\right) - \cos\left(a\right)\right)} \cos\left(3 \, b x + 4 \, c\right) - 150 \, {\left(\cos\left(b x + 2 \, a\right) + \cos\left(b x + 2 \, c\right)\right)} \cos\left(2 \, b x + a + 2 \, c\right) + 30 \, \cos\left(b x + 2 \, a\right) \cos\left(a\right) + 30 \, \cos\left(b x + 2 \, c\right) \cos\left(a\right) - 15 \, {\left(\cos\left(10 \, b x + a + 10 \, c\right)^{2} \cos\left(-a + c\right) + 25 \, \cos\left(8 \, b x + a + 8 \, c\right)^{2} \cos\left(-a + c\right) + 100 \, \cos\left(6 \, b x + a + 6 \, c\right)^{2} \cos\left(-a + c\right) + 100 \, \cos\left(4 \, b x + a + 4 \, c\right)^{2} \cos\left(-a + c\right) + 25 \, \cos\left(2 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) - 10 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(10 \, b x + a + 10 \, c\right)^{2} + 25 \, \cos\left(-a + c\right) \sin\left(8 \, b x + a + 8 \, c\right)^{2} + 100 \, \cos\left(-a + c\right) \sin\left(6 \, b x + a + 6 \, c\right)^{2} + 100 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right)^{2} + 25 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right)^{2} - 10 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) - 2 \, {\left(5 \, \cos\left(8 \, b x + a + 8 \, c\right) \cos\left(-a + c\right) - 10 \, \cos\left(6 \, b x + a + 6 \, c\right) \cos\left(-a + c\right) + 10 \, \cos\left(4 \, b x + a + 4 \, c\right) \cos\left(-a + c\right) - 5 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) + \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(10 \, b x + a + 10 \, c\right) - 10 \, {\left(10 \, \cos\left(6 \, b x + a + 6 \, c\right) \cos\left(-a + c\right) - 10 \, \cos\left(4 \, b x + a + 4 \, c\right) \cos\left(-a + c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) - \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(8 \, b x + a + 8 \, c\right) - 20 \, {\left(10 \, \cos\left(4 \, b x + a + 4 \, c\right) \cos\left(-a + c\right) - 5 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) + \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) - 20 \, {\left(5 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) - \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(-a + c\right) - 2 \, {\left(5 \, \cos\left(-a + c\right) \sin\left(8 \, b x + a + 8 \, c\right) - 10 \, \cos\left(-a + c\right) \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right) - 5 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) + \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(10 \, b x + a + 10 \, c\right) - 10 \, {\left(10 \, \cos\left(-a + c\right) \sin\left(6 \, b x + a + 6 \, c\right) - 10 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) - \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(8 \, b x + a + 8 \, c\right) - 20 \, {\left(10 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right) - 5 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) + \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) - 20 \, {\left(5 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) - \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + 15 \, {\left(\cos\left(10 \, b x + a + 10 \, c\right)^{2} \cos\left(-a + c\right) + 25 \, \cos\left(8 \, b x + a + 8 \, c\right)^{2} \cos\left(-a + c\right) + 100 \, \cos\left(6 \, b x + a + 6 \, c\right)^{2} \cos\left(-a + c\right) + 100 \, \cos\left(4 \, b x + a + 4 \, c\right)^{2} \cos\left(-a + c\right) + 25 \, \cos\left(2 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) - 10 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(10 \, b x + a + 10 \, c\right)^{2} + 25 \, \cos\left(-a + c\right) \sin\left(8 \, b x + a + 8 \, c\right)^{2} + 100 \, \cos\left(-a + c\right) \sin\left(6 \, b x + a + 6 \, c\right)^{2} + 100 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right)^{2} + 25 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right)^{2} - 10 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) - 2 \, {\left(5 \, \cos\left(8 \, b x + a + 8 \, c\right) \cos\left(-a + c\right) - 10 \, \cos\left(6 \, b x + a + 6 \, c\right) \cos\left(-a + c\right) + 10 \, \cos\left(4 \, b x + a + 4 \, c\right) \cos\left(-a + c\right) - 5 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) + \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(10 \, b x + a + 10 \, c\right) - 10 \, {\left(10 \, \cos\left(6 \, b x + a + 6 \, c\right) \cos\left(-a + c\right) - 10 \, \cos\left(4 \, b x + a + 4 \, c\right) \cos\left(-a + c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) - \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(8 \, b x + a + 8 \, c\right) - 20 \, {\left(10 \, \cos\left(4 \, b x + a + 4 \, c\right) \cos\left(-a + c\right) - 5 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) + \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) - 20 \, {\left(5 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) - \cos\left(a\right) \cos\left(-a + c\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(-a + c\right) - 2 \, {\left(5 \, \cos\left(-a + c\right) \sin\left(8 \, b x + a + 8 \, c\right) - 10 \, \cos\left(-a + c\right) \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right) - 5 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) + \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(10 \, b x + a + 10 \, c\right) - 10 \, {\left(10 \, \cos\left(-a + c\right) \sin\left(6 \, b x + a + 6 \, c\right) - 10 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) - \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(8 \, b x + a + 8 \, c\right) - 20 \, {\left(10 \, \cos\left(-a + c\right) \sin\left(4 \, b x + a + 4 \, c\right) - 5 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) + \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) - 20 \, {\left(5 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) - \cos\left(-a + c\right) \sin\left(a\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + 2 \, {\left(15 \, \sin\left(9 \, b x + 2 \, a + 8 \, c\right) + 15 \, \sin\left(9 \, b x + 10 \, c\right) - 70 \, \sin\left(7 \, b x + 2 \, a + 6 \, c\right) - 70 \, \sin\left(7 \, b x + 8 \, c\right) - 128 \, \sin\left(5 \, b x + 2 \, a + 4 \, c\right) + 128 \, \sin\left(5 \, b x + 6 \, c\right) + 70 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) + 70 \, \sin\left(3 \, b x + 4 \, c\right) - 15 \, \sin\left(b x + 2 \, a\right) - 15 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(10 \, b x + a + 10 \, c\right) - 30 \, {\left(5 \, \sin\left(8 \, b x + a + 8 \, c\right) - 10 \, \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, \sin\left(4 \, b x + a + 4 \, c\right) - 5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(9 \, b x + 2 \, a + 8 \, c\right) - 30 \, {\left(5 \, \sin\left(8 \, b x + a + 8 \, c\right) - 10 \, \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, \sin\left(4 \, b x + a + 4 \, c\right) - 5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(9 \, b x + 10 \, c\right) + 10 \, {\left(70 \, \sin\left(7 \, b x + 2 \, a + 6 \, c\right) + 70 \, \sin\left(7 \, b x + 8 \, c\right) + 128 \, \sin\left(5 \, b x + 2 \, a + 4 \, c\right) - 128 \, \sin\left(5 \, b x + 6 \, c\right) - 70 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) - 70 \, \sin\left(3 \, b x + 4 \, c\right) + 15 \, \sin\left(b x + 2 \, a\right) + 15 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(8 \, b x + a + 8 \, c\right) - 140 \, {\left(10 \, \sin\left(6 \, b x + a + 6 \, c\right) - 10 \, \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) - \sin\left(a\right)\right)} \sin\left(7 \, b x + 2 \, a + 6 \, c\right) - 140 \, {\left(10 \, \sin\left(6 \, b x + a + 6 \, c\right) - 10 \, \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) - \sin\left(a\right)\right)} \sin\left(7 \, b x + 8 \, c\right) - 20 \, {\left(128 \, \sin\left(5 \, b x + 2 \, a + 4 \, c\right) - 128 \, \sin\left(5 \, b x + 6 \, c\right) - 70 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) - 70 \, \sin\left(3 \, b x + 4 \, c\right) + 15 \, \sin\left(b x + 2 \, a\right) + 15 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) + 256 \, {\left(10 \, \sin\left(4 \, b x + a + 4 \, c\right) - 5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(5 \, b x + 2 \, a + 4 \, c\right) - 256 \, {\left(10 \, \sin\left(4 \, b x + a + 4 \, c\right) - 5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(5 \, b x + 6 \, c\right) - 100 \, {\left(14 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) + 14 \, \sin\left(3 \, b x + 4 \, c\right) - 3 \, \sin\left(b x + 2 \, a\right) - 3 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right) + 140 \, {\left(5 \, \sin\left(2 \, b x + a + 2 \, c\right) - \sin\left(a\right)\right)} \sin\left(3 \, b x + 2 \, a + 2 \, c\right) + 140 \, {\left(5 \, \sin\left(2 \, b x + a + 2 \, c\right) - \sin\left(a\right)\right)} \sin\left(3 \, b x + 4 \, c\right) - 150 \, {\left(\sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, c\right)\right)} \sin\left(2 \, b x + a + 2 \, c\right) + 30 \, \sin\left(b x + 2 \, a\right) \sin\left(a\right) + 30 \, \sin\left(b x + 2 \, c\right) \sin\left(a\right)}{80 \, {\left(b \cos\left(10 \, b x + a + 10 \, c\right)^{2} + 25 \, b \cos\left(8 \, b x + a + 8 \, c\right)^{2} + 100 \, b \cos\left(6 \, b x + a + 6 \, c\right)^{2} + 100 \, b \cos\left(4 \, b x + a + 4 \, c\right)^{2} + 25 \, b \cos\left(2 \, b x + a + 2 \, c\right)^{2} - 10 \, b \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) + b \sin\left(10 \, b x + a + 10 \, c\right)^{2} + 25 \, b \sin\left(8 \, b x + a + 8 \, c\right)^{2} + 100 \, b \sin\left(6 \, b x + a + 6 \, c\right)^{2} + 100 \, b \sin\left(4 \, b x + a + 4 \, c\right)^{2} + 25 \, b \sin\left(2 \, b x + a + 2 \, c\right)^{2} - 10 \, b \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b - 2 \, {\left(5 \, b \cos\left(8 \, b x + a + 8 \, c\right) - 10 \, b \cos\left(6 \, b x + a + 6 \, c\right) + 10 \, b \cos\left(4 \, b x + a + 4 \, c\right) - 5 \, b \cos\left(2 \, b x + a + 2 \, c\right) + b \cos\left(a\right)\right)} \cos\left(10 \, b x + a + 10 \, c\right) - 10 \, {\left(10 \, b \cos\left(6 \, b x + a + 6 \, c\right) - 10 \, b \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, b \cos\left(2 \, b x + a + 2 \, c\right) - b \cos\left(a\right)\right)} \cos\left(8 \, b x + a + 8 \, c\right) - 20 \, {\left(10 \, b \cos\left(4 \, b x + a + 4 \, c\right) - 5 \, b \cos\left(2 \, b x + a + 2 \, c\right) + b \cos\left(a\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) - 20 \, {\left(5 \, b \cos\left(2 \, b x + a + 2 \, c\right) - b \cos\left(a\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) - 2 \, {\left(5 \, b \sin\left(8 \, b x + a + 8 \, c\right) - 10 \, b \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, b \sin\left(4 \, b x + a + 4 \, c\right) - 5 \, b \sin\left(2 \, b x + a + 2 \, c\right) + b \sin\left(a\right)\right)} \sin\left(10 \, b x + a + 10 \, c\right) - 10 \, {\left(10 \, b \sin\left(6 \, b x + a + 6 \, c\right) - 10 \, b \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, b \sin\left(2 \, b x + a + 2 \, c\right) - b \sin\left(a\right)\right)} \sin\left(8 \, b x + a + 8 \, c\right) - 20 \, {\left(10 \, b \sin\left(4 \, b x + a + 4 \, c\right) - 5 \, b \sin\left(2 \, b x + a + 2 \, c\right) + b \sin\left(a\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) - 20 \, {\left(5 \, b \sin\left(2 \, b x + a + 2 \, c\right) - b \sin\left(a\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right)\right)}}"," ",0,"1/80*(2*(15*cos(9*b*x + 2*a + 8*c) + 15*cos(9*b*x + 10*c) - 70*cos(7*b*x + 2*a + 6*c) - 70*cos(7*b*x + 8*c) - 128*cos(5*b*x + 2*a + 4*c) + 128*cos(5*b*x + 6*c) + 70*cos(3*b*x + 2*a + 2*c) + 70*cos(3*b*x + 4*c) - 15*cos(b*x + 2*a) - 15*cos(b*x + 2*c))*cos(10*b*x + a + 10*c) - 30*(5*cos(8*b*x + a + 8*c) - 10*cos(6*b*x + a + 6*c) + 10*cos(4*b*x + a + 4*c) - 5*cos(2*b*x + a + 2*c) + cos(a))*cos(9*b*x + 2*a + 8*c) - 30*(5*cos(8*b*x + a + 8*c) - 10*cos(6*b*x + a + 6*c) + 10*cos(4*b*x + a + 4*c) - 5*cos(2*b*x + a + 2*c) + cos(a))*cos(9*b*x + 10*c) + 10*(70*cos(7*b*x + 2*a + 6*c) + 70*cos(7*b*x + 8*c) + 128*cos(5*b*x + 2*a + 4*c) - 128*cos(5*b*x + 6*c) - 70*cos(3*b*x + 2*a + 2*c) - 70*cos(3*b*x + 4*c) + 15*cos(b*x + 2*a) + 15*cos(b*x + 2*c))*cos(8*b*x + a + 8*c) - 140*(10*cos(6*b*x + a + 6*c) - 10*cos(4*b*x + a + 4*c) + 5*cos(2*b*x + a + 2*c) - cos(a))*cos(7*b*x + 2*a + 6*c) - 140*(10*cos(6*b*x + a + 6*c) - 10*cos(4*b*x + a + 4*c) + 5*cos(2*b*x + a + 2*c) - cos(a))*cos(7*b*x + 8*c) - 20*(128*cos(5*b*x + 2*a + 4*c) - 128*cos(5*b*x + 6*c) - 70*cos(3*b*x + 2*a + 2*c) - 70*cos(3*b*x + 4*c) + 15*cos(b*x + 2*a) + 15*cos(b*x + 2*c))*cos(6*b*x + a + 6*c) + 256*(10*cos(4*b*x + a + 4*c) - 5*cos(2*b*x + a + 2*c) + cos(a))*cos(5*b*x + 2*a + 4*c) - 256*(10*cos(4*b*x + a + 4*c) - 5*cos(2*b*x + a + 2*c) + cos(a))*cos(5*b*x + 6*c) - 100*(14*cos(3*b*x + 2*a + 2*c) + 14*cos(3*b*x + 4*c) - 3*cos(b*x + 2*a) - 3*cos(b*x + 2*c))*cos(4*b*x + a + 4*c) + 140*(5*cos(2*b*x + a + 2*c) - cos(a))*cos(3*b*x + 2*a + 2*c) + 140*(5*cos(2*b*x + a + 2*c) - cos(a))*cos(3*b*x + 4*c) - 150*(cos(b*x + 2*a) + cos(b*x + 2*c))*cos(2*b*x + a + 2*c) + 30*cos(b*x + 2*a)*cos(a) + 30*cos(b*x + 2*c)*cos(a) - 15*(cos(10*b*x + a + 10*c)^2*cos(-a + c) + 25*cos(8*b*x + a + 8*c)^2*cos(-a + c) + 100*cos(6*b*x + a + 6*c)^2*cos(-a + c) + 100*cos(4*b*x + a + 4*c)^2*cos(-a + c) + 25*cos(2*b*x + a + 2*c)^2*cos(-a + c) - 10*cos(2*b*x + a + 2*c)*cos(a)*cos(-a + c) + cos(-a + c)*sin(10*b*x + a + 10*c)^2 + 25*cos(-a + c)*sin(8*b*x + a + 8*c)^2 + 100*cos(-a + c)*sin(6*b*x + a + 6*c)^2 + 100*cos(-a + c)*sin(4*b*x + a + 4*c)^2 + 25*cos(-a + c)*sin(2*b*x + a + 2*c)^2 - 10*cos(-a + c)*sin(2*b*x + a + 2*c)*sin(a) - 2*(5*cos(8*b*x + a + 8*c)*cos(-a + c) - 10*cos(6*b*x + a + 6*c)*cos(-a + c) + 10*cos(4*b*x + a + 4*c)*cos(-a + c) - 5*cos(2*b*x + a + 2*c)*cos(-a + c) + cos(a)*cos(-a + c))*cos(10*b*x + a + 10*c) - 10*(10*cos(6*b*x + a + 6*c)*cos(-a + c) - 10*cos(4*b*x + a + 4*c)*cos(-a + c) + 5*cos(2*b*x + a + 2*c)*cos(-a + c) - cos(a)*cos(-a + c))*cos(8*b*x + a + 8*c) - 20*(10*cos(4*b*x + a + 4*c)*cos(-a + c) - 5*cos(2*b*x + a + 2*c)*cos(-a + c) + cos(a)*cos(-a + c))*cos(6*b*x + a + 6*c) - 20*(5*cos(2*b*x + a + 2*c)*cos(-a + c) - cos(a)*cos(-a + c))*cos(4*b*x + a + 4*c) + (cos(a)^2 + sin(a)^2)*cos(-a + c) - 2*(5*cos(-a + c)*sin(8*b*x + a + 8*c) - 10*cos(-a + c)*sin(6*b*x + a + 6*c) + 10*cos(-a + c)*sin(4*b*x + a + 4*c) - 5*cos(-a + c)*sin(2*b*x + a + 2*c) + cos(-a + c)*sin(a))*sin(10*b*x + a + 10*c) - 10*(10*cos(-a + c)*sin(6*b*x + a + 6*c) - 10*cos(-a + c)*sin(4*b*x + a + 4*c) + 5*cos(-a + c)*sin(2*b*x + a + 2*c) - cos(-a + c)*sin(a))*sin(8*b*x + a + 8*c) - 20*(10*cos(-a + c)*sin(4*b*x + a + 4*c) - 5*cos(-a + c)*sin(2*b*x + a + 2*c) + cos(-a + c)*sin(a))*sin(6*b*x + a + 6*c) - 20*(5*cos(-a + c)*sin(2*b*x + a + 2*c) - cos(-a + c)*sin(a))*sin(4*b*x + a + 4*c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) + 15*(cos(10*b*x + a + 10*c)^2*cos(-a + c) + 25*cos(8*b*x + a + 8*c)^2*cos(-a + c) + 100*cos(6*b*x + a + 6*c)^2*cos(-a + c) + 100*cos(4*b*x + a + 4*c)^2*cos(-a + c) + 25*cos(2*b*x + a + 2*c)^2*cos(-a + c) - 10*cos(2*b*x + a + 2*c)*cos(a)*cos(-a + c) + cos(-a + c)*sin(10*b*x + a + 10*c)^2 + 25*cos(-a + c)*sin(8*b*x + a + 8*c)^2 + 100*cos(-a + c)*sin(6*b*x + a + 6*c)^2 + 100*cos(-a + c)*sin(4*b*x + a + 4*c)^2 + 25*cos(-a + c)*sin(2*b*x + a + 2*c)^2 - 10*cos(-a + c)*sin(2*b*x + a + 2*c)*sin(a) - 2*(5*cos(8*b*x + a + 8*c)*cos(-a + c) - 10*cos(6*b*x + a + 6*c)*cos(-a + c) + 10*cos(4*b*x + a + 4*c)*cos(-a + c) - 5*cos(2*b*x + a + 2*c)*cos(-a + c) + cos(a)*cos(-a + c))*cos(10*b*x + a + 10*c) - 10*(10*cos(6*b*x + a + 6*c)*cos(-a + c) - 10*cos(4*b*x + a + 4*c)*cos(-a + c) + 5*cos(2*b*x + a + 2*c)*cos(-a + c) - cos(a)*cos(-a + c))*cos(8*b*x + a + 8*c) - 20*(10*cos(4*b*x + a + 4*c)*cos(-a + c) - 5*cos(2*b*x + a + 2*c)*cos(-a + c) + cos(a)*cos(-a + c))*cos(6*b*x + a + 6*c) - 20*(5*cos(2*b*x + a + 2*c)*cos(-a + c) - cos(a)*cos(-a + c))*cos(4*b*x + a + 4*c) + (cos(a)^2 + sin(a)^2)*cos(-a + c) - 2*(5*cos(-a + c)*sin(8*b*x + a + 8*c) - 10*cos(-a + c)*sin(6*b*x + a + 6*c) + 10*cos(-a + c)*sin(4*b*x + a + 4*c) - 5*cos(-a + c)*sin(2*b*x + a + 2*c) + cos(-a + c)*sin(a))*sin(10*b*x + a + 10*c) - 10*(10*cos(-a + c)*sin(6*b*x + a + 6*c) - 10*cos(-a + c)*sin(4*b*x + a + 4*c) + 5*cos(-a + c)*sin(2*b*x + a + 2*c) - cos(-a + c)*sin(a))*sin(8*b*x + a + 8*c) - 20*(10*cos(-a + c)*sin(4*b*x + a + 4*c) - 5*cos(-a + c)*sin(2*b*x + a + 2*c) + cos(-a + c)*sin(a))*sin(6*b*x + a + 6*c) - 20*(5*cos(-a + c)*sin(2*b*x + a + 2*c) - cos(-a + c)*sin(a))*sin(4*b*x + a + 4*c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2) + 2*(15*sin(9*b*x + 2*a + 8*c) + 15*sin(9*b*x + 10*c) - 70*sin(7*b*x + 2*a + 6*c) - 70*sin(7*b*x + 8*c) - 128*sin(5*b*x + 2*a + 4*c) + 128*sin(5*b*x + 6*c) + 70*sin(3*b*x + 2*a + 2*c) + 70*sin(3*b*x + 4*c) - 15*sin(b*x + 2*a) - 15*sin(b*x + 2*c))*sin(10*b*x + a + 10*c) - 30*(5*sin(8*b*x + a + 8*c) - 10*sin(6*b*x + a + 6*c) + 10*sin(4*b*x + a + 4*c) - 5*sin(2*b*x + a + 2*c) + sin(a))*sin(9*b*x + 2*a + 8*c) - 30*(5*sin(8*b*x + a + 8*c) - 10*sin(6*b*x + a + 6*c) + 10*sin(4*b*x + a + 4*c) - 5*sin(2*b*x + a + 2*c) + sin(a))*sin(9*b*x + 10*c) + 10*(70*sin(7*b*x + 2*a + 6*c) + 70*sin(7*b*x + 8*c) + 128*sin(5*b*x + 2*a + 4*c) - 128*sin(5*b*x + 6*c) - 70*sin(3*b*x + 2*a + 2*c) - 70*sin(3*b*x + 4*c) + 15*sin(b*x + 2*a) + 15*sin(b*x + 2*c))*sin(8*b*x + a + 8*c) - 140*(10*sin(6*b*x + a + 6*c) - 10*sin(4*b*x + a + 4*c) + 5*sin(2*b*x + a + 2*c) - sin(a))*sin(7*b*x + 2*a + 6*c) - 140*(10*sin(6*b*x + a + 6*c) - 10*sin(4*b*x + a + 4*c) + 5*sin(2*b*x + a + 2*c) - sin(a))*sin(7*b*x + 8*c) - 20*(128*sin(5*b*x + 2*a + 4*c) - 128*sin(5*b*x + 6*c) - 70*sin(3*b*x + 2*a + 2*c) - 70*sin(3*b*x + 4*c) + 15*sin(b*x + 2*a) + 15*sin(b*x + 2*c))*sin(6*b*x + a + 6*c) + 256*(10*sin(4*b*x + a + 4*c) - 5*sin(2*b*x + a + 2*c) + sin(a))*sin(5*b*x + 2*a + 4*c) - 256*(10*sin(4*b*x + a + 4*c) - 5*sin(2*b*x + a + 2*c) + sin(a))*sin(5*b*x + 6*c) - 100*(14*sin(3*b*x + 2*a + 2*c) + 14*sin(3*b*x + 4*c) - 3*sin(b*x + 2*a) - 3*sin(b*x + 2*c))*sin(4*b*x + a + 4*c) + 140*(5*sin(2*b*x + a + 2*c) - sin(a))*sin(3*b*x + 2*a + 2*c) + 140*(5*sin(2*b*x + a + 2*c) - sin(a))*sin(3*b*x + 4*c) - 150*(sin(b*x + 2*a) + sin(b*x + 2*c))*sin(2*b*x + a + 2*c) + 30*sin(b*x + 2*a)*sin(a) + 30*sin(b*x + 2*c)*sin(a))/(b*cos(10*b*x + a + 10*c)^2 + 25*b*cos(8*b*x + a + 8*c)^2 + 100*b*cos(6*b*x + a + 6*c)^2 + 100*b*cos(4*b*x + a + 4*c)^2 + 25*b*cos(2*b*x + a + 2*c)^2 - 10*b*cos(2*b*x + a + 2*c)*cos(a) + b*sin(10*b*x + a + 10*c)^2 + 25*b*sin(8*b*x + a + 8*c)^2 + 100*b*sin(6*b*x + a + 6*c)^2 + 100*b*sin(4*b*x + a + 4*c)^2 + 25*b*sin(2*b*x + a + 2*c)^2 - 10*b*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*b - 2*(5*b*cos(8*b*x + a + 8*c) - 10*b*cos(6*b*x + a + 6*c) + 10*b*cos(4*b*x + a + 4*c) - 5*b*cos(2*b*x + a + 2*c) + b*cos(a))*cos(10*b*x + a + 10*c) - 10*(10*b*cos(6*b*x + a + 6*c) - 10*b*cos(4*b*x + a + 4*c) + 5*b*cos(2*b*x + a + 2*c) - b*cos(a))*cos(8*b*x + a + 8*c) - 20*(10*b*cos(4*b*x + a + 4*c) - 5*b*cos(2*b*x + a + 2*c) + b*cos(a))*cos(6*b*x + a + 6*c) - 20*(5*b*cos(2*b*x + a + 2*c) - b*cos(a))*cos(4*b*x + a + 4*c) - 2*(5*b*sin(8*b*x + a + 8*c) - 10*b*sin(6*b*x + a + 6*c) + 10*b*sin(4*b*x + a + 4*c) - 5*b*sin(2*b*x + a + 2*c) + b*sin(a))*sin(10*b*x + a + 10*c) - 10*(10*b*sin(6*b*x + a + 6*c) - 10*b*sin(4*b*x + a + 4*c) + 5*b*sin(2*b*x + a + 2*c) - b*sin(a))*sin(8*b*x + a + 8*c) - 20*(10*b*sin(4*b*x + a + 4*c) - 5*b*sin(2*b*x + a + 2*c) + b*sin(a))*sin(6*b*x + a + 6*c) - 20*(5*b*sin(2*b*x + a + 2*c) - b*sin(a))*sin(4*b*x + a + 4*c))","B",0
201,0,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(d*x+c)^n,x, algorithm=""maxima"")","\int \sin\left(d x + c\right)^{n} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*sin(b*x + a)^2, x)","F",0
202,1,371,0,0.351222," ","integrate(sin(b*x+a)^2*sin(d*x+c),x, algorithm=""maxima"")","-\frac{{\left(2 \, b d \cos\left(c\right) - d^{2} \cos\left(c\right)\right)} \cos\left({\left(2 \, b + d\right)} x + 2 \, a + 2 \, c\right) + {\left(2 \, b d \cos\left(c\right) - d^{2} \cos\left(c\right)\right)} \cos\left({\left(2 \, b + d\right)} x + 2 \, a\right) - {\left(2 \, b d \cos\left(c\right) + d^{2} \cos\left(c\right)\right)} \cos\left(-{\left(2 \, b - d\right)} x - 2 \, a + 2 \, c\right) - {\left(2 \, b d \cos\left(c\right) + d^{2} \cos\left(c\right)\right)} \cos\left(-{\left(2 \, b - d\right)} x - 2 \, a\right) - 2 \, {\left(4 \, b^{2} \cos\left(c\right) - d^{2} \cos\left(c\right)\right)} \cos\left(d x + 2 \, c\right) - 2 \, {\left(4 \, b^{2} \cos\left(c\right) - d^{2} \cos\left(c\right)\right)} \cos\left(d x\right) + {\left(2 \, b d \sin\left(c\right) - d^{2} \sin\left(c\right)\right)} \sin\left({\left(2 \, b + d\right)} x + 2 \, a + 2 \, c\right) - {\left(2 \, b d \sin\left(c\right) - d^{2} \sin\left(c\right)\right)} \sin\left({\left(2 \, b + d\right)} x + 2 \, a\right) - {\left(2 \, b d \sin\left(c\right) + d^{2} \sin\left(c\right)\right)} \sin\left(-{\left(2 \, b - d\right)} x - 2 \, a + 2 \, c\right) + {\left(2 \, b d \sin\left(c\right) + d^{2} \sin\left(c\right)\right)} \sin\left(-{\left(2 \, b - d\right)} x - 2 \, a\right) - 2 \, {\left(4 \, b^{2} \sin\left(c\right) - d^{2} \sin\left(c\right)\right)} \sin\left(d x + 2 \, c\right) + 2 \, {\left(4 \, b^{2} \sin\left(c\right) - d^{2} \sin\left(c\right)\right)} \sin\left(d x\right)}{8 \, {\left({\left(\cos\left(c\right)^{2} + \sin\left(c\right)^{2}\right)} d^{3} - 4 \, {\left(b^{2} \cos\left(c\right)^{2} + b^{2} \sin\left(c\right)^{2}\right)} d\right)}}"," ",0,"-1/8*((2*b*d*cos(c) - d^2*cos(c))*cos((2*b + d)*x + 2*a + 2*c) + (2*b*d*cos(c) - d^2*cos(c))*cos((2*b + d)*x + 2*a) - (2*b*d*cos(c) + d^2*cos(c))*cos(-(2*b - d)*x - 2*a + 2*c) - (2*b*d*cos(c) + d^2*cos(c))*cos(-(2*b - d)*x - 2*a) - 2*(4*b^2*cos(c) - d^2*cos(c))*cos(d*x + 2*c) - 2*(4*b^2*cos(c) - d^2*cos(c))*cos(d*x) + (2*b*d*sin(c) - d^2*sin(c))*sin((2*b + d)*x + 2*a + 2*c) - (2*b*d*sin(c) - d^2*sin(c))*sin((2*b + d)*x + 2*a) - (2*b*d*sin(c) + d^2*sin(c))*sin(-(2*b - d)*x - 2*a + 2*c) + (2*b*d*sin(c) + d^2*sin(c))*sin(-(2*b - d)*x - 2*a) - 2*(4*b^2*sin(c) - d^2*sin(c))*sin(d*x + 2*c) + 2*(4*b^2*sin(c) - d^2*sin(c))*sin(d*x))/((cos(c)^2 + sin(c)^2)*d^3 - 4*(b^2*cos(c)^2 + b^2*sin(c)^2)*d)","B",0
203,1,620,0,0.378085," ","integrate(sin(b*x+a)^2*sin(d*x+c)^2,x, algorithm=""maxima"")","\frac{8 \, {\left({\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{3} - {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2}\right)} d\right)} x + {\left(b^{2} d \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, {\left(b + d\right)} x + 2 \, a + 4 \, c\right) - {\left(b^{2} d \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, {\left(b + d\right)} x + 2 \, a\right) - {\left(b^{2} d \sin\left(2 \, c\right) + b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(-2 \, {\left(b - d\right)} x - 2 \, a + 4 \, c\right) + {\left(b^{2} d \sin\left(2 \, c\right) + b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(-2 \, {\left(b - d\right)} x - 2 \, a\right) - 2 \, {\left(b^{2} d \sin\left(2 \, c\right) - d^{3} \sin\left(2 \, c\right)\right)} \cos\left(2 \, b x + 2 \, a + 2 \, c\right) + 2 \, {\left(b^{2} d \sin\left(2 \, c\right) - d^{3} \sin\left(2 \, c\right)\right)} \cos\left(2 \, b x + 2 \, a - 2 \, c\right) + 2 \, {\left(b^{3} \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x\right) - 2 \, {\left(b^{3} \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x + 4 \, c\right) - {\left(b^{2} d \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, {\left(b + d\right)} x + 2 \, a + 4 \, c\right) - {\left(b^{2} d \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, {\left(b + d\right)} x + 2 \, a\right) + {\left(b^{2} d \cos\left(2 \, c\right) + b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(-2 \, {\left(b - d\right)} x - 2 \, a + 4 \, c\right) + {\left(b^{2} d \cos\left(2 \, c\right) + b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(-2 \, {\left(b - d\right)} x - 2 \, a\right) + 2 \, {\left(b^{2} d \cos\left(2 \, c\right) - d^{3} \cos\left(2 \, c\right)\right)} \sin\left(2 \, b x + 2 \, a + 2 \, c\right) + 2 \, {\left(b^{2} d \cos\left(2 \, c\right) - d^{3} \cos\left(2 \, c\right)\right)} \sin\left(2 \, b x + 2 \, a - 2 \, c\right) + 2 \, {\left(b^{3} \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, d x\right) + 2 \, {\left(b^{3} \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, d x + 4 \, c\right)}{32 \, {\left({\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{3} - {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2}\right)} d\right)}}"," ",0,"1/32*(8*((b*cos(2*c)^2 + b*sin(2*c)^2)*d^3 - (b^3*cos(2*c)^2 + b^3*sin(2*c)^2)*d)*x + (b^2*d*sin(2*c) - b*d^2*sin(2*c))*cos(2*(b + d)*x + 2*a + 4*c) - (b^2*d*sin(2*c) - b*d^2*sin(2*c))*cos(2*(b + d)*x + 2*a) - (b^2*d*sin(2*c) + b*d^2*sin(2*c))*cos(-2*(b - d)*x - 2*a + 4*c) + (b^2*d*sin(2*c) + b*d^2*sin(2*c))*cos(-2*(b - d)*x - 2*a) - 2*(b^2*d*sin(2*c) - d^3*sin(2*c))*cos(2*b*x + 2*a + 2*c) + 2*(b^2*d*sin(2*c) - d^3*sin(2*c))*cos(2*b*x + 2*a - 2*c) + 2*(b^3*sin(2*c) - b*d^2*sin(2*c))*cos(2*d*x) - 2*(b^3*sin(2*c) - b*d^2*sin(2*c))*cos(2*d*x + 4*c) - (b^2*d*cos(2*c) - b*d^2*cos(2*c))*sin(2*(b + d)*x + 2*a + 4*c) - (b^2*d*cos(2*c) - b*d^2*cos(2*c))*sin(2*(b + d)*x + 2*a) + (b^2*d*cos(2*c) + b*d^2*cos(2*c))*sin(-2*(b - d)*x - 2*a + 4*c) + (b^2*d*cos(2*c) + b*d^2*cos(2*c))*sin(-2*(b - d)*x - 2*a) + 2*(b^2*d*cos(2*c) - d^3*cos(2*c))*sin(2*b*x + 2*a + 2*c) + 2*(b^2*d*cos(2*c) - d^3*cos(2*c))*sin(2*b*x + 2*a - 2*c) + 2*(b^3*cos(2*c) - b*d^2*cos(2*c))*sin(2*d*x) + 2*(b^3*cos(2*c) - b*d^2*cos(2*c))*sin(2*d*x + 4*c))/((b*cos(2*c)^2 + b*sin(2*c)^2)*d^3 - (b^3*cos(2*c)^2 + b^3*sin(2*c)^2)*d)","B",0
204,1,1362,0,0.422544," ","integrate(sin(b*x+a)^2*sin(d*x+c)^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) + 3 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a + 6 \, c\right) + 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) + 3 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a\right) - 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + d\right)} x + 2 \, a + 4 \, c\right) - 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + d\right)} x + 2 \, a - 2 \, c\right) + 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) - 9 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - d\right)} x - 2 \, a + 4 \, c\right) + 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) - 9 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - d\right)} x - 2 \, a - 2 \, c\right) - 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) - 3 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a + 6 \, c\right) - 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) - 3 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a\right) - 2 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left(3 \, d x\right) - 2 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left(3 \, d x + 6 \, c\right) + 18 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left(d x + 4 \, c\right) + 18 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \cos\left(d x - 2 \, c\right) + 3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) + 3 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a + 6 \, c\right) - 3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) + 3 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a\right) - 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + d\right)} x + 2 \, a + 4 \, c\right) + 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + d\right)} x + 2 \, a - 2 \, c\right) + 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) - 9 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - d\right)} x - 2 \, a + 4 \, c\right) - 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) - 9 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - d\right)} x - 2 \, a - 2 \, c\right) - 3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) - 3 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a + 6 \, c\right) + 3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) - 3 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a\right) + 2 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left(3 \, d x\right) - 2 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left(3 \, d x + 6 \, c\right) + 18 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left(d x + 4 \, c\right) - 18 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \sin\left(d x - 2 \, c\right)}{96 \, {\left(9 \, {\left(\cos\left(3 \, c\right)^{2} + \sin\left(3 \, c\right)^{2}\right)} d^{5} - 40 \, {\left(b^{2} \cos\left(3 \, c\right)^{2} + b^{2} \sin\left(3 \, c\right)^{2}\right)} d^{3} + 16 \, {\left(b^{4} \cos\left(3 \, c\right)^{2} + b^{4} \sin\left(3 \, c\right)^{2}\right)} d\right)}}"," ",0,"-1/96*(3*(8*b^3*d*cos(3*c) - 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) + 3*d^4*cos(3*c))*cos((2*b + 3*d)*x + 2*a + 6*c) + 3*(8*b^3*d*cos(3*c) - 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) + 3*d^4*cos(3*c))*cos((2*b + 3*d)*x + 2*a) - 9*(8*b^3*d*cos(3*c) - 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) + 9*d^4*cos(3*c))*cos((2*b + d)*x + 2*a + 4*c) - 9*(8*b^3*d*cos(3*c) - 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) + 9*d^4*cos(3*c))*cos((2*b + d)*x + 2*a - 2*c) + 9*(8*b^3*d*cos(3*c) + 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) - 9*d^4*cos(3*c))*cos(-(2*b - d)*x - 2*a + 4*c) + 9*(8*b^3*d*cos(3*c) + 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) - 9*d^4*cos(3*c))*cos(-(2*b - d)*x - 2*a - 2*c) - 3*(8*b^3*d*cos(3*c) + 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) - 3*d^4*cos(3*c))*cos(-(2*b - 3*d)*x - 2*a + 6*c) - 3*(8*b^3*d*cos(3*c) + 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) - 3*d^4*cos(3*c))*cos(-(2*b - 3*d)*x - 2*a) - 2*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*cos(3*d*x) - 2*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*cos(3*d*x + 6*c) + 18*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*cos(d*x + 4*c) + 18*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*cos(d*x - 2*c) + 3*(8*b^3*d*sin(3*c) - 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) + 3*d^4*sin(3*c))*sin((2*b + 3*d)*x + 2*a + 6*c) - 3*(8*b^3*d*sin(3*c) - 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) + 3*d^4*sin(3*c))*sin((2*b + 3*d)*x + 2*a) - 9*(8*b^3*d*sin(3*c) - 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) + 9*d^4*sin(3*c))*sin((2*b + d)*x + 2*a + 4*c) + 9*(8*b^3*d*sin(3*c) - 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) + 9*d^4*sin(3*c))*sin((2*b + d)*x + 2*a - 2*c) + 9*(8*b^3*d*sin(3*c) + 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) - 9*d^4*sin(3*c))*sin(-(2*b - d)*x - 2*a + 4*c) - 9*(8*b^3*d*sin(3*c) + 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) - 9*d^4*sin(3*c))*sin(-(2*b - d)*x - 2*a - 2*c) - 3*(8*b^3*d*sin(3*c) + 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) - 3*d^4*sin(3*c))*sin(-(2*b - 3*d)*x - 2*a + 6*c) + 3*(8*b^3*d*sin(3*c) + 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) - 3*d^4*sin(3*c))*sin(-(2*b - 3*d)*x - 2*a) + 2*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*sin(3*d*x) - 2*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*sin(3*d*x + 6*c) + 18*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*sin(d*x + 4*c) - 18*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*sin(d*x - 2*c))/(9*(cos(3*c)^2 + sin(3*c)^2)*d^5 - 40*(b^2*cos(3*c)^2 + b^2*sin(3*c)^2)*d^3 + 16*(b^4*cos(3*c)^2 + b^4*sin(3*c)^2)*d)","B",0
205,0,0,0,0.000000," ","integrate(sin(b*x+a)^3*sin(d*x+c)^n,x, algorithm=""maxima"")","\int \sin\left(d x + c\right)^{n} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*sin(b*x + a)^3, x)","F",0
206,1,789,0,0.402962," ","integrate(sin(b*x+a)^3*sin(d*x+c),x, algorithm=""maxima"")","-\frac{{\left(3 \, b^{3} \sin\left(c\right) - b^{2} d \sin\left(c\right) - 3 \, b d^{2} \sin\left(c\right) + d^{3} \sin\left(c\right)\right)} \cos\left({\left(3 \, b + d\right)} x + 3 \, a + 2 \, c\right) - {\left(3 \, b^{3} \sin\left(c\right) - b^{2} d \sin\left(c\right) - 3 \, b d^{2} \sin\left(c\right) + d^{3} \sin\left(c\right)\right)} \cos\left({\left(3 \, b + d\right)} x + 3 \, a\right) + {\left(3 \, b^{3} \sin\left(c\right) + b^{2} d \sin\left(c\right) - 3 \, b d^{2} \sin\left(c\right) - d^{3} \sin\left(c\right)\right)} \cos\left(-{\left(3 \, b - d\right)} x - 3 \, a + 2 \, c\right) - {\left(3 \, b^{3} \sin\left(c\right) + b^{2} d \sin\left(c\right) - 3 \, b d^{2} \sin\left(c\right) - d^{3} \sin\left(c\right)\right)} \cos\left(-{\left(3 \, b - d\right)} x - 3 \, a\right) - 3 \, {\left(9 \, b^{3} \sin\left(c\right) - 9 \, b^{2} d \sin\left(c\right) - b d^{2} \sin\left(c\right) + d^{3} \sin\left(c\right)\right)} \cos\left({\left(b + d\right)} x + a + 2 \, c\right) + 3 \, {\left(9 \, b^{3} \sin\left(c\right) - 9 \, b^{2} d \sin\left(c\right) - b d^{2} \sin\left(c\right) + d^{3} \sin\left(c\right)\right)} \cos\left({\left(b + d\right)} x + a\right) - 3 \, {\left(9 \, b^{3} \sin\left(c\right) + 9 \, b^{2} d \sin\left(c\right) - b d^{2} \sin\left(c\right) - d^{3} \sin\left(c\right)\right)} \cos\left(-{\left(b - d\right)} x - a + 2 \, c\right) + 3 \, {\left(9 \, b^{3} \sin\left(c\right) + 9 \, b^{2} d \sin\left(c\right) - b d^{2} \sin\left(c\right) - d^{3} \sin\left(c\right)\right)} \cos\left(-{\left(b - d\right)} x - a\right) - {\left(3 \, b^{3} \cos\left(c\right) - b^{2} d \cos\left(c\right) - 3 \, b d^{2} \cos\left(c\right) + d^{3} \cos\left(c\right)\right)} \sin\left({\left(3 \, b + d\right)} x + 3 \, a + 2 \, c\right) - {\left(3 \, b^{3} \cos\left(c\right) - b^{2} d \cos\left(c\right) - 3 \, b d^{2} \cos\left(c\right) + d^{3} \cos\left(c\right)\right)} \sin\left({\left(3 \, b + d\right)} x + 3 \, a\right) - {\left(3 \, b^{3} \cos\left(c\right) + b^{2} d \cos\left(c\right) - 3 \, b d^{2} \cos\left(c\right) - d^{3} \cos\left(c\right)\right)} \sin\left(-{\left(3 \, b - d\right)} x - 3 \, a + 2 \, c\right) - {\left(3 \, b^{3} \cos\left(c\right) + b^{2} d \cos\left(c\right) - 3 \, b d^{2} \cos\left(c\right) - d^{3} \cos\left(c\right)\right)} \sin\left(-{\left(3 \, b - d\right)} x - 3 \, a\right) + 3 \, {\left(9 \, b^{3} \cos\left(c\right) - 9 \, b^{2} d \cos\left(c\right) - b d^{2} \cos\left(c\right) + d^{3} \cos\left(c\right)\right)} \sin\left({\left(b + d\right)} x + a + 2 \, c\right) + 3 \, {\left(9 \, b^{3} \cos\left(c\right) - 9 \, b^{2} d \cos\left(c\right) - b d^{2} \cos\left(c\right) + d^{3} \cos\left(c\right)\right)} \sin\left({\left(b + d\right)} x + a\right) + 3 \, {\left(9 \, b^{3} \cos\left(c\right) + 9 \, b^{2} d \cos\left(c\right) - b d^{2} \cos\left(c\right) - d^{3} \cos\left(c\right)\right)} \sin\left(-{\left(b - d\right)} x - a + 2 \, c\right) + 3 \, {\left(9 \, b^{3} \cos\left(c\right) + 9 \, b^{2} d \cos\left(c\right) - b d^{2} \cos\left(c\right) - d^{3} \cos\left(c\right)\right)} \sin\left(-{\left(b - d\right)} x - a\right)}{16 \, {\left(9 \, b^{4} \cos\left(c\right)^{2} + 9 \, b^{4} \sin\left(c\right)^{2} + {\left(\cos\left(c\right)^{2} + \sin\left(c\right)^{2}\right)} d^{4} - 10 \, {\left(b^{2} \cos\left(c\right)^{2} + b^{2} \sin\left(c\right)^{2}\right)} d^{2}\right)}}"," ",0,"-1/16*((3*b^3*sin(c) - b^2*d*sin(c) - 3*b*d^2*sin(c) + d^3*sin(c))*cos((3*b + d)*x + 3*a + 2*c) - (3*b^3*sin(c) - b^2*d*sin(c) - 3*b*d^2*sin(c) + d^3*sin(c))*cos((3*b + d)*x + 3*a) + (3*b^3*sin(c) + b^2*d*sin(c) - 3*b*d^2*sin(c) - d^3*sin(c))*cos(-(3*b - d)*x - 3*a + 2*c) - (3*b^3*sin(c) + b^2*d*sin(c) - 3*b*d^2*sin(c) - d^3*sin(c))*cos(-(3*b - d)*x - 3*a) - 3*(9*b^3*sin(c) - 9*b^2*d*sin(c) - b*d^2*sin(c) + d^3*sin(c))*cos((b + d)*x + a + 2*c) + 3*(9*b^3*sin(c) - 9*b^2*d*sin(c) - b*d^2*sin(c) + d^3*sin(c))*cos((b + d)*x + a) - 3*(9*b^3*sin(c) + 9*b^2*d*sin(c) - b*d^2*sin(c) - d^3*sin(c))*cos(-(b - d)*x - a + 2*c) + 3*(9*b^3*sin(c) + 9*b^2*d*sin(c) - b*d^2*sin(c) - d^3*sin(c))*cos(-(b - d)*x - a) - (3*b^3*cos(c) - b^2*d*cos(c) - 3*b*d^2*cos(c) + d^3*cos(c))*sin((3*b + d)*x + 3*a + 2*c) - (3*b^3*cos(c) - b^2*d*cos(c) - 3*b*d^2*cos(c) + d^3*cos(c))*sin((3*b + d)*x + 3*a) - (3*b^3*cos(c) + b^2*d*cos(c) - 3*b*d^2*cos(c) - d^3*cos(c))*sin(-(3*b - d)*x - 3*a + 2*c) - (3*b^3*cos(c) + b^2*d*cos(c) - 3*b*d^2*cos(c) - d^3*cos(c))*sin(-(3*b - d)*x - 3*a) + 3*(9*b^3*cos(c) - 9*b^2*d*cos(c) - b*d^2*cos(c) + d^3*cos(c))*sin((b + d)*x + a + 2*c) + 3*(9*b^3*cos(c) - 9*b^2*d*cos(c) - b*d^2*cos(c) + d^3*cos(c))*sin((b + d)*x + a) + 3*(9*b^3*cos(c) + 9*b^2*d*cos(c) - b*d^2*cos(c) - d^3*cos(c))*sin(-(b - d)*x - a + 2*c) + 3*(9*b^3*cos(c) + 9*b^2*d*cos(c) - b*d^2*cos(c) - d^3*cos(c))*sin(-(b - d)*x - a))/(9*b^4*cos(c)^2 + 9*b^4*sin(c)^2 + (cos(c)^2 + sin(c)^2)*d^4 - 10*(b^2*cos(c)^2 + b^2*sin(c)^2)*d^2)","B",0
207,1,1360,0,0.432605," ","integrate(sin(b*x+a)^3*sin(d*x+c)^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(3 \, b^{4} \cos\left(2 \, c\right) - 2 \, b^{3} d \cos\left(2 \, c\right) - 12 \, b^{2} d^{2} \cos\left(2 \, c\right) + 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left({\left(3 \, b + 2 \, d\right)} x + 3 \, a + 4 \, c\right) + 3 \, {\left(3 \, b^{4} \cos\left(2 \, c\right) - 2 \, b^{3} d \cos\left(2 \, c\right) - 12 \, b^{2} d^{2} \cos\left(2 \, c\right) + 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left({\left(3 \, b + 2 \, d\right)} x + 3 \, a\right) + 3 \, {\left(3 \, b^{4} \cos\left(2 \, c\right) + 2 \, b^{3} d \cos\left(2 \, c\right) - 12 \, b^{2} d^{2} \cos\left(2 \, c\right) - 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left(-{\left(3 \, b - 2 \, d\right)} x - 3 \, a + 4 \, c\right) + 3 \, {\left(3 \, b^{4} \cos\left(2 \, c\right) + 2 \, b^{3} d \cos\left(2 \, c\right) - 12 \, b^{2} d^{2} \cos\left(2 \, c\right) - 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left(-{\left(3 \, b - 2 \, d\right)} x - 3 \, a\right) - 9 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 18 \, b^{3} d \cos\left(2 \, c\right) - 4 \, b^{2} d^{2} \cos\left(2 \, c\right) + 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left({\left(b + 2 \, d\right)} x + a + 4 \, c\right) - 9 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 18 \, b^{3} d \cos\left(2 \, c\right) - 4 \, b^{2} d^{2} \cos\left(2 \, c\right) + 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left({\left(b + 2 \, d\right)} x + a\right) - 9 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) + 18 \, b^{3} d \cos\left(2 \, c\right) - 4 \, b^{2} d^{2} \cos\left(2 \, c\right) - 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left(-{\left(b - 2 \, d\right)} x - a + 4 \, c\right) - 9 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) + 18 \, b^{3} d \cos\left(2 \, c\right) - 4 \, b^{2} d^{2} \cos\left(2 \, c\right) - 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left(-{\left(b - 2 \, d\right)} x - a\right) - 2 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 40 \, b^{2} d^{2} \cos\left(2 \, c\right) + 16 \, d^{4} \cos\left(2 \, c\right)\right)} \cos\left(3 \, b x + 3 \, a + 2 \, c\right) - 2 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 40 \, b^{2} d^{2} \cos\left(2 \, c\right) + 16 \, d^{4} \cos\left(2 \, c\right)\right)} \cos\left(3 \, b x + 3 \, a - 2 \, c\right) + 18 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 40 \, b^{2} d^{2} \cos\left(2 \, c\right) + 16 \, d^{4} \cos\left(2 \, c\right)\right)} \cos\left(b x + a + 2 \, c\right) + 18 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 40 \, b^{2} d^{2} \cos\left(2 \, c\right) + 16 \, d^{4} \cos\left(2 \, c\right)\right)} \cos\left(b x + a - 2 \, c\right) + 3 \, {\left(3 \, b^{4} \sin\left(2 \, c\right) - 2 \, b^{3} d \sin\left(2 \, c\right) - 12 \, b^{2} d^{2} \sin\left(2 \, c\right) + 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left({\left(3 \, b + 2 \, d\right)} x + 3 \, a + 4 \, c\right) - 3 \, {\left(3 \, b^{4} \sin\left(2 \, c\right) - 2 \, b^{3} d \sin\left(2 \, c\right) - 12 \, b^{2} d^{2} \sin\left(2 \, c\right) + 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left({\left(3 \, b + 2 \, d\right)} x + 3 \, a\right) + 3 \, {\left(3 \, b^{4} \sin\left(2 \, c\right) + 2 \, b^{3} d \sin\left(2 \, c\right) - 12 \, b^{2} d^{2} \sin\left(2 \, c\right) - 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left(-{\left(3 \, b - 2 \, d\right)} x - 3 \, a + 4 \, c\right) - 3 \, {\left(3 \, b^{4} \sin\left(2 \, c\right) + 2 \, b^{3} d \sin\left(2 \, c\right) - 12 \, b^{2} d^{2} \sin\left(2 \, c\right) - 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left(-{\left(3 \, b - 2 \, d\right)} x - 3 \, a\right) - 9 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 18 \, b^{3} d \sin\left(2 \, c\right) - 4 \, b^{2} d^{2} \sin\left(2 \, c\right) + 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left({\left(b + 2 \, d\right)} x + a + 4 \, c\right) + 9 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 18 \, b^{3} d \sin\left(2 \, c\right) - 4 \, b^{2} d^{2} \sin\left(2 \, c\right) + 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left({\left(b + 2 \, d\right)} x + a\right) - 9 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) + 18 \, b^{3} d \sin\left(2 \, c\right) - 4 \, b^{2} d^{2} \sin\left(2 \, c\right) - 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left(-{\left(b - 2 \, d\right)} x - a + 4 \, c\right) + 9 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) + 18 \, b^{3} d \sin\left(2 \, c\right) - 4 \, b^{2} d^{2} \sin\left(2 \, c\right) - 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left(-{\left(b - 2 \, d\right)} x - a\right) - 2 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 40 \, b^{2} d^{2} \sin\left(2 \, c\right) + 16 \, d^{4} \sin\left(2 \, c\right)\right)} \sin\left(3 \, b x + 3 \, a + 2 \, c\right) + 2 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 40 \, b^{2} d^{2} \sin\left(2 \, c\right) + 16 \, d^{4} \sin\left(2 \, c\right)\right)} \sin\left(3 \, b x + 3 \, a - 2 \, c\right) + 18 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 40 \, b^{2} d^{2} \sin\left(2 \, c\right) + 16 \, d^{4} \sin\left(2 \, c\right)\right)} \sin\left(b x + a + 2 \, c\right) - 18 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 40 \, b^{2} d^{2} \sin\left(2 \, c\right) + 16 \, d^{4} \sin\left(2 \, c\right)\right)} \sin\left(b x + a - 2 \, c\right)}{96 \, {\left(9 \, b^{5} \cos\left(2 \, c\right)^{2} + 9 \, b^{5} \sin\left(2 \, c\right)^{2} + 16 \, {\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{4} - 40 \, {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"-1/96*(3*(3*b^4*cos(2*c) - 2*b^3*d*cos(2*c) - 12*b^2*d^2*cos(2*c) + 8*b*d^3*cos(2*c))*cos((3*b + 2*d)*x + 3*a + 4*c) + 3*(3*b^4*cos(2*c) - 2*b^3*d*cos(2*c) - 12*b^2*d^2*cos(2*c) + 8*b*d^3*cos(2*c))*cos((3*b + 2*d)*x + 3*a) + 3*(3*b^4*cos(2*c) + 2*b^3*d*cos(2*c) - 12*b^2*d^2*cos(2*c) - 8*b*d^3*cos(2*c))*cos(-(3*b - 2*d)*x - 3*a + 4*c) + 3*(3*b^4*cos(2*c) + 2*b^3*d*cos(2*c) - 12*b^2*d^2*cos(2*c) - 8*b*d^3*cos(2*c))*cos(-(3*b - 2*d)*x - 3*a) - 9*(9*b^4*cos(2*c) - 18*b^3*d*cos(2*c) - 4*b^2*d^2*cos(2*c) + 8*b*d^3*cos(2*c))*cos((b + 2*d)*x + a + 4*c) - 9*(9*b^4*cos(2*c) - 18*b^3*d*cos(2*c) - 4*b^2*d^2*cos(2*c) + 8*b*d^3*cos(2*c))*cos((b + 2*d)*x + a) - 9*(9*b^4*cos(2*c) + 18*b^3*d*cos(2*c) - 4*b^2*d^2*cos(2*c) - 8*b*d^3*cos(2*c))*cos(-(b - 2*d)*x - a + 4*c) - 9*(9*b^4*cos(2*c) + 18*b^3*d*cos(2*c) - 4*b^2*d^2*cos(2*c) - 8*b*d^3*cos(2*c))*cos(-(b - 2*d)*x - a) - 2*(9*b^4*cos(2*c) - 40*b^2*d^2*cos(2*c) + 16*d^4*cos(2*c))*cos(3*b*x + 3*a + 2*c) - 2*(9*b^4*cos(2*c) - 40*b^2*d^2*cos(2*c) + 16*d^4*cos(2*c))*cos(3*b*x + 3*a - 2*c) + 18*(9*b^4*cos(2*c) - 40*b^2*d^2*cos(2*c) + 16*d^4*cos(2*c))*cos(b*x + a + 2*c) + 18*(9*b^4*cos(2*c) - 40*b^2*d^2*cos(2*c) + 16*d^4*cos(2*c))*cos(b*x + a - 2*c) + 3*(3*b^4*sin(2*c) - 2*b^3*d*sin(2*c) - 12*b^2*d^2*sin(2*c) + 8*b*d^3*sin(2*c))*sin((3*b + 2*d)*x + 3*a + 4*c) - 3*(3*b^4*sin(2*c) - 2*b^3*d*sin(2*c) - 12*b^2*d^2*sin(2*c) + 8*b*d^3*sin(2*c))*sin((3*b + 2*d)*x + 3*a) + 3*(3*b^4*sin(2*c) + 2*b^3*d*sin(2*c) - 12*b^2*d^2*sin(2*c) - 8*b*d^3*sin(2*c))*sin(-(3*b - 2*d)*x - 3*a + 4*c) - 3*(3*b^4*sin(2*c) + 2*b^3*d*sin(2*c) - 12*b^2*d^2*sin(2*c) - 8*b*d^3*sin(2*c))*sin(-(3*b - 2*d)*x - 3*a) - 9*(9*b^4*sin(2*c) - 18*b^3*d*sin(2*c) - 4*b^2*d^2*sin(2*c) + 8*b*d^3*sin(2*c))*sin((b + 2*d)*x + a + 4*c) + 9*(9*b^4*sin(2*c) - 18*b^3*d*sin(2*c) - 4*b^2*d^2*sin(2*c) + 8*b*d^3*sin(2*c))*sin((b + 2*d)*x + a) - 9*(9*b^4*sin(2*c) + 18*b^3*d*sin(2*c) - 4*b^2*d^2*sin(2*c) - 8*b*d^3*sin(2*c))*sin(-(b - 2*d)*x - a + 4*c) + 9*(9*b^4*sin(2*c) + 18*b^3*d*sin(2*c) - 4*b^2*d^2*sin(2*c) - 8*b*d^3*sin(2*c))*sin(-(b - 2*d)*x - a) - 2*(9*b^4*sin(2*c) - 40*b^2*d^2*sin(2*c) + 16*d^4*sin(2*c))*sin(3*b*x + 3*a + 2*c) + 2*(9*b^4*sin(2*c) - 40*b^2*d^2*sin(2*c) + 16*d^4*sin(2*c))*sin(3*b*x + 3*a - 2*c) + 18*(9*b^4*sin(2*c) - 40*b^2*d^2*sin(2*c) + 16*d^4*sin(2*c))*sin(b*x + a + 2*c) - 18*(9*b^4*sin(2*c) - 40*b^2*d^2*sin(2*c) + 16*d^4*sin(2*c))*sin(b*x + a - 2*c))/(9*b^5*cos(2*c)^2 + 9*b^5*sin(2*c)^2 + 16*(b*cos(2*c)^2 + b*sin(2*c)^2)*d^4 - 40*(b^3*cos(2*c)^2 + b^3*sin(2*c)^2)*d^2)","B",0
208,1,2612,0,0.574379," ","integrate(sin(b*x+a)^3*sin(d*x+c)^3,x, algorithm=""maxima"")","-\frac{9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) - b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) + 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(3 \, b + d\right)} x + 3 \, a + 4 \, c\right) - 9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) - b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) + 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(3 \, b + d\right)} x + 3 \, a - 2 \, c\right) + 9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) + b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) - 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(3 \, b - d\right)} x - 3 \, a + 4 \, c\right) - 9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) + b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) - 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(3 \, b - d\right)} x - 3 \, a - 2 \, c\right) + 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) + 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) - 3 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) - 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) + 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) - 3 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a\right) - {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(3 \, {\left(b + d\right)} x + 3 \, a + 6 \, c\right) + {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(3 \, {\left(b + d\right)} x + 3 \, a\right) - 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a + 4 \, c\right) + 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a - 2 \, c\right) - 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a + 4 \, c\right) + 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a - 2 \, c\right) - {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-3 \, {\left(b - d\right)} x - 3 \, a + 6 \, c\right) + {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-3 \, {\left(b - d\right)} x - 3 \, a\right) + 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) - 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) + 3 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) - 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) - 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) + 3 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a\right) - 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) - b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) + 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(3 \, b + d\right)} x + 3 \, a + 4 \, c\right) - 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) - b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) + 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(3 \, b + d\right)} x + 3 \, a - 2 \, c\right) - 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) + b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) - 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(3 \, b - d\right)} x - 3 \, a + 4 \, c\right) - 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) + b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) - 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(3 \, b - d\right)} x - 3 \, a - 2 \, c\right) - 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) + 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) - 3 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) - 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) + 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) - 3 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a\right) + {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(3 \, {\left(b + d\right)} x + 3 \, a + 6 \, c\right) + {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(3 \, {\left(b + d\right)} x + 3 \, a\right) + 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a + 4 \, c\right) + 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a - 2 \, c\right) + 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a + 4 \, c\right) + 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a - 2 \, c\right) + {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-3 \, {\left(b - d\right)} x - 3 \, a + 6 \, c\right) + {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-3 \, {\left(b - d\right)} x - 3 \, a\right) - 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) - 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) + 3 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) - 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) - 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) + 3 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a\right)}{192 \, {\left(9 \, b^{6} \cos\left(3 \, c\right)^{2} + 9 \, b^{6} \sin\left(3 \, c\right)^{2} - 9 \, {\left(\cos\left(3 \, c\right)^{2} + \sin\left(3 \, c\right)^{2}\right)} d^{6} + 91 \, {\left(b^{2} \cos\left(3 \, c\right)^{2} + b^{2} \sin\left(3 \, c\right)^{2}\right)} d^{4} - 91 \, {\left(b^{4} \cos\left(3 \, c\right)^{2} + b^{4} \sin\left(3 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"-1/192*(9*(3*b^5*sin(3*c) - b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) + 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos((3*b + d)*x + 3*a + 4*c) - 9*(3*b^5*sin(3*c) - b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) + 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos((3*b + d)*x + 3*a - 2*c) + 9*(3*b^5*sin(3*c) + b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) - 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-(3*b - d)*x - 3*a + 4*c) - 9*(3*b^5*sin(3*c) + b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) - 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-(3*b - d)*x - 3*a - 2*c) + 9*(9*b^5*sin(3*c) - 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) + 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) - 3*d^5*sin(3*c))*cos((b + 3*d)*x + a + 6*c) - 9*(9*b^5*sin(3*c) - 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) + 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) - 3*d^5*sin(3*c))*cos((b + 3*d)*x + a) - (9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos(3*(b + d)*x + 3*a + 6*c) + (9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos(3*(b + d)*x + 3*a) - 27*(9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos((b + d)*x + a + 4*c) + 27*(9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos((b + d)*x + a - 2*c) - 27*(9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-(b - d)*x - a + 4*c) + 27*(9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-(b - d)*x - a - 2*c) - (9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-3*(b - d)*x - 3*a + 6*c) + (9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-3*(b - d)*x - 3*a) + 9*(9*b^5*sin(3*c) + 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) - 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) + 3*d^5*sin(3*c))*cos(-(b - 3*d)*x - a + 6*c) - 9*(9*b^5*sin(3*c) + 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) - 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) + 3*d^5*sin(3*c))*cos(-(b - 3*d)*x - a) - 9*(3*b^5*cos(3*c) - b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) + 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin((3*b + d)*x + 3*a + 4*c) - 9*(3*b^5*cos(3*c) - b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) + 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin((3*b + d)*x + 3*a - 2*c) - 9*(3*b^5*cos(3*c) + b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) - 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-(3*b - d)*x - 3*a + 4*c) - 9*(3*b^5*cos(3*c) + b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) - 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-(3*b - d)*x - 3*a - 2*c) - 9*(9*b^5*cos(3*c) - 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) + 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) - 3*d^5*cos(3*c))*sin((b + 3*d)*x + a + 6*c) - 9*(9*b^5*cos(3*c) - 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) + 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) - 3*d^5*cos(3*c))*sin((b + 3*d)*x + a) + (9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin(3*(b + d)*x + 3*a + 6*c) + (9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin(3*(b + d)*x + 3*a) + 27*(9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin((b + d)*x + a + 4*c) + 27*(9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin((b + d)*x + a - 2*c) + 27*(9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-(b - d)*x - a + 4*c) + 27*(9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-(b - d)*x - a - 2*c) + (9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-3*(b - d)*x - 3*a + 6*c) + (9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-3*(b - d)*x - 3*a) - 9*(9*b^5*cos(3*c) + 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) - 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) + 3*d^5*cos(3*c))*sin(-(b - 3*d)*x - a + 6*c) - 9*(9*b^5*cos(3*c) + 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) - 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) + 3*d^5*cos(3*c))*sin(-(b - 3*d)*x - a))/(9*b^6*cos(3*c)^2 + 9*b^6*sin(3*c)^2 - 9*(cos(3*c)^2 + sin(3*c)^2)*d^6 + 91*(b^2*cos(3*c)^2 + b^2*sin(3*c)^2)*d^4 - 91*(b^4*cos(3*c)^2 + b^4*sin(3*c)^2)*d^2)","B",0
209,0,0,0,0.000000," ","integrate(cos(d*x+c)^n*sin(b*x+a),x, algorithm=""maxima"")","\int \cos\left(d x + c\right)^{n} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(cos(d*x + c)^n*sin(b*x + a), x)","F",0
210,1,912,0,0.390870," ","integrate(cos(d*x+c)^3*sin(b*x+a),x, algorithm=""maxima"")","-\frac{{\left(b^{3} \cos\left(3 \, c\right) - 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) + 3 \, d^{3} \cos\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) + {\left(b^{3} \cos\left(3 \, c\right) - 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) + 3 \, d^{3} \cos\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a\right) + 3 \, {\left(b^{3} \cos\left(3 \, c\right) - b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) + 9 \, d^{3} \cos\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a + 4 \, c\right) + 3 \, {\left(b^{3} \cos\left(3 \, c\right) - b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) + 9 \, d^{3} \cos\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a - 2 \, c\right) + 3 \, {\left(b^{3} \cos\left(3 \, c\right) + b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) - 9 \, d^{3} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a + 4 \, c\right) + 3 \, {\left(b^{3} \cos\left(3 \, c\right) + b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) - 9 \, d^{3} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a - 2 \, c\right) + {\left(b^{3} \cos\left(3 \, c\right) + 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) - 3 \, d^{3} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) + {\left(b^{3} \cos\left(3 \, c\right) + 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) - 3 \, d^{3} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a\right) + {\left(b^{3} \sin\left(3 \, c\right) - 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) + 3 \, d^{3} \sin\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) - {\left(b^{3} \sin\left(3 \, c\right) - 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) + 3 \, d^{3} \sin\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a\right) + 3 \, {\left(b^{3} \sin\left(3 \, c\right) - b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) + 9 \, d^{3} \sin\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a + 4 \, c\right) - 3 \, {\left(b^{3} \sin\left(3 \, c\right) - b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) + 9 \, d^{3} \sin\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a - 2 \, c\right) + 3 \, {\left(b^{3} \sin\left(3 \, c\right) + b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) - 9 \, d^{3} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a + 4 \, c\right) - 3 \, {\left(b^{3} \sin\left(3 \, c\right) + b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) - 9 \, d^{3} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a - 2 \, c\right) + {\left(b^{3} \sin\left(3 \, c\right) + 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) - 3 \, d^{3} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) - {\left(b^{3} \sin\left(3 \, c\right) + 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) - 3 \, d^{3} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a\right)}{16 \, {\left(b^{4} \cos\left(3 \, c\right)^{2} + b^{4} \sin\left(3 \, c\right)^{2} + 9 \, {\left(\cos\left(3 \, c\right)^{2} + \sin\left(3 \, c\right)^{2}\right)} d^{4} - 10 \, {\left(b^{2} \cos\left(3 \, c\right)^{2} + b^{2} \sin\left(3 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"-1/16*((b^3*cos(3*c) - 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) + 3*d^3*cos(3*c))*cos((b + 3*d)*x + a + 6*c) + (b^3*cos(3*c) - 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) + 3*d^3*cos(3*c))*cos((b + 3*d)*x + a) + 3*(b^3*cos(3*c) - b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) + 9*d^3*cos(3*c))*cos((b + d)*x + a + 4*c) + 3*(b^3*cos(3*c) - b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) + 9*d^3*cos(3*c))*cos((b + d)*x + a - 2*c) + 3*(b^3*cos(3*c) + b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) - 9*d^3*cos(3*c))*cos(-(b - d)*x - a + 4*c) + 3*(b^3*cos(3*c) + b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) - 9*d^3*cos(3*c))*cos(-(b - d)*x - a - 2*c) + (b^3*cos(3*c) + 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) - 3*d^3*cos(3*c))*cos(-(b - 3*d)*x - a + 6*c) + (b^3*cos(3*c) + 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) - 3*d^3*cos(3*c))*cos(-(b - 3*d)*x - a) + (b^3*sin(3*c) - 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) + 3*d^3*sin(3*c))*sin((b + 3*d)*x + a + 6*c) - (b^3*sin(3*c) - 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) + 3*d^3*sin(3*c))*sin((b + 3*d)*x + a) + 3*(b^3*sin(3*c) - b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) + 9*d^3*sin(3*c))*sin((b + d)*x + a + 4*c) - 3*(b^3*sin(3*c) - b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) + 9*d^3*sin(3*c))*sin((b + d)*x + a - 2*c) + 3*(b^3*sin(3*c) + b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) - 9*d^3*sin(3*c))*sin(-(b - d)*x - a + 4*c) - 3*(b^3*sin(3*c) + b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) - 9*d^3*sin(3*c))*sin(-(b - d)*x - a - 2*c) + (b^3*sin(3*c) + 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) - 3*d^3*sin(3*c))*sin(-(b - 3*d)*x - a + 6*c) - (b^3*sin(3*c) + 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) - 3*d^3*sin(3*c))*sin(-(b - 3*d)*x - a))/(b^4*cos(3*c)^2 + b^4*sin(3*c)^2 + 9*(cos(3*c)^2 + sin(3*c)^2)*d^4 - 10*(b^2*cos(3*c)^2 + b^2*sin(3*c)^2)*d^2)","B",0
211,1,414,0,0.347877," ","integrate(cos(d*x+c)^2*sin(b*x+a),x, algorithm=""maxima"")","-\frac{{\left(b^{2} \cos\left(2 \, c\right) - 2 \, b d \cos\left(2 \, c\right)\right)} \cos\left({\left(b + 2 \, d\right)} x + a + 4 \, c\right) + {\left(b^{2} \cos\left(2 \, c\right) - 2 \, b d \cos\left(2 \, c\right)\right)} \cos\left({\left(b + 2 \, d\right)} x + a\right) + {\left(b^{2} \cos\left(2 \, c\right) + 2 \, b d \cos\left(2 \, c\right)\right)} \cos\left(-{\left(b - 2 \, d\right)} x - a + 4 \, c\right) + {\left(b^{2} \cos\left(2 \, c\right) + 2 \, b d \cos\left(2 \, c\right)\right)} \cos\left(-{\left(b - 2 \, d\right)} x - a\right) + 2 \, {\left(b^{2} \cos\left(2 \, c\right) - 4 \, d^{2} \cos\left(2 \, c\right)\right)} \cos\left(b x + a + 2 \, c\right) + 2 \, {\left(b^{2} \cos\left(2 \, c\right) - 4 \, d^{2} \cos\left(2 \, c\right)\right)} \cos\left(b x + a - 2 \, c\right) + {\left(b^{2} \sin\left(2 \, c\right) - 2 \, b d \sin\left(2 \, c\right)\right)} \sin\left({\left(b + 2 \, d\right)} x + a + 4 \, c\right) - {\left(b^{2} \sin\left(2 \, c\right) - 2 \, b d \sin\left(2 \, c\right)\right)} \sin\left({\left(b + 2 \, d\right)} x + a\right) + {\left(b^{2} \sin\left(2 \, c\right) + 2 \, b d \sin\left(2 \, c\right)\right)} \sin\left(-{\left(b - 2 \, d\right)} x - a + 4 \, c\right) - {\left(b^{2} \sin\left(2 \, c\right) + 2 \, b d \sin\left(2 \, c\right)\right)} \sin\left(-{\left(b - 2 \, d\right)} x - a\right) + 2 \, {\left(b^{2} \sin\left(2 \, c\right) - 4 \, d^{2} \sin\left(2 \, c\right)\right)} \sin\left(b x + a + 2 \, c\right) - 2 \, {\left(b^{2} \sin\left(2 \, c\right) - 4 \, d^{2} \sin\left(2 \, c\right)\right)} \sin\left(b x + a - 2 \, c\right)}{8 \, {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2} - 4 \, {\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"-1/8*((b^2*cos(2*c) - 2*b*d*cos(2*c))*cos((b + 2*d)*x + a + 4*c) + (b^2*cos(2*c) - 2*b*d*cos(2*c))*cos((b + 2*d)*x + a) + (b^2*cos(2*c) + 2*b*d*cos(2*c))*cos(-(b - 2*d)*x - a + 4*c) + (b^2*cos(2*c) + 2*b*d*cos(2*c))*cos(-(b - 2*d)*x - a) + 2*(b^2*cos(2*c) - 4*d^2*cos(2*c))*cos(b*x + a + 2*c) + 2*(b^2*cos(2*c) - 4*d^2*cos(2*c))*cos(b*x + a - 2*c) + (b^2*sin(2*c) - 2*b*d*sin(2*c))*sin((b + 2*d)*x + a + 4*c) - (b^2*sin(2*c) - 2*b*d*sin(2*c))*sin((b + 2*d)*x + a) + (b^2*sin(2*c) + 2*b*d*sin(2*c))*sin(-(b - 2*d)*x - a + 4*c) - (b^2*sin(2*c) + 2*b*d*sin(2*c))*sin(-(b - 2*d)*x - a) + 2*(b^2*sin(2*c) - 4*d^2*sin(2*c))*sin(b*x + a + 2*c) - 2*(b^2*sin(2*c) - 4*d^2*sin(2*c))*sin(b*x + a - 2*c))/(b^3*cos(2*c)^2 + b^3*sin(2*c)^2 - 4*(b*cos(2*c)^2 + b*sin(2*c)^2)*d^2)","B",0
212,1,40,0,0.311544," ","integrate(cos(d*x+c)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{\cos\left(b x + d x + a + c\right)}{2 \, {\left(b + d\right)}} - \frac{\cos\left(-b x + d x - a + c\right)}{2 \, {\left(b - d\right)}}"," ",0,"-1/2*cos(b*x + d*x + a + c)/(b + d) - 1/2*cos(-b*x + d*x - a + c)/(b - d)","A",0
213,1,73,0,0.341866," ","integrate(sec(b*x+c)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{2 \, b x \sin\left(-a + c\right) + \cos\left(-a + c\right) \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, c\right) + \cos\left(2 \, c\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, c\right) + \sin\left(2 \, c\right)^{2}\right)}{2 \, b}"," ",0,"-1/2*(2*b*x*sin(-a + c) + cos(-a + c)*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*c) + cos(2*c)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*c) + sin(2*c)^2))/b","B",0
214,1,387,0,0.518963," ","integrate(sec(b*x+c)^2*sin(b*x+a),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(b x + 2 \, a\right) + \cos\left(b x + 2 \, c\right)\right)} \cos\left(2 \, b x + a + 2 \, c\right) + 2 \, \cos\left(b x + 2 \, a\right) \cos\left(a\right) + 2 \, \cos\left(b x + 2 \, c\right) \cos\left(a\right) + {\left(\cos\left(2 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) + 2 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \sin\left(-a + c\right) + \sin\left(2 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) + 2 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) \sin\left(-a + c\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(-a + c\right)\right)} \log\left(\frac{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} - 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} - 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}\right) + 2 \, {\left(\sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, c\right)\right)} \sin\left(2 \, b x + a + 2 \, c\right) + 2 \, \sin\left(b x + 2 \, a\right) \sin\left(a\right) + 2 \, \sin\left(b x + 2 \, c\right) \sin\left(a\right)}{2 \, {\left(b \cos\left(2 \, b x + a + 2 \, c\right)^{2} + 2 \, b \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) + b \sin\left(2 \, b x + a + 2 \, c\right)^{2} + 2 \, b \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b\right)}}"," ",0,"1/2*(2*(cos(b*x + 2*a) + cos(b*x + 2*c))*cos(2*b*x + a + 2*c) + 2*cos(b*x + 2*a)*cos(a) + 2*cos(b*x + 2*c)*cos(a) + (cos(2*b*x + a + 2*c)^2*sin(-a + c) + 2*cos(2*b*x + a + 2*c)*cos(a)*sin(-a + c) + sin(2*b*x + a + 2*c)^2*sin(-a + c) + 2*sin(2*b*x + a + 2*c)*sin(a)*sin(-a + c) + (cos(a)^2 + sin(a)^2)*sin(-a + c))*log((cos(b*x + 2*c)^2 + cos(c)^2 - 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 + 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)/(cos(b*x + 2*c)^2 + cos(c)^2 + 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 - 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)) + 2*(sin(b*x + 2*a) + sin(b*x + 2*c))*sin(2*b*x + a + 2*c) + 2*sin(b*x + 2*a)*sin(a) + 2*sin(b*x + 2*c)*sin(a))/(b*cos(2*b*x + a + 2*c)^2 + 2*b*cos(2*b*x + a + 2*c)*cos(a) + b*sin(2*b*x + a + 2*c)^2 + 2*b*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*b)","B",0
215,1,391,0,0.342821," ","integrate(sec(b*x+c)^3*sin(b*x+a),x, algorithm=""maxima"")","\frac{{\left(2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) + \cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) + 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) + \cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(2 \, b x + a + 3 \, c\right) + {\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(a + c\right) + 2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) \cos\left(a + c\right) + {\left(2 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) + \sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right) + 2 \, {\left(2 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) + \sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(2 \, b x + a + 3 \, c\right) + {\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(a + c\right) + 2 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) \sin\left(a + c\right)}{b \cos\left(4 \, b x + a + 5 \, c\right)^{2} + 4 \, b \cos\left(2 \, b x + a + 3 \, c\right)^{2} + 4 \, b \cos\left(2 \, b x + a + 3 \, c\right) \cos\left(a + c\right) + b \cos\left(a + c\right)^{2} + b \sin\left(4 \, b x + a + 5 \, c\right)^{2} + 4 \, b \sin\left(2 \, b x + a + 3 \, c\right)^{2} + 4 \, b \sin\left(2 \, b x + a + 3 \, c\right) \sin\left(a + c\right) + b \sin\left(a + c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, b x + a + 3 \, c\right) + b \cos\left(a + c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) + 2 \, {\left(2 \, b \sin\left(2 \, b x + a + 3 \, c\right) + b \sin\left(a + c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right)}"," ",0,"((2*cos(2*b*x + 2*a + 2*c) + cos(2*a) - cos(2*c))*cos(4*b*x + a + 5*c) + 2*(2*cos(2*b*x + 2*a + 2*c) + cos(2*a) - cos(2*c))*cos(2*b*x + a + 3*c) + (cos(2*a) - cos(2*c))*cos(a + c) + 2*cos(2*b*x + 2*a + 2*c)*cos(a + c) + (2*sin(2*b*x + 2*a + 2*c) + sin(2*a) - sin(2*c))*sin(4*b*x + a + 5*c) + 2*(2*sin(2*b*x + 2*a + 2*c) + sin(2*a) - sin(2*c))*sin(2*b*x + a + 3*c) + (sin(2*a) - sin(2*c))*sin(a + c) + 2*sin(2*b*x + 2*a + 2*c)*sin(a + c))/(b*cos(4*b*x + a + 5*c)^2 + 4*b*cos(2*b*x + a + 3*c)^2 + 4*b*cos(2*b*x + a + 3*c)*cos(a + c) + b*cos(a + c)^2 + b*sin(4*b*x + a + 5*c)^2 + 4*b*sin(2*b*x + a + 3*c)^2 + 4*b*sin(2*b*x + a + 3*c)*sin(a + c) + b*sin(a + c)^2 + 2*(2*b*cos(2*b*x + a + 3*c) + b*cos(a + c))*cos(4*b*x + a + 5*c) + 2*(2*b*sin(2*b*x + a + 3*c) + b*sin(a + c))*sin(4*b*x + a + 5*c))","B",0
216,1,1424,0,0.577017," ","integrate(sec(b*x+c)^4*sin(b*x+a),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, \cos\left(5 \, b x + 2 \, a + 4 \, c\right) - 3 \, \cos\left(5 \, b x + 6 \, c\right) - 8 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) - 8 \, \cos\left(3 \, b x + 4 \, c\right) - 3 \, \cos\left(b x + 2 \, a\right) + 3 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) + 6 \, {\left(3 \, \cos\left(4 \, b x + a + 4 \, c\right) + 3 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(5 \, b x + 2 \, a + 4 \, c\right) - 6 \, {\left(3 \, \cos\left(4 \, b x + a + 4 \, c\right) + 3 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(5 \, b x + 6 \, c\right) - 6 \, {\left(8 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) + 8 \, \cos\left(3 \, b x + 4 \, c\right) + 3 \, \cos\left(b x + 2 \, a\right) - 3 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) - 16 \, {\left(3 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(3 \, b x + 2 \, a + 2 \, c\right) - 16 \, {\left(3 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(3 \, b x + 4 \, c\right) - 18 \, {\left(\cos\left(b x + 2 \, a\right) - \cos\left(b x + 2 \, c\right)\right)} \cos\left(2 \, b x + a + 2 \, c\right) - 6 \, \cos\left(b x + 2 \, a\right) \cos\left(a\right) + 6 \, \cos\left(b x + 2 \, c\right) \cos\left(a\right) - 3 \, {\left(\cos\left(6 \, b x + a + 6 \, c\right)^{2} \sin\left(-a + c\right) + 9 \, \cos\left(4 \, b x + a + 4 \, c\right)^{2} \sin\left(-a + c\right) + 9 \, \cos\left(2 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) + 6 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \sin\left(-a + c\right) + \sin\left(6 \, b x + a + 6 \, c\right)^{2} \sin\left(-a + c\right) + 9 \, \sin\left(4 \, b x + a + 4 \, c\right)^{2} \sin\left(-a + c\right) + 9 \, \sin\left(2 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) + 6 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) \sin\left(-a + c\right) + 2 \, {\left(3 \, \cos\left(4 \, b x + a + 4 \, c\right) \sin\left(-a + c\right) + 3 \, \cos\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \cos\left(a\right) \sin\left(-a + c\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) + 6 \, {\left(3 \, \cos\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \cos\left(a\right) \sin\left(-a + c\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) + 2 \, {\left(3 \, \sin\left(4 \, b x + a + 4 \, c\right) \sin\left(-a + c\right) + 3 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \sin\left(a\right) \sin\left(-a + c\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) + 6 \, {\left(3 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \sin\left(a\right) \sin\left(-a + c\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(-a + c\right)\right)} \log\left(\frac{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} - 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} - 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}\right) + 2 \, {\left(3 \, \sin\left(5 \, b x + 2 \, a + 4 \, c\right) - 3 \, \sin\left(5 \, b x + 6 \, c\right) - 8 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) - 8 \, \sin\left(3 \, b x + 4 \, c\right) - 3 \, \sin\left(b x + 2 \, a\right) + 3 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) + 6 \, {\left(3 \, \sin\left(4 \, b x + a + 4 \, c\right) + 3 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(5 \, b x + 2 \, a + 4 \, c\right) - 6 \, {\left(3 \, \sin\left(4 \, b x + a + 4 \, c\right) + 3 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(5 \, b x + 6 \, c\right) - 6 \, {\left(8 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) + 8 \, \sin\left(3 \, b x + 4 \, c\right) + 3 \, \sin\left(b x + 2 \, a\right) - 3 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right) - 16 \, {\left(3 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(3 \, b x + 2 \, a + 2 \, c\right) - 16 \, {\left(3 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(3 \, b x + 4 \, c\right) - 18 \, {\left(\sin\left(b x + 2 \, a\right) - \sin\left(b x + 2 \, c\right)\right)} \sin\left(2 \, b x + a + 2 \, c\right) - 6 \, \sin\left(b x + 2 \, a\right) \sin\left(a\right) + 6 \, \sin\left(b x + 2 \, c\right) \sin\left(a\right)}{12 \, {\left(b \cos\left(6 \, b x + a + 6 \, c\right)^{2} + 9 \, b \cos\left(4 \, b x + a + 4 \, c\right)^{2} + 9 \, b \cos\left(2 \, b x + a + 2 \, c\right)^{2} + 6 \, b \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) + b \sin\left(6 \, b x + a + 6 \, c\right)^{2} + 9 \, b \sin\left(4 \, b x + a + 4 \, c\right)^{2} + 9 \, b \sin\left(2 \, b x + a + 2 \, c\right)^{2} + 6 \, b \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b + 2 \, {\left(3 \, b \cos\left(4 \, b x + a + 4 \, c\right) + 3 \, b \cos\left(2 \, b x + a + 2 \, c\right) + b \cos\left(a\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) + 6 \, {\left(3 \, b \cos\left(2 \, b x + a + 2 \, c\right) + b \cos\left(a\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) + 2 \, {\left(3 \, b \sin\left(4 \, b x + a + 4 \, c\right) + 3 \, b \sin\left(2 \, b x + a + 2 \, c\right) + b \sin\left(a\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) + 6 \, {\left(3 \, b \sin\left(2 \, b x + a + 2 \, c\right) + b \sin\left(a\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right)\right)}}"," ",0,"-1/12*(2*(3*cos(5*b*x + 2*a + 4*c) - 3*cos(5*b*x + 6*c) - 8*cos(3*b*x + 2*a + 2*c) - 8*cos(3*b*x + 4*c) - 3*cos(b*x + 2*a) + 3*cos(b*x + 2*c))*cos(6*b*x + a + 6*c) + 6*(3*cos(4*b*x + a + 4*c) + 3*cos(2*b*x + a + 2*c) + cos(a))*cos(5*b*x + 2*a + 4*c) - 6*(3*cos(4*b*x + a + 4*c) + 3*cos(2*b*x + a + 2*c) + cos(a))*cos(5*b*x + 6*c) - 6*(8*cos(3*b*x + 2*a + 2*c) + 8*cos(3*b*x + 4*c) + 3*cos(b*x + 2*a) - 3*cos(b*x + 2*c))*cos(4*b*x + a + 4*c) - 16*(3*cos(2*b*x + a + 2*c) + cos(a))*cos(3*b*x + 2*a + 2*c) - 16*(3*cos(2*b*x + a + 2*c) + cos(a))*cos(3*b*x + 4*c) - 18*(cos(b*x + 2*a) - cos(b*x + 2*c))*cos(2*b*x + a + 2*c) - 6*cos(b*x + 2*a)*cos(a) + 6*cos(b*x + 2*c)*cos(a) - 3*(cos(6*b*x + a + 6*c)^2*sin(-a + c) + 9*cos(4*b*x + a + 4*c)^2*sin(-a + c) + 9*cos(2*b*x + a + 2*c)^2*sin(-a + c) + 6*cos(2*b*x + a + 2*c)*cos(a)*sin(-a + c) + sin(6*b*x + a + 6*c)^2*sin(-a + c) + 9*sin(4*b*x + a + 4*c)^2*sin(-a + c) + 9*sin(2*b*x + a + 2*c)^2*sin(-a + c) + 6*sin(2*b*x + a + 2*c)*sin(a)*sin(-a + c) + 2*(3*cos(4*b*x + a + 4*c)*sin(-a + c) + 3*cos(2*b*x + a + 2*c)*sin(-a + c) + cos(a)*sin(-a + c))*cos(6*b*x + a + 6*c) + 6*(3*cos(2*b*x + a + 2*c)*sin(-a + c) + cos(a)*sin(-a + c))*cos(4*b*x + a + 4*c) + 2*(3*sin(4*b*x + a + 4*c)*sin(-a + c) + 3*sin(2*b*x + a + 2*c)*sin(-a + c) + sin(a)*sin(-a + c))*sin(6*b*x + a + 6*c) + 6*(3*sin(2*b*x + a + 2*c)*sin(-a + c) + sin(a)*sin(-a + c))*sin(4*b*x + a + 4*c) + (cos(a)^2 + sin(a)^2)*sin(-a + c))*log((cos(b*x + 2*c)^2 + cos(c)^2 - 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 + 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)/(cos(b*x + 2*c)^2 + cos(c)^2 + 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 - 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)) + 2*(3*sin(5*b*x + 2*a + 4*c) - 3*sin(5*b*x + 6*c) - 8*sin(3*b*x + 2*a + 2*c) - 8*sin(3*b*x + 4*c) - 3*sin(b*x + 2*a) + 3*sin(b*x + 2*c))*sin(6*b*x + a + 6*c) + 6*(3*sin(4*b*x + a + 4*c) + 3*sin(2*b*x + a + 2*c) + sin(a))*sin(5*b*x + 2*a + 4*c) - 6*(3*sin(4*b*x + a + 4*c) + 3*sin(2*b*x + a + 2*c) + sin(a))*sin(5*b*x + 6*c) - 6*(8*sin(3*b*x + 2*a + 2*c) + 8*sin(3*b*x + 4*c) + 3*sin(b*x + 2*a) - 3*sin(b*x + 2*c))*sin(4*b*x + a + 4*c) - 16*(3*sin(2*b*x + a + 2*c) + sin(a))*sin(3*b*x + 2*a + 2*c) - 16*(3*sin(2*b*x + a + 2*c) + sin(a))*sin(3*b*x + 4*c) - 18*(sin(b*x + 2*a) - sin(b*x + 2*c))*sin(2*b*x + a + 2*c) - 6*sin(b*x + 2*a)*sin(a) + 6*sin(b*x + 2*c)*sin(a))/(b*cos(6*b*x + a + 6*c)^2 + 9*b*cos(4*b*x + a + 4*c)^2 + 9*b*cos(2*b*x + a + 2*c)^2 + 6*b*cos(2*b*x + a + 2*c)*cos(a) + b*sin(6*b*x + a + 6*c)^2 + 9*b*sin(4*b*x + a + 4*c)^2 + 9*b*sin(2*b*x + a + 2*c)^2 + 6*b*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*b + 2*(3*b*cos(4*b*x + a + 4*c) + 3*b*cos(2*b*x + a + 2*c) + b*cos(a))*cos(6*b*x + a + 6*c) + 6*(3*b*cos(2*b*x + a + 2*c) + b*cos(a))*cos(4*b*x + a + 4*c) + 2*(3*b*sin(4*b*x + a + 4*c) + 3*b*sin(2*b*x + a + 2*c) + b*sin(a))*sin(6*b*x + a + 6*c) + 6*(3*b*sin(2*b*x + a + 2*c) + b*sin(a))*sin(4*b*x + a + 4*c))","B",0
217,1,1074,0,0.351533," ","integrate(sec(b*x+c)^5*sin(b*x+a),x, algorithm=""maxima"")","\frac{2 \, {\left({\left(6 \, \cos\left(4 \, b x + 2 \, a + 4 \, c\right) + 4 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \cos\left(2 \, b x + 4 \, c\right) + \cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(8 \, b x + a + 9 \, c\right) + 4 \, {\left(6 \, \cos\left(4 \, b x + 2 \, a + 4 \, c\right) + 4 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \cos\left(2 \, b x + 4 \, c\right) + \cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(6 \, b x + a + 7 \, c\right) + 6 \, {\left(4 \, \cos\left(2 \, b x + a + 3 \, c\right) + \cos\left(a + c\right)\right)} \cos\left(4 \, b x + 2 \, a + 4 \, c\right) + 6 \, {\left(6 \, \cos\left(4 \, b x + 2 \, a + 4 \, c\right) + 4 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \cos\left(2 \, b x + 4 \, c\right) + \cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) + 4 \, {\left(4 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) + \cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(2 \, b x + a + 3 \, c\right) - 4 \, {\left(4 \, \cos\left(2 \, b x + a + 3 \, c\right) + \cos\left(a + c\right)\right)} \cos\left(2 \, b x + 4 \, c\right) + {\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(a + c\right) + 4 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) \cos\left(a + c\right) + {\left(6 \, \sin\left(4 \, b x + 2 \, a + 4 \, c\right) + 4 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \sin\left(2 \, b x + 4 \, c\right) + \sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(8 \, b x + a + 9 \, c\right) + 4 \, {\left(6 \, \sin\left(4 \, b x + 2 \, a + 4 \, c\right) + 4 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \sin\left(2 \, b x + 4 \, c\right) + \sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(6 \, b x + a + 7 \, c\right) + 6 \, {\left(4 \, \sin\left(2 \, b x + a + 3 \, c\right) + \sin\left(a + c\right)\right)} \sin\left(4 \, b x + 2 \, a + 4 \, c\right) + 6 \, {\left(6 \, \sin\left(4 \, b x + 2 \, a + 4 \, c\right) + 4 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - 4 \, \sin\left(2 \, b x + 4 \, c\right) + \sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right) + 4 \, {\left(4 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) + \sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(2 \, b x + a + 3 \, c\right) - 4 \, {\left(4 \, \sin\left(2 \, b x + a + 3 \, c\right) + \sin\left(a + c\right)\right)} \sin\left(2 \, b x + 4 \, c\right) + {\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(a + c\right) + 4 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) \sin\left(a + c\right)\right)}}{3 \, {\left(b \cos\left(8 \, b x + a + 9 \, c\right)^{2} + 16 \, b \cos\left(6 \, b x + a + 7 \, c\right)^{2} + 36 \, b \cos\left(4 \, b x + a + 5 \, c\right)^{2} + 16 \, b \cos\left(2 \, b x + a + 3 \, c\right)^{2} + 8 \, b \cos\left(2 \, b x + a + 3 \, c\right) \cos\left(a + c\right) + b \cos\left(a + c\right)^{2} + b \sin\left(8 \, b x + a + 9 \, c\right)^{2} + 16 \, b \sin\left(6 \, b x + a + 7 \, c\right)^{2} + 36 \, b \sin\left(4 \, b x + a + 5 \, c\right)^{2} + 16 \, b \sin\left(2 \, b x + a + 3 \, c\right)^{2} + 8 \, b \sin\left(2 \, b x + a + 3 \, c\right) \sin\left(a + c\right) + b \sin\left(a + c\right)^{2} + 2 \, {\left(4 \, b \cos\left(6 \, b x + a + 7 \, c\right) + 6 \, b \cos\left(4 \, b x + a + 5 \, c\right) + 4 \, b \cos\left(2 \, b x + a + 3 \, c\right) + b \cos\left(a + c\right)\right)} \cos\left(8 \, b x + a + 9 \, c\right) + 8 \, {\left(6 \, b \cos\left(4 \, b x + a + 5 \, c\right) + 4 \, b \cos\left(2 \, b x + a + 3 \, c\right) + b \cos\left(a + c\right)\right)} \cos\left(6 \, b x + a + 7 \, c\right) + 12 \, {\left(4 \, b \cos\left(2 \, b x + a + 3 \, c\right) + b \cos\left(a + c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) + 2 \, {\left(4 \, b \sin\left(6 \, b x + a + 7 \, c\right) + 6 \, b \sin\left(4 \, b x + a + 5 \, c\right) + 4 \, b \sin\left(2 \, b x + a + 3 \, c\right) + b \sin\left(a + c\right)\right)} \sin\left(8 \, b x + a + 9 \, c\right) + 8 \, {\left(6 \, b \sin\left(4 \, b x + a + 5 \, c\right) + 4 \, b \sin\left(2 \, b x + a + 3 \, c\right) + b \sin\left(a + c\right)\right)} \sin\left(6 \, b x + a + 7 \, c\right) + 12 \, {\left(4 \, b \sin\left(2 \, b x + a + 3 \, c\right) + b \sin\left(a + c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right)\right)}}"," ",0,"2/3*((6*cos(4*b*x + 2*a + 4*c) + 4*cos(2*b*x + 2*a + 2*c) - 4*cos(2*b*x + 4*c) + cos(2*a) - cos(2*c))*cos(8*b*x + a + 9*c) + 4*(6*cos(4*b*x + 2*a + 4*c) + 4*cos(2*b*x + 2*a + 2*c) - 4*cos(2*b*x + 4*c) + cos(2*a) - cos(2*c))*cos(6*b*x + a + 7*c) + 6*(4*cos(2*b*x + a + 3*c) + cos(a + c))*cos(4*b*x + 2*a + 4*c) + 6*(6*cos(4*b*x + 2*a + 4*c) + 4*cos(2*b*x + 2*a + 2*c) - 4*cos(2*b*x + 4*c) + cos(2*a) - cos(2*c))*cos(4*b*x + a + 5*c) + 4*(4*cos(2*b*x + 2*a + 2*c) + cos(2*a) - cos(2*c))*cos(2*b*x + a + 3*c) - 4*(4*cos(2*b*x + a + 3*c) + cos(a + c))*cos(2*b*x + 4*c) + (cos(2*a) - cos(2*c))*cos(a + c) + 4*cos(2*b*x + 2*a + 2*c)*cos(a + c) + (6*sin(4*b*x + 2*a + 4*c) + 4*sin(2*b*x + 2*a + 2*c) - 4*sin(2*b*x + 4*c) + sin(2*a) - sin(2*c))*sin(8*b*x + a + 9*c) + 4*(6*sin(4*b*x + 2*a + 4*c) + 4*sin(2*b*x + 2*a + 2*c) - 4*sin(2*b*x + 4*c) + sin(2*a) - sin(2*c))*sin(6*b*x + a + 7*c) + 6*(4*sin(2*b*x + a + 3*c) + sin(a + c))*sin(4*b*x + 2*a + 4*c) + 6*(6*sin(4*b*x + 2*a + 4*c) + 4*sin(2*b*x + 2*a + 2*c) - 4*sin(2*b*x + 4*c) + sin(2*a) - sin(2*c))*sin(4*b*x + a + 5*c) + 4*(4*sin(2*b*x + 2*a + 2*c) + sin(2*a) - sin(2*c))*sin(2*b*x + a + 3*c) - 4*(4*sin(2*b*x + a + 3*c) + sin(a + c))*sin(2*b*x + 4*c) + (sin(2*a) - sin(2*c))*sin(a + c) + 4*sin(2*b*x + 2*a + 2*c)*sin(a + c))/(b*cos(8*b*x + a + 9*c)^2 + 16*b*cos(6*b*x + a + 7*c)^2 + 36*b*cos(4*b*x + a + 5*c)^2 + 16*b*cos(2*b*x + a + 3*c)^2 + 8*b*cos(2*b*x + a + 3*c)*cos(a + c) + b*cos(a + c)^2 + b*sin(8*b*x + a + 9*c)^2 + 16*b*sin(6*b*x + a + 7*c)^2 + 36*b*sin(4*b*x + a + 5*c)^2 + 16*b*sin(2*b*x + a + 3*c)^2 + 8*b*sin(2*b*x + a + 3*c)*sin(a + c) + b*sin(a + c)^2 + 2*(4*b*cos(6*b*x + a + 7*c) + 6*b*cos(4*b*x + a + 5*c) + 4*b*cos(2*b*x + a + 3*c) + b*cos(a + c))*cos(8*b*x + a + 9*c) + 8*(6*b*cos(4*b*x + a + 5*c) + 4*b*cos(2*b*x + a + 3*c) + b*cos(a + c))*cos(6*b*x + a + 7*c) + 12*(4*b*cos(2*b*x + a + 3*c) + b*cos(a + c))*cos(4*b*x + a + 5*c) + 2*(4*b*sin(6*b*x + a + 7*c) + 6*b*sin(4*b*x + a + 5*c) + 4*b*sin(2*b*x + a + 3*c) + b*sin(a + c))*sin(8*b*x + a + 9*c) + 8*(6*b*sin(4*b*x + a + 5*c) + 4*b*sin(2*b*x + a + 3*c) + b*sin(a + c))*sin(6*b*x + a + 7*c) + 12*(4*b*sin(2*b*x + a + 3*c) + b*sin(a + c))*sin(4*b*x + a + 5*c))","B",0
218,1,3096,0,0.685713," ","integrate(sec(b*x+c)^6*sin(b*x+a),x, algorithm=""maxima"")","-\frac{2 \, {\left(15 \, \cos\left(9 \, b x + 2 \, a + 8 \, c\right) - 15 \, \cos\left(9 \, b x + 10 \, c\right) + 70 \, \cos\left(7 \, b x + 2 \, a + 6 \, c\right) - 70 \, \cos\left(7 \, b x + 8 \, c\right) - 128 \, \cos\left(5 \, b x + 2 \, a + 4 \, c\right) - 128 \, \cos\left(5 \, b x + 6 \, c\right) - 70 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) + 70 \, \cos\left(3 \, b x + 4 \, c\right) - 15 \, \cos\left(b x + 2 \, a\right) + 15 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(10 \, b x + a + 10 \, c\right) + 30 \, {\left(5 \, \cos\left(8 \, b x + a + 8 \, c\right) + 10 \, \cos\left(6 \, b x + a + 6 \, c\right) + 10 \, \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(9 \, b x + 2 \, a + 8 \, c\right) - 30 \, {\left(5 \, \cos\left(8 \, b x + a + 8 \, c\right) + 10 \, \cos\left(6 \, b x + a + 6 \, c\right) + 10 \, \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(9 \, b x + 10 \, c\right) + 10 \, {\left(70 \, \cos\left(7 \, b x + 2 \, a + 6 \, c\right) - 70 \, \cos\left(7 \, b x + 8 \, c\right) - 128 \, \cos\left(5 \, b x + 2 \, a + 4 \, c\right) - 128 \, \cos\left(5 \, b x + 6 \, c\right) - 70 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) + 70 \, \cos\left(3 \, b x + 4 \, c\right) - 15 \, \cos\left(b x + 2 \, a\right) + 15 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(8 \, b x + a + 8 \, c\right) + 140 \, {\left(10 \, \cos\left(6 \, b x + a + 6 \, c\right) + 10 \, \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(7 \, b x + 2 \, a + 6 \, c\right) - 140 \, {\left(10 \, \cos\left(6 \, b x + a + 6 \, c\right) + 10 \, \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(7 \, b x + 8 \, c\right) - 20 \, {\left(128 \, \cos\left(5 \, b x + 2 \, a + 4 \, c\right) + 128 \, \cos\left(5 \, b x + 6 \, c\right) + 70 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) - 70 \, \cos\left(3 \, b x + 4 \, c\right) + 15 \, \cos\left(b x + 2 \, a\right) - 15 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) - 256 \, {\left(10 \, \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(5 \, b x + 2 \, a + 4 \, c\right) - 256 \, {\left(10 \, \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(5 \, b x + 6 \, c\right) - 100 \, {\left(14 \, \cos\left(3 \, b x + 2 \, a + 2 \, c\right) - 14 \, \cos\left(3 \, b x + 4 \, c\right) + 3 \, \cos\left(b x + 2 \, a\right) - 3 \, \cos\left(b x + 2 \, c\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) - 140 \, {\left(5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(3 \, b x + 2 \, a + 2 \, c\right) + 140 \, {\left(5 \, \cos\left(2 \, b x + a + 2 \, c\right) + \cos\left(a\right)\right)} \cos\left(3 \, b x + 4 \, c\right) - 150 \, {\left(\cos\left(b x + 2 \, a\right) - \cos\left(b x + 2 \, c\right)\right)} \cos\left(2 \, b x + a + 2 \, c\right) - 30 \, \cos\left(b x + 2 \, a\right) \cos\left(a\right) + 30 \, \cos\left(b x + 2 \, c\right) \cos\left(a\right) - 15 \, {\left(\cos\left(10 \, b x + a + 10 \, c\right)^{2} \sin\left(-a + c\right) + 25 \, \cos\left(8 \, b x + a + 8 \, c\right)^{2} \sin\left(-a + c\right) + 100 \, \cos\left(6 \, b x + a + 6 \, c\right)^{2} \sin\left(-a + c\right) + 100 \, \cos\left(4 \, b x + a + 4 \, c\right)^{2} \sin\left(-a + c\right) + 25 \, \cos\left(2 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) + 10 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \sin\left(-a + c\right) + \sin\left(10 \, b x + a + 10 \, c\right)^{2} \sin\left(-a + c\right) + 25 \, \sin\left(8 \, b x + a + 8 \, c\right)^{2} \sin\left(-a + c\right) + 100 \, \sin\left(6 \, b x + a + 6 \, c\right)^{2} \sin\left(-a + c\right) + 100 \, \sin\left(4 \, b x + a + 4 \, c\right)^{2} \sin\left(-a + c\right) + 25 \, \sin\left(2 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) + 10 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) \sin\left(-a + c\right) + 2 \, {\left(5 \, \cos\left(8 \, b x + a + 8 \, c\right) \sin\left(-a + c\right) + 10 \, \cos\left(6 \, b x + a + 6 \, c\right) \sin\left(-a + c\right) + 10 \, \cos\left(4 \, b x + a + 4 \, c\right) \sin\left(-a + c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \cos\left(a\right) \sin\left(-a + c\right)\right)} \cos\left(10 \, b x + a + 10 \, c\right) + 10 \, {\left(10 \, \cos\left(6 \, b x + a + 6 \, c\right) \sin\left(-a + c\right) + 10 \, \cos\left(4 \, b x + a + 4 \, c\right) \sin\left(-a + c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \cos\left(a\right) \sin\left(-a + c\right)\right)} \cos\left(8 \, b x + a + 8 \, c\right) + 20 \, {\left(10 \, \cos\left(4 \, b x + a + 4 \, c\right) \sin\left(-a + c\right) + 5 \, \cos\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \cos\left(a\right) \sin\left(-a + c\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) + 20 \, {\left(5 \, \cos\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \cos\left(a\right) \sin\left(-a + c\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) + 2 \, {\left(5 \, \sin\left(8 \, b x + a + 8 \, c\right) \sin\left(-a + c\right) + 10 \, \sin\left(6 \, b x + a + 6 \, c\right) \sin\left(-a + c\right) + 10 \, \sin\left(4 \, b x + a + 4 \, c\right) \sin\left(-a + c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \sin\left(a\right) \sin\left(-a + c\right)\right)} \sin\left(10 \, b x + a + 10 \, c\right) + 10 \, {\left(10 \, \sin\left(6 \, b x + a + 6 \, c\right) \sin\left(-a + c\right) + 10 \, \sin\left(4 \, b x + a + 4 \, c\right) \sin\left(-a + c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \sin\left(a\right) \sin\left(-a + c\right)\right)} \sin\left(8 \, b x + a + 8 \, c\right) + 20 \, {\left(10 \, \sin\left(4 \, b x + a + 4 \, c\right) \sin\left(-a + c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \sin\left(a\right) \sin\left(-a + c\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) + 20 \, {\left(5 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \sin\left(a\right) \sin\left(-a + c\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(-a + c\right)\right)} \log\left(\frac{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} - 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} - 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}\right) + 2 \, {\left(15 \, \sin\left(9 \, b x + 2 \, a + 8 \, c\right) - 15 \, \sin\left(9 \, b x + 10 \, c\right) + 70 \, \sin\left(7 \, b x + 2 \, a + 6 \, c\right) - 70 \, \sin\left(7 \, b x + 8 \, c\right) - 128 \, \sin\left(5 \, b x + 2 \, a + 4 \, c\right) - 128 \, \sin\left(5 \, b x + 6 \, c\right) - 70 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) + 70 \, \sin\left(3 \, b x + 4 \, c\right) - 15 \, \sin\left(b x + 2 \, a\right) + 15 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(10 \, b x + a + 10 \, c\right) + 30 \, {\left(5 \, \sin\left(8 \, b x + a + 8 \, c\right) + 10 \, \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(9 \, b x + 2 \, a + 8 \, c\right) - 30 \, {\left(5 \, \sin\left(8 \, b x + a + 8 \, c\right) + 10 \, \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(9 \, b x + 10 \, c\right) + 10 \, {\left(70 \, \sin\left(7 \, b x + 2 \, a + 6 \, c\right) - 70 \, \sin\left(7 \, b x + 8 \, c\right) - 128 \, \sin\left(5 \, b x + 2 \, a + 4 \, c\right) - 128 \, \sin\left(5 \, b x + 6 \, c\right) - 70 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) + 70 \, \sin\left(3 \, b x + 4 \, c\right) - 15 \, \sin\left(b x + 2 \, a\right) + 15 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(8 \, b x + a + 8 \, c\right) + 140 \, {\left(10 \, \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(7 \, b x + 2 \, a + 6 \, c\right) - 140 \, {\left(10 \, \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(7 \, b x + 8 \, c\right) - 20 \, {\left(128 \, \sin\left(5 \, b x + 2 \, a + 4 \, c\right) + 128 \, \sin\left(5 \, b x + 6 \, c\right) + 70 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) - 70 \, \sin\left(3 \, b x + 4 \, c\right) + 15 \, \sin\left(b x + 2 \, a\right) - 15 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) - 256 \, {\left(10 \, \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(5 \, b x + 2 \, a + 4 \, c\right) - 256 \, {\left(10 \, \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(5 \, b x + 6 \, c\right) - 100 \, {\left(14 \, \sin\left(3 \, b x + 2 \, a + 2 \, c\right) - 14 \, \sin\left(3 \, b x + 4 \, c\right) + 3 \, \sin\left(b x + 2 \, a\right) - 3 \, \sin\left(b x + 2 \, c\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right) - 140 \, {\left(5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(3 \, b x + 2 \, a + 2 \, c\right) + 140 \, {\left(5 \, \sin\left(2 \, b x + a + 2 \, c\right) + \sin\left(a\right)\right)} \sin\left(3 \, b x + 4 \, c\right) - 150 \, {\left(\sin\left(b x + 2 \, a\right) - \sin\left(b x + 2 \, c\right)\right)} \sin\left(2 \, b x + a + 2 \, c\right) - 30 \, \sin\left(b x + 2 \, a\right) \sin\left(a\right) + 30 \, \sin\left(b x + 2 \, c\right) \sin\left(a\right)}{80 \, {\left(b \cos\left(10 \, b x + a + 10 \, c\right)^{2} + 25 \, b \cos\left(8 \, b x + a + 8 \, c\right)^{2} + 100 \, b \cos\left(6 \, b x + a + 6 \, c\right)^{2} + 100 \, b \cos\left(4 \, b x + a + 4 \, c\right)^{2} + 25 \, b \cos\left(2 \, b x + a + 2 \, c\right)^{2} + 10 \, b \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) + b \sin\left(10 \, b x + a + 10 \, c\right)^{2} + 25 \, b \sin\left(8 \, b x + a + 8 \, c\right)^{2} + 100 \, b \sin\left(6 \, b x + a + 6 \, c\right)^{2} + 100 \, b \sin\left(4 \, b x + a + 4 \, c\right)^{2} + 25 \, b \sin\left(2 \, b x + a + 2 \, c\right)^{2} + 10 \, b \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b + 2 \, {\left(5 \, b \cos\left(8 \, b x + a + 8 \, c\right) + 10 \, b \cos\left(6 \, b x + a + 6 \, c\right) + 10 \, b \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, b \cos\left(2 \, b x + a + 2 \, c\right) + b \cos\left(a\right)\right)} \cos\left(10 \, b x + a + 10 \, c\right) + 10 \, {\left(10 \, b \cos\left(6 \, b x + a + 6 \, c\right) + 10 \, b \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, b \cos\left(2 \, b x + a + 2 \, c\right) + b \cos\left(a\right)\right)} \cos\left(8 \, b x + a + 8 \, c\right) + 20 \, {\left(10 \, b \cos\left(4 \, b x + a + 4 \, c\right) + 5 \, b \cos\left(2 \, b x + a + 2 \, c\right) + b \cos\left(a\right)\right)} \cos\left(6 \, b x + a + 6 \, c\right) + 20 \, {\left(5 \, b \cos\left(2 \, b x + a + 2 \, c\right) + b \cos\left(a\right)\right)} \cos\left(4 \, b x + a + 4 \, c\right) + 2 \, {\left(5 \, b \sin\left(8 \, b x + a + 8 \, c\right) + 10 \, b \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, b \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, b \sin\left(2 \, b x + a + 2 \, c\right) + b \sin\left(a\right)\right)} \sin\left(10 \, b x + a + 10 \, c\right) + 10 \, {\left(10 \, b \sin\left(6 \, b x + a + 6 \, c\right) + 10 \, b \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, b \sin\left(2 \, b x + a + 2 \, c\right) + b \sin\left(a\right)\right)} \sin\left(8 \, b x + a + 8 \, c\right) + 20 \, {\left(10 \, b \sin\left(4 \, b x + a + 4 \, c\right) + 5 \, b \sin\left(2 \, b x + a + 2 \, c\right) + b \sin\left(a\right)\right)} \sin\left(6 \, b x + a + 6 \, c\right) + 20 \, {\left(5 \, b \sin\left(2 \, b x + a + 2 \, c\right) + b \sin\left(a\right)\right)} \sin\left(4 \, b x + a + 4 \, c\right)\right)}}"," ",0,"-1/80*(2*(15*cos(9*b*x + 2*a + 8*c) - 15*cos(9*b*x + 10*c) + 70*cos(7*b*x + 2*a + 6*c) - 70*cos(7*b*x + 8*c) - 128*cos(5*b*x + 2*a + 4*c) - 128*cos(5*b*x + 6*c) - 70*cos(3*b*x + 2*a + 2*c) + 70*cos(3*b*x + 4*c) - 15*cos(b*x + 2*a) + 15*cos(b*x + 2*c))*cos(10*b*x + a + 10*c) + 30*(5*cos(8*b*x + a + 8*c) + 10*cos(6*b*x + a + 6*c) + 10*cos(4*b*x + a + 4*c) + 5*cos(2*b*x + a + 2*c) + cos(a))*cos(9*b*x + 2*a + 8*c) - 30*(5*cos(8*b*x + a + 8*c) + 10*cos(6*b*x + a + 6*c) + 10*cos(4*b*x + a + 4*c) + 5*cos(2*b*x + a + 2*c) + cos(a))*cos(9*b*x + 10*c) + 10*(70*cos(7*b*x + 2*a + 6*c) - 70*cos(7*b*x + 8*c) - 128*cos(5*b*x + 2*a + 4*c) - 128*cos(5*b*x + 6*c) - 70*cos(3*b*x + 2*a + 2*c) + 70*cos(3*b*x + 4*c) - 15*cos(b*x + 2*a) + 15*cos(b*x + 2*c))*cos(8*b*x + a + 8*c) + 140*(10*cos(6*b*x + a + 6*c) + 10*cos(4*b*x + a + 4*c) + 5*cos(2*b*x + a + 2*c) + cos(a))*cos(7*b*x + 2*a + 6*c) - 140*(10*cos(6*b*x + a + 6*c) + 10*cos(4*b*x + a + 4*c) + 5*cos(2*b*x + a + 2*c) + cos(a))*cos(7*b*x + 8*c) - 20*(128*cos(5*b*x + 2*a + 4*c) + 128*cos(5*b*x + 6*c) + 70*cos(3*b*x + 2*a + 2*c) - 70*cos(3*b*x + 4*c) + 15*cos(b*x + 2*a) - 15*cos(b*x + 2*c))*cos(6*b*x + a + 6*c) - 256*(10*cos(4*b*x + a + 4*c) + 5*cos(2*b*x + a + 2*c) + cos(a))*cos(5*b*x + 2*a + 4*c) - 256*(10*cos(4*b*x + a + 4*c) + 5*cos(2*b*x + a + 2*c) + cos(a))*cos(5*b*x + 6*c) - 100*(14*cos(3*b*x + 2*a + 2*c) - 14*cos(3*b*x + 4*c) + 3*cos(b*x + 2*a) - 3*cos(b*x + 2*c))*cos(4*b*x + a + 4*c) - 140*(5*cos(2*b*x + a + 2*c) + cos(a))*cos(3*b*x + 2*a + 2*c) + 140*(5*cos(2*b*x + a + 2*c) + cos(a))*cos(3*b*x + 4*c) - 150*(cos(b*x + 2*a) - cos(b*x + 2*c))*cos(2*b*x + a + 2*c) - 30*cos(b*x + 2*a)*cos(a) + 30*cos(b*x + 2*c)*cos(a) - 15*(cos(10*b*x + a + 10*c)^2*sin(-a + c) + 25*cos(8*b*x + a + 8*c)^2*sin(-a + c) + 100*cos(6*b*x + a + 6*c)^2*sin(-a + c) + 100*cos(4*b*x + a + 4*c)^2*sin(-a + c) + 25*cos(2*b*x + a + 2*c)^2*sin(-a + c) + 10*cos(2*b*x + a + 2*c)*cos(a)*sin(-a + c) + sin(10*b*x + a + 10*c)^2*sin(-a + c) + 25*sin(8*b*x + a + 8*c)^2*sin(-a + c) + 100*sin(6*b*x + a + 6*c)^2*sin(-a + c) + 100*sin(4*b*x + a + 4*c)^2*sin(-a + c) + 25*sin(2*b*x + a + 2*c)^2*sin(-a + c) + 10*sin(2*b*x + a + 2*c)*sin(a)*sin(-a + c) + 2*(5*cos(8*b*x + a + 8*c)*sin(-a + c) + 10*cos(6*b*x + a + 6*c)*sin(-a + c) + 10*cos(4*b*x + a + 4*c)*sin(-a + c) + 5*cos(2*b*x + a + 2*c)*sin(-a + c) + cos(a)*sin(-a + c))*cos(10*b*x + a + 10*c) + 10*(10*cos(6*b*x + a + 6*c)*sin(-a + c) + 10*cos(4*b*x + a + 4*c)*sin(-a + c) + 5*cos(2*b*x + a + 2*c)*sin(-a + c) + cos(a)*sin(-a + c))*cos(8*b*x + a + 8*c) + 20*(10*cos(4*b*x + a + 4*c)*sin(-a + c) + 5*cos(2*b*x + a + 2*c)*sin(-a + c) + cos(a)*sin(-a + c))*cos(6*b*x + a + 6*c) + 20*(5*cos(2*b*x + a + 2*c)*sin(-a + c) + cos(a)*sin(-a + c))*cos(4*b*x + a + 4*c) + 2*(5*sin(8*b*x + a + 8*c)*sin(-a + c) + 10*sin(6*b*x + a + 6*c)*sin(-a + c) + 10*sin(4*b*x + a + 4*c)*sin(-a + c) + 5*sin(2*b*x + a + 2*c)*sin(-a + c) + sin(a)*sin(-a + c))*sin(10*b*x + a + 10*c) + 10*(10*sin(6*b*x + a + 6*c)*sin(-a + c) + 10*sin(4*b*x + a + 4*c)*sin(-a + c) + 5*sin(2*b*x + a + 2*c)*sin(-a + c) + sin(a)*sin(-a + c))*sin(8*b*x + a + 8*c) + 20*(10*sin(4*b*x + a + 4*c)*sin(-a + c) + 5*sin(2*b*x + a + 2*c)*sin(-a + c) + sin(a)*sin(-a + c))*sin(6*b*x + a + 6*c) + 20*(5*sin(2*b*x + a + 2*c)*sin(-a + c) + sin(a)*sin(-a + c))*sin(4*b*x + a + 4*c) + (cos(a)^2 + sin(a)^2)*sin(-a + c))*log((cos(b*x + 2*c)^2 + cos(c)^2 - 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 + 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)/(cos(b*x + 2*c)^2 + cos(c)^2 + 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 - 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)) + 2*(15*sin(9*b*x + 2*a + 8*c) - 15*sin(9*b*x + 10*c) + 70*sin(7*b*x + 2*a + 6*c) - 70*sin(7*b*x + 8*c) - 128*sin(5*b*x + 2*a + 4*c) - 128*sin(5*b*x + 6*c) - 70*sin(3*b*x + 2*a + 2*c) + 70*sin(3*b*x + 4*c) - 15*sin(b*x + 2*a) + 15*sin(b*x + 2*c))*sin(10*b*x + a + 10*c) + 30*(5*sin(8*b*x + a + 8*c) + 10*sin(6*b*x + a + 6*c) + 10*sin(4*b*x + a + 4*c) + 5*sin(2*b*x + a + 2*c) + sin(a))*sin(9*b*x + 2*a + 8*c) - 30*(5*sin(8*b*x + a + 8*c) + 10*sin(6*b*x + a + 6*c) + 10*sin(4*b*x + a + 4*c) + 5*sin(2*b*x + a + 2*c) + sin(a))*sin(9*b*x + 10*c) + 10*(70*sin(7*b*x + 2*a + 6*c) - 70*sin(7*b*x + 8*c) - 128*sin(5*b*x + 2*a + 4*c) - 128*sin(5*b*x + 6*c) - 70*sin(3*b*x + 2*a + 2*c) + 70*sin(3*b*x + 4*c) - 15*sin(b*x + 2*a) + 15*sin(b*x + 2*c))*sin(8*b*x + a + 8*c) + 140*(10*sin(6*b*x + a + 6*c) + 10*sin(4*b*x + a + 4*c) + 5*sin(2*b*x + a + 2*c) + sin(a))*sin(7*b*x + 2*a + 6*c) - 140*(10*sin(6*b*x + a + 6*c) + 10*sin(4*b*x + a + 4*c) + 5*sin(2*b*x + a + 2*c) + sin(a))*sin(7*b*x + 8*c) - 20*(128*sin(5*b*x + 2*a + 4*c) + 128*sin(5*b*x + 6*c) + 70*sin(3*b*x + 2*a + 2*c) - 70*sin(3*b*x + 4*c) + 15*sin(b*x + 2*a) - 15*sin(b*x + 2*c))*sin(6*b*x + a + 6*c) - 256*(10*sin(4*b*x + a + 4*c) + 5*sin(2*b*x + a + 2*c) + sin(a))*sin(5*b*x + 2*a + 4*c) - 256*(10*sin(4*b*x + a + 4*c) + 5*sin(2*b*x + a + 2*c) + sin(a))*sin(5*b*x + 6*c) - 100*(14*sin(3*b*x + 2*a + 2*c) - 14*sin(3*b*x + 4*c) + 3*sin(b*x + 2*a) - 3*sin(b*x + 2*c))*sin(4*b*x + a + 4*c) - 140*(5*sin(2*b*x + a + 2*c) + sin(a))*sin(3*b*x + 2*a + 2*c) + 140*(5*sin(2*b*x + a + 2*c) + sin(a))*sin(3*b*x + 4*c) - 150*(sin(b*x + 2*a) - sin(b*x + 2*c))*sin(2*b*x + a + 2*c) - 30*sin(b*x + 2*a)*sin(a) + 30*sin(b*x + 2*c)*sin(a))/(b*cos(10*b*x + a + 10*c)^2 + 25*b*cos(8*b*x + a + 8*c)^2 + 100*b*cos(6*b*x + a + 6*c)^2 + 100*b*cos(4*b*x + a + 4*c)^2 + 25*b*cos(2*b*x + a + 2*c)^2 + 10*b*cos(2*b*x + a + 2*c)*cos(a) + b*sin(10*b*x + a + 10*c)^2 + 25*b*sin(8*b*x + a + 8*c)^2 + 100*b*sin(6*b*x + a + 6*c)^2 + 100*b*sin(4*b*x + a + 4*c)^2 + 25*b*sin(2*b*x + a + 2*c)^2 + 10*b*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*b + 2*(5*b*cos(8*b*x + a + 8*c) + 10*b*cos(6*b*x + a + 6*c) + 10*b*cos(4*b*x + a + 4*c) + 5*b*cos(2*b*x + a + 2*c) + b*cos(a))*cos(10*b*x + a + 10*c) + 10*(10*b*cos(6*b*x + a + 6*c) + 10*b*cos(4*b*x + a + 4*c) + 5*b*cos(2*b*x + a + 2*c) + b*cos(a))*cos(8*b*x + a + 8*c) + 20*(10*b*cos(4*b*x + a + 4*c) + 5*b*cos(2*b*x + a + 2*c) + b*cos(a))*cos(6*b*x + a + 6*c) + 20*(5*b*cos(2*b*x + a + 2*c) + b*cos(a))*cos(4*b*x + a + 4*c) + 2*(5*b*sin(8*b*x + a + 8*c) + 10*b*sin(6*b*x + a + 6*c) + 10*b*sin(4*b*x + a + 4*c) + 5*b*sin(2*b*x + a + 2*c) + b*sin(a))*sin(10*b*x + a + 10*c) + 10*(10*b*sin(6*b*x + a + 6*c) + 10*b*sin(4*b*x + a + 4*c) + 5*b*sin(2*b*x + a + 2*c) + b*sin(a))*sin(8*b*x + a + 8*c) + 20*(10*b*sin(4*b*x + a + 4*c) + 5*b*sin(2*b*x + a + 2*c) + b*sin(a))*sin(6*b*x + a + 6*c) + 20*(5*b*sin(2*b*x + a + 2*c) + b*sin(a))*sin(4*b*x + a + 4*c))","B",0
219,0,0,0,0.000000," ","integrate(cos(d*x+c)^n*sin(b*x+a)^2,x, algorithm=""maxima"")","\int \cos\left(d x + c\right)^{n} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(cos(d*x + c)^n*sin(b*x + a)^2, x)","F",0
220,1,371,0,0.349655," ","integrate(cos(d*x+c)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, b d \sin\left(c\right) - d^{2} \sin\left(c\right)\right)} \cos\left({\left(2 \, b + d\right)} x + 2 \, a + 2 \, c\right) - {\left(2 \, b d \sin\left(c\right) - d^{2} \sin\left(c\right)\right)} \cos\left({\left(2 \, b + d\right)} x + 2 \, a\right) - {\left(2 \, b d \sin\left(c\right) + d^{2} \sin\left(c\right)\right)} \cos\left(-{\left(2 \, b - d\right)} x - 2 \, a + 2 \, c\right) + {\left(2 \, b d \sin\left(c\right) + d^{2} \sin\left(c\right)\right)} \cos\left(-{\left(2 \, b - d\right)} x - 2 \, a\right) - 2 \, {\left(4 \, b^{2} \sin\left(c\right) - d^{2} \sin\left(c\right)\right)} \cos\left(d x + 2 \, c\right) + 2 \, {\left(4 \, b^{2} \sin\left(c\right) - d^{2} \sin\left(c\right)\right)} \cos\left(d x\right) - {\left(2 \, b d \cos\left(c\right) - d^{2} \cos\left(c\right)\right)} \sin\left({\left(2 \, b + d\right)} x + 2 \, a + 2 \, c\right) - {\left(2 \, b d \cos\left(c\right) - d^{2} \cos\left(c\right)\right)} \sin\left({\left(2 \, b + d\right)} x + 2 \, a\right) + {\left(2 \, b d \cos\left(c\right) + d^{2} \cos\left(c\right)\right)} \sin\left(-{\left(2 \, b - d\right)} x - 2 \, a + 2 \, c\right) + {\left(2 \, b d \cos\left(c\right) + d^{2} \cos\left(c\right)\right)} \sin\left(-{\left(2 \, b - d\right)} x - 2 \, a\right) + 2 \, {\left(4 \, b^{2} \cos\left(c\right) - d^{2} \cos\left(c\right)\right)} \sin\left(d x + 2 \, c\right) + 2 \, {\left(4 \, b^{2} \cos\left(c\right) - d^{2} \cos\left(c\right)\right)} \sin\left(d x\right)}{8 \, {\left({\left(\cos\left(c\right)^{2} + \sin\left(c\right)^{2}\right)} d^{3} - 4 \, {\left(b^{2} \cos\left(c\right)^{2} + b^{2} \sin\left(c\right)^{2}\right)} d\right)}}"," ",0,"-1/8*((2*b*d*sin(c) - d^2*sin(c))*cos((2*b + d)*x + 2*a + 2*c) - (2*b*d*sin(c) - d^2*sin(c))*cos((2*b + d)*x + 2*a) - (2*b*d*sin(c) + d^2*sin(c))*cos(-(2*b - d)*x - 2*a + 2*c) + (2*b*d*sin(c) + d^2*sin(c))*cos(-(2*b - d)*x - 2*a) - 2*(4*b^2*sin(c) - d^2*sin(c))*cos(d*x + 2*c) + 2*(4*b^2*sin(c) - d^2*sin(c))*cos(d*x) - (2*b*d*cos(c) - d^2*cos(c))*sin((2*b + d)*x + 2*a + 2*c) - (2*b*d*cos(c) - d^2*cos(c))*sin((2*b + d)*x + 2*a) + (2*b*d*cos(c) + d^2*cos(c))*sin(-(2*b - d)*x - 2*a + 2*c) + (2*b*d*cos(c) + d^2*cos(c))*sin(-(2*b - d)*x - 2*a) + 2*(4*b^2*cos(c) - d^2*cos(c))*sin(d*x + 2*c) + 2*(4*b^2*cos(c) - d^2*cos(c))*sin(d*x))/((cos(c)^2 + sin(c)^2)*d^3 - 4*(b^2*cos(c)^2 + b^2*sin(c)^2)*d)","B",0
221,1,620,0,0.378714," ","integrate(cos(d*x+c)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{8 \, {\left({\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{3} - {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2}\right)} d\right)} x - {\left(b^{2} d \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, {\left(b + d\right)} x + 2 \, a + 4 \, c\right) + {\left(b^{2} d \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, {\left(b + d\right)} x + 2 \, a\right) + {\left(b^{2} d \sin\left(2 \, c\right) + b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(-2 \, {\left(b - d\right)} x - 2 \, a + 4 \, c\right) - {\left(b^{2} d \sin\left(2 \, c\right) + b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(-2 \, {\left(b - d\right)} x - 2 \, a\right) - 2 \, {\left(b^{2} d \sin\left(2 \, c\right) - d^{3} \sin\left(2 \, c\right)\right)} \cos\left(2 \, b x + 2 \, a + 2 \, c\right) + 2 \, {\left(b^{2} d \sin\left(2 \, c\right) - d^{3} \sin\left(2 \, c\right)\right)} \cos\left(2 \, b x + 2 \, a - 2 \, c\right) - 2 \, {\left(b^{3} \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x\right) + 2 \, {\left(b^{3} \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x + 4 \, c\right) + {\left(b^{2} d \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, {\left(b + d\right)} x + 2 \, a + 4 \, c\right) + {\left(b^{2} d \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, {\left(b + d\right)} x + 2 \, a\right) - {\left(b^{2} d \cos\left(2 \, c\right) + b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(-2 \, {\left(b - d\right)} x - 2 \, a + 4 \, c\right) - {\left(b^{2} d \cos\left(2 \, c\right) + b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(-2 \, {\left(b - d\right)} x - 2 \, a\right) + 2 \, {\left(b^{2} d \cos\left(2 \, c\right) - d^{3} \cos\left(2 \, c\right)\right)} \sin\left(2 \, b x + 2 \, a + 2 \, c\right) + 2 \, {\left(b^{2} d \cos\left(2 \, c\right) - d^{3} \cos\left(2 \, c\right)\right)} \sin\left(2 \, b x + 2 \, a - 2 \, c\right) - 2 \, {\left(b^{3} \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, d x\right) - 2 \, {\left(b^{3} \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, d x + 4 \, c\right)}{32 \, {\left({\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{3} - {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2}\right)} d\right)}}"," ",0,"1/32*(8*((b*cos(2*c)^2 + b*sin(2*c)^2)*d^3 - (b^3*cos(2*c)^2 + b^3*sin(2*c)^2)*d)*x - (b^2*d*sin(2*c) - b*d^2*sin(2*c))*cos(2*(b + d)*x + 2*a + 4*c) + (b^2*d*sin(2*c) - b*d^2*sin(2*c))*cos(2*(b + d)*x + 2*a) + (b^2*d*sin(2*c) + b*d^2*sin(2*c))*cos(-2*(b - d)*x - 2*a + 4*c) - (b^2*d*sin(2*c) + b*d^2*sin(2*c))*cos(-2*(b - d)*x - 2*a) - 2*(b^2*d*sin(2*c) - d^3*sin(2*c))*cos(2*b*x + 2*a + 2*c) + 2*(b^2*d*sin(2*c) - d^3*sin(2*c))*cos(2*b*x + 2*a - 2*c) - 2*(b^3*sin(2*c) - b*d^2*sin(2*c))*cos(2*d*x) + 2*(b^3*sin(2*c) - b*d^2*sin(2*c))*cos(2*d*x + 4*c) + (b^2*d*cos(2*c) - b*d^2*cos(2*c))*sin(2*(b + d)*x + 2*a + 4*c) + (b^2*d*cos(2*c) - b*d^2*cos(2*c))*sin(2*(b + d)*x + 2*a) - (b^2*d*cos(2*c) + b*d^2*cos(2*c))*sin(-2*(b - d)*x - 2*a + 4*c) - (b^2*d*cos(2*c) + b*d^2*cos(2*c))*sin(-2*(b - d)*x - 2*a) + 2*(b^2*d*cos(2*c) - d^3*cos(2*c))*sin(2*b*x + 2*a + 2*c) + 2*(b^2*d*cos(2*c) - d^3*cos(2*c))*sin(2*b*x + 2*a - 2*c) - 2*(b^3*cos(2*c) - b*d^2*cos(2*c))*sin(2*d*x) - 2*(b^3*cos(2*c) - b*d^2*cos(2*c))*sin(2*d*x + 4*c))/((b*cos(2*c)^2 + b*sin(2*c)^2)*d^3 - (b^3*cos(2*c)^2 + b^3*sin(2*c)^2)*d)","B",0
222,1,1362,0,0.430776," ","integrate(cos(d*x+c)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) + 3 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a + 6 \, c\right) - 3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) + 3 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a\right) + 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + d\right)} x + 2 \, a + 4 \, c\right) - 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + d\right)} x + 2 \, a - 2 \, c\right) - 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) - 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - d\right)} x - 2 \, a + 4 \, c\right) + 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) - 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - d\right)} x - 2 \, a - 2 \, c\right) - 3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) - 3 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a + 6 \, c\right) + 3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) - 3 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a\right) + 2 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(3 \, d x\right) - 2 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(3 \, d x + 6 \, c\right) - 18 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(d x + 4 \, c\right) + 18 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(d x - 2 \, c\right) - 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) + 3 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a + 6 \, c\right) - 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) + 3 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a\right) - 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + d\right)} x + 2 \, a + 4 \, c\right) - 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + d\right)} x + 2 \, a - 2 \, c\right) + 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) - 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - d\right)} x - 2 \, a + 4 \, c\right) + 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) - 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - d\right)} x - 2 \, a - 2 \, c\right) + 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) - 3 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a + 6 \, c\right) + 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) - 3 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a\right) + 2 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(3 \, d x\right) + 2 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(3 \, d x + 6 \, c\right) + 18 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(d x + 4 \, c\right) + 18 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(d x - 2 \, c\right)}{96 \, {\left(9 \, {\left(\cos\left(3 \, c\right)^{2} + \sin\left(3 \, c\right)^{2}\right)} d^{5} - 40 \, {\left(b^{2} \cos\left(3 \, c\right)^{2} + b^{2} \sin\left(3 \, c\right)^{2}\right)} d^{3} + 16 \, {\left(b^{4} \cos\left(3 \, c\right)^{2} + b^{4} \sin\left(3 \, c\right)^{2}\right)} d\right)}}"," ",0,"1/96*(3*(8*b^3*d*sin(3*c) - 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) + 3*d^4*sin(3*c))*cos((2*b + 3*d)*x + 2*a + 6*c) - 3*(8*b^3*d*sin(3*c) - 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) + 3*d^4*sin(3*c))*cos((2*b + 3*d)*x + 2*a) + 9*(8*b^3*d*sin(3*c) - 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) + 9*d^4*sin(3*c))*cos((2*b + d)*x + 2*a + 4*c) - 9*(8*b^3*d*sin(3*c) - 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) + 9*d^4*sin(3*c))*cos((2*b + d)*x + 2*a - 2*c) - 9*(8*b^3*d*sin(3*c) + 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) - 9*d^4*sin(3*c))*cos(-(2*b - d)*x - 2*a + 4*c) + 9*(8*b^3*d*sin(3*c) + 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) - 9*d^4*sin(3*c))*cos(-(2*b - d)*x - 2*a - 2*c) - 3*(8*b^3*d*sin(3*c) + 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) - 3*d^4*sin(3*c))*cos(-(2*b - 3*d)*x - 2*a + 6*c) + 3*(8*b^3*d*sin(3*c) + 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) - 3*d^4*sin(3*c))*cos(-(2*b - 3*d)*x - 2*a) + 2*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*cos(3*d*x) - 2*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*cos(3*d*x + 6*c) - 18*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*cos(d*x + 4*c) + 18*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*cos(d*x - 2*c) - 3*(8*b^3*d*cos(3*c) - 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) + 3*d^4*cos(3*c))*sin((2*b + 3*d)*x + 2*a + 6*c) - 3*(8*b^3*d*cos(3*c) - 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) + 3*d^4*cos(3*c))*sin((2*b + 3*d)*x + 2*a) - 9*(8*b^3*d*cos(3*c) - 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) + 9*d^4*cos(3*c))*sin((2*b + d)*x + 2*a + 4*c) - 9*(8*b^3*d*cos(3*c) - 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) + 9*d^4*cos(3*c))*sin((2*b + d)*x + 2*a - 2*c) + 9*(8*b^3*d*cos(3*c) + 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) - 9*d^4*cos(3*c))*sin(-(2*b - d)*x - 2*a + 4*c) + 9*(8*b^3*d*cos(3*c) + 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) - 9*d^4*cos(3*c))*sin(-(2*b - d)*x - 2*a - 2*c) + 3*(8*b^3*d*cos(3*c) + 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) - 3*d^4*cos(3*c))*sin(-(2*b - 3*d)*x - 2*a + 6*c) + 3*(8*b^3*d*cos(3*c) + 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) - 3*d^4*cos(3*c))*sin(-(2*b - 3*d)*x - 2*a) + 2*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*sin(3*d*x) + 2*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*sin(3*d*x + 6*c) + 18*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*sin(d*x + 4*c) + 18*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*sin(d*x - 2*c))/(9*(cos(3*c)^2 + sin(3*c)^2)*d^5 - 40*(b^2*cos(3*c)^2 + b^2*sin(3*c)^2)*d^3 + 16*(b^4*cos(3*c)^2 + b^4*sin(3*c)^2)*d)","B",0
223,0,0,0,0.000000," ","integrate(cos(d*x+c)^n*sin(b*x+a)^3,x, algorithm=""maxima"")","\int \cos\left(d x + c\right)^{n} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(cos(d*x + c)^n*sin(b*x + a)^3, x)","F",0
224,1,785,0,0.383459," ","integrate(cos(d*x+c)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(3 \, b^{3} \cos\left(c\right) - b^{2} d \cos\left(c\right) - 3 \, b d^{2} \cos\left(c\right) + d^{3} \cos\left(c\right)\right)} \cos\left({\left(3 \, b + d\right)} x + 3 \, a + 2 \, c\right) + {\left(3 \, b^{3} \cos\left(c\right) - b^{2} d \cos\left(c\right) - 3 \, b d^{2} \cos\left(c\right) + d^{3} \cos\left(c\right)\right)} \cos\left({\left(3 \, b + d\right)} x + 3 \, a\right) + {\left(3 \, b^{3} \cos\left(c\right) + b^{2} d \cos\left(c\right) - 3 \, b d^{2} \cos\left(c\right) - d^{3} \cos\left(c\right)\right)} \cos\left(-{\left(3 \, b - d\right)} x - 3 \, a + 2 \, c\right) + {\left(3 \, b^{3} \cos\left(c\right) + b^{2} d \cos\left(c\right) - 3 \, b d^{2} \cos\left(c\right) - d^{3} \cos\left(c\right)\right)} \cos\left(-{\left(3 \, b - d\right)} x - 3 \, a\right) - 3 \, {\left(9 \, b^{3} \cos\left(c\right) - 9 \, b^{2} d \cos\left(c\right) - b d^{2} \cos\left(c\right) + d^{3} \cos\left(c\right)\right)} \cos\left({\left(b + d\right)} x + a + 2 \, c\right) - 3 \, {\left(9 \, b^{3} \cos\left(c\right) - 9 \, b^{2} d \cos\left(c\right) - b d^{2} \cos\left(c\right) + d^{3} \cos\left(c\right)\right)} \cos\left({\left(b + d\right)} x + a\right) - 3 \, {\left(9 \, b^{3} \cos\left(c\right) + 9 \, b^{2} d \cos\left(c\right) - b d^{2} \cos\left(c\right) - d^{3} \cos\left(c\right)\right)} \cos\left(-{\left(b - d\right)} x - a + 2 \, c\right) - 3 \, {\left(9 \, b^{3} \cos\left(c\right) + 9 \, b^{2} d \cos\left(c\right) - b d^{2} \cos\left(c\right) - d^{3} \cos\left(c\right)\right)} \cos\left(-{\left(b - d\right)} x - a\right) + {\left(3 \, b^{3} \sin\left(c\right) - b^{2} d \sin\left(c\right) - 3 \, b d^{2} \sin\left(c\right) + d^{3} \sin\left(c\right)\right)} \sin\left({\left(3 \, b + d\right)} x + 3 \, a + 2 \, c\right) - {\left(3 \, b^{3} \sin\left(c\right) - b^{2} d \sin\left(c\right) - 3 \, b d^{2} \sin\left(c\right) + d^{3} \sin\left(c\right)\right)} \sin\left({\left(3 \, b + d\right)} x + 3 \, a\right) + {\left(3 \, b^{3} \sin\left(c\right) + b^{2} d \sin\left(c\right) - 3 \, b d^{2} \sin\left(c\right) - d^{3} \sin\left(c\right)\right)} \sin\left(-{\left(3 \, b - d\right)} x - 3 \, a + 2 \, c\right) - {\left(3 \, b^{3} \sin\left(c\right) + b^{2} d \sin\left(c\right) - 3 \, b d^{2} \sin\left(c\right) - d^{3} \sin\left(c\right)\right)} \sin\left(-{\left(3 \, b - d\right)} x - 3 \, a\right) - 3 \, {\left(9 \, b^{3} \sin\left(c\right) - 9 \, b^{2} d \sin\left(c\right) - b d^{2} \sin\left(c\right) + d^{3} \sin\left(c\right)\right)} \sin\left({\left(b + d\right)} x + a + 2 \, c\right) + 3 \, {\left(9 \, b^{3} \sin\left(c\right) - 9 \, b^{2} d \sin\left(c\right) - b d^{2} \sin\left(c\right) + d^{3} \sin\left(c\right)\right)} \sin\left({\left(b + d\right)} x + a\right) - 3 \, {\left(9 \, b^{3} \sin\left(c\right) + 9 \, b^{2} d \sin\left(c\right) - b d^{2} \sin\left(c\right) - d^{3} \sin\left(c\right)\right)} \sin\left(-{\left(b - d\right)} x - a + 2 \, c\right) + 3 \, {\left(9 \, b^{3} \sin\left(c\right) + 9 \, b^{2} d \sin\left(c\right) - b d^{2} \sin\left(c\right) - d^{3} \sin\left(c\right)\right)} \sin\left(-{\left(b - d\right)} x - a\right)}{16 \, {\left(9 \, b^{4} \cos\left(c\right)^{2} + 9 \, b^{4} \sin\left(c\right)^{2} + {\left(\cos\left(c\right)^{2} + \sin\left(c\right)^{2}\right)} d^{4} - 10 \, {\left(b^{2} \cos\left(c\right)^{2} + b^{2} \sin\left(c\right)^{2}\right)} d^{2}\right)}}"," ",0,"1/16*((3*b^3*cos(c) - b^2*d*cos(c) - 3*b*d^2*cos(c) + d^3*cos(c))*cos((3*b + d)*x + 3*a + 2*c) + (3*b^3*cos(c) - b^2*d*cos(c) - 3*b*d^2*cos(c) + d^3*cos(c))*cos((3*b + d)*x + 3*a) + (3*b^3*cos(c) + b^2*d*cos(c) - 3*b*d^2*cos(c) - d^3*cos(c))*cos(-(3*b - d)*x - 3*a + 2*c) + (3*b^3*cos(c) + b^2*d*cos(c) - 3*b*d^2*cos(c) - d^3*cos(c))*cos(-(3*b - d)*x - 3*a) - 3*(9*b^3*cos(c) - 9*b^2*d*cos(c) - b*d^2*cos(c) + d^3*cos(c))*cos((b + d)*x + a + 2*c) - 3*(9*b^3*cos(c) - 9*b^2*d*cos(c) - b*d^2*cos(c) + d^3*cos(c))*cos((b + d)*x + a) - 3*(9*b^3*cos(c) + 9*b^2*d*cos(c) - b*d^2*cos(c) - d^3*cos(c))*cos(-(b - d)*x - a + 2*c) - 3*(9*b^3*cos(c) + 9*b^2*d*cos(c) - b*d^2*cos(c) - d^3*cos(c))*cos(-(b - d)*x - a) + (3*b^3*sin(c) - b^2*d*sin(c) - 3*b*d^2*sin(c) + d^3*sin(c))*sin((3*b + d)*x + 3*a + 2*c) - (3*b^3*sin(c) - b^2*d*sin(c) - 3*b*d^2*sin(c) + d^3*sin(c))*sin((3*b + d)*x + 3*a) + (3*b^3*sin(c) + b^2*d*sin(c) - 3*b*d^2*sin(c) - d^3*sin(c))*sin(-(3*b - d)*x - 3*a + 2*c) - (3*b^3*sin(c) + b^2*d*sin(c) - 3*b*d^2*sin(c) - d^3*sin(c))*sin(-(3*b - d)*x - 3*a) - 3*(9*b^3*sin(c) - 9*b^2*d*sin(c) - b*d^2*sin(c) + d^3*sin(c))*sin((b + d)*x + a + 2*c) + 3*(9*b^3*sin(c) - 9*b^2*d*sin(c) - b*d^2*sin(c) + d^3*sin(c))*sin((b + d)*x + a) - 3*(9*b^3*sin(c) + 9*b^2*d*sin(c) - b*d^2*sin(c) - d^3*sin(c))*sin(-(b - d)*x - a + 2*c) + 3*(9*b^3*sin(c) + 9*b^2*d*sin(c) - b*d^2*sin(c) - d^3*sin(c))*sin(-(b - d)*x - a))/(9*b^4*cos(c)^2 + 9*b^4*sin(c)^2 + (cos(c)^2 + sin(c)^2)*d^4 - 10*(b^2*cos(c)^2 + b^2*sin(c)^2)*d^2)","B",0
225,1,1360,0,0.419503," ","integrate(cos(d*x+c)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(3 \, b^{4} \cos\left(2 \, c\right) - 2 \, b^{3} d \cos\left(2 \, c\right) - 12 \, b^{2} d^{2} \cos\left(2 \, c\right) + 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left({\left(3 \, b + 2 \, d\right)} x + 3 \, a + 4 \, c\right) + 3 \, {\left(3 \, b^{4} \cos\left(2 \, c\right) - 2 \, b^{3} d \cos\left(2 \, c\right) - 12 \, b^{2} d^{2} \cos\left(2 \, c\right) + 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left({\left(3 \, b + 2 \, d\right)} x + 3 \, a\right) + 3 \, {\left(3 \, b^{4} \cos\left(2 \, c\right) + 2 \, b^{3} d \cos\left(2 \, c\right) - 12 \, b^{2} d^{2} \cos\left(2 \, c\right) - 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left(-{\left(3 \, b - 2 \, d\right)} x - 3 \, a + 4 \, c\right) + 3 \, {\left(3 \, b^{4} \cos\left(2 \, c\right) + 2 \, b^{3} d \cos\left(2 \, c\right) - 12 \, b^{2} d^{2} \cos\left(2 \, c\right) - 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left(-{\left(3 \, b - 2 \, d\right)} x - 3 \, a\right) - 9 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 18 \, b^{3} d \cos\left(2 \, c\right) - 4 \, b^{2} d^{2} \cos\left(2 \, c\right) + 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left({\left(b + 2 \, d\right)} x + a + 4 \, c\right) - 9 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 18 \, b^{3} d \cos\left(2 \, c\right) - 4 \, b^{2} d^{2} \cos\left(2 \, c\right) + 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left({\left(b + 2 \, d\right)} x + a\right) - 9 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) + 18 \, b^{3} d \cos\left(2 \, c\right) - 4 \, b^{2} d^{2} \cos\left(2 \, c\right) - 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left(-{\left(b - 2 \, d\right)} x - a + 4 \, c\right) - 9 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) + 18 \, b^{3} d \cos\left(2 \, c\right) - 4 \, b^{2} d^{2} \cos\left(2 \, c\right) - 8 \, b d^{3} \cos\left(2 \, c\right)\right)} \cos\left(-{\left(b - 2 \, d\right)} x - a\right) + 2 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 40 \, b^{2} d^{2} \cos\left(2 \, c\right) + 16 \, d^{4} \cos\left(2 \, c\right)\right)} \cos\left(3 \, b x + 3 \, a + 2 \, c\right) + 2 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 40 \, b^{2} d^{2} \cos\left(2 \, c\right) + 16 \, d^{4} \cos\left(2 \, c\right)\right)} \cos\left(3 \, b x + 3 \, a - 2 \, c\right) - 18 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 40 \, b^{2} d^{2} \cos\left(2 \, c\right) + 16 \, d^{4} \cos\left(2 \, c\right)\right)} \cos\left(b x + a + 2 \, c\right) - 18 \, {\left(9 \, b^{4} \cos\left(2 \, c\right) - 40 \, b^{2} d^{2} \cos\left(2 \, c\right) + 16 \, d^{4} \cos\left(2 \, c\right)\right)} \cos\left(b x + a - 2 \, c\right) + 3 \, {\left(3 \, b^{4} \sin\left(2 \, c\right) - 2 \, b^{3} d \sin\left(2 \, c\right) - 12 \, b^{2} d^{2} \sin\left(2 \, c\right) + 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left({\left(3 \, b + 2 \, d\right)} x + 3 \, a + 4 \, c\right) - 3 \, {\left(3 \, b^{4} \sin\left(2 \, c\right) - 2 \, b^{3} d \sin\left(2 \, c\right) - 12 \, b^{2} d^{2} \sin\left(2 \, c\right) + 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left({\left(3 \, b + 2 \, d\right)} x + 3 \, a\right) + 3 \, {\left(3 \, b^{4} \sin\left(2 \, c\right) + 2 \, b^{3} d \sin\left(2 \, c\right) - 12 \, b^{2} d^{2} \sin\left(2 \, c\right) - 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left(-{\left(3 \, b - 2 \, d\right)} x - 3 \, a + 4 \, c\right) - 3 \, {\left(3 \, b^{4} \sin\left(2 \, c\right) + 2 \, b^{3} d \sin\left(2 \, c\right) - 12 \, b^{2} d^{2} \sin\left(2 \, c\right) - 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left(-{\left(3 \, b - 2 \, d\right)} x - 3 \, a\right) - 9 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 18 \, b^{3} d \sin\left(2 \, c\right) - 4 \, b^{2} d^{2} \sin\left(2 \, c\right) + 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left({\left(b + 2 \, d\right)} x + a + 4 \, c\right) + 9 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 18 \, b^{3} d \sin\left(2 \, c\right) - 4 \, b^{2} d^{2} \sin\left(2 \, c\right) + 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left({\left(b + 2 \, d\right)} x + a\right) - 9 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) + 18 \, b^{3} d \sin\left(2 \, c\right) - 4 \, b^{2} d^{2} \sin\left(2 \, c\right) - 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left(-{\left(b - 2 \, d\right)} x - a + 4 \, c\right) + 9 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) + 18 \, b^{3} d \sin\left(2 \, c\right) - 4 \, b^{2} d^{2} \sin\left(2 \, c\right) - 8 \, b d^{3} \sin\left(2 \, c\right)\right)} \sin\left(-{\left(b - 2 \, d\right)} x - a\right) + 2 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 40 \, b^{2} d^{2} \sin\left(2 \, c\right) + 16 \, d^{4} \sin\left(2 \, c\right)\right)} \sin\left(3 \, b x + 3 \, a + 2 \, c\right) - 2 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 40 \, b^{2} d^{2} \sin\left(2 \, c\right) + 16 \, d^{4} \sin\left(2 \, c\right)\right)} \sin\left(3 \, b x + 3 \, a - 2 \, c\right) - 18 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 40 \, b^{2} d^{2} \sin\left(2 \, c\right) + 16 \, d^{4} \sin\left(2 \, c\right)\right)} \sin\left(b x + a + 2 \, c\right) + 18 \, {\left(9 \, b^{4} \sin\left(2 \, c\right) - 40 \, b^{2} d^{2} \sin\left(2 \, c\right) + 16 \, d^{4} \sin\left(2 \, c\right)\right)} \sin\left(b x + a - 2 \, c\right)}{96 \, {\left(9 \, b^{5} \cos\left(2 \, c\right)^{2} + 9 \, b^{5} \sin\left(2 \, c\right)^{2} + 16 \, {\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{4} - 40 \, {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"1/96*(3*(3*b^4*cos(2*c) - 2*b^3*d*cos(2*c) - 12*b^2*d^2*cos(2*c) + 8*b*d^3*cos(2*c))*cos((3*b + 2*d)*x + 3*a + 4*c) + 3*(3*b^4*cos(2*c) - 2*b^3*d*cos(2*c) - 12*b^2*d^2*cos(2*c) + 8*b*d^3*cos(2*c))*cos((3*b + 2*d)*x + 3*a) + 3*(3*b^4*cos(2*c) + 2*b^3*d*cos(2*c) - 12*b^2*d^2*cos(2*c) - 8*b*d^3*cos(2*c))*cos(-(3*b - 2*d)*x - 3*a + 4*c) + 3*(3*b^4*cos(2*c) + 2*b^3*d*cos(2*c) - 12*b^2*d^2*cos(2*c) - 8*b*d^3*cos(2*c))*cos(-(3*b - 2*d)*x - 3*a) - 9*(9*b^4*cos(2*c) - 18*b^3*d*cos(2*c) - 4*b^2*d^2*cos(2*c) + 8*b*d^3*cos(2*c))*cos((b + 2*d)*x + a + 4*c) - 9*(9*b^4*cos(2*c) - 18*b^3*d*cos(2*c) - 4*b^2*d^2*cos(2*c) + 8*b*d^3*cos(2*c))*cos((b + 2*d)*x + a) - 9*(9*b^4*cos(2*c) + 18*b^3*d*cos(2*c) - 4*b^2*d^2*cos(2*c) - 8*b*d^3*cos(2*c))*cos(-(b - 2*d)*x - a + 4*c) - 9*(9*b^4*cos(2*c) + 18*b^3*d*cos(2*c) - 4*b^2*d^2*cos(2*c) - 8*b*d^3*cos(2*c))*cos(-(b - 2*d)*x - a) + 2*(9*b^4*cos(2*c) - 40*b^2*d^2*cos(2*c) + 16*d^4*cos(2*c))*cos(3*b*x + 3*a + 2*c) + 2*(9*b^4*cos(2*c) - 40*b^2*d^2*cos(2*c) + 16*d^4*cos(2*c))*cos(3*b*x + 3*a - 2*c) - 18*(9*b^4*cos(2*c) - 40*b^2*d^2*cos(2*c) + 16*d^4*cos(2*c))*cos(b*x + a + 2*c) - 18*(9*b^4*cos(2*c) - 40*b^2*d^2*cos(2*c) + 16*d^4*cos(2*c))*cos(b*x + a - 2*c) + 3*(3*b^4*sin(2*c) - 2*b^3*d*sin(2*c) - 12*b^2*d^2*sin(2*c) + 8*b*d^3*sin(2*c))*sin((3*b + 2*d)*x + 3*a + 4*c) - 3*(3*b^4*sin(2*c) - 2*b^3*d*sin(2*c) - 12*b^2*d^2*sin(2*c) + 8*b*d^3*sin(2*c))*sin((3*b + 2*d)*x + 3*a) + 3*(3*b^4*sin(2*c) + 2*b^3*d*sin(2*c) - 12*b^2*d^2*sin(2*c) - 8*b*d^3*sin(2*c))*sin(-(3*b - 2*d)*x - 3*a + 4*c) - 3*(3*b^4*sin(2*c) + 2*b^3*d*sin(2*c) - 12*b^2*d^2*sin(2*c) - 8*b*d^3*sin(2*c))*sin(-(3*b - 2*d)*x - 3*a) - 9*(9*b^4*sin(2*c) - 18*b^3*d*sin(2*c) - 4*b^2*d^2*sin(2*c) + 8*b*d^3*sin(2*c))*sin((b + 2*d)*x + a + 4*c) + 9*(9*b^4*sin(2*c) - 18*b^3*d*sin(2*c) - 4*b^2*d^2*sin(2*c) + 8*b*d^3*sin(2*c))*sin((b + 2*d)*x + a) - 9*(9*b^4*sin(2*c) + 18*b^3*d*sin(2*c) - 4*b^2*d^2*sin(2*c) - 8*b*d^3*sin(2*c))*sin(-(b - 2*d)*x - a + 4*c) + 9*(9*b^4*sin(2*c) + 18*b^3*d*sin(2*c) - 4*b^2*d^2*sin(2*c) - 8*b*d^3*sin(2*c))*sin(-(b - 2*d)*x - a) + 2*(9*b^4*sin(2*c) - 40*b^2*d^2*sin(2*c) + 16*d^4*sin(2*c))*sin(3*b*x + 3*a + 2*c) - 2*(9*b^4*sin(2*c) - 40*b^2*d^2*sin(2*c) + 16*d^4*sin(2*c))*sin(3*b*x + 3*a - 2*c) - 18*(9*b^4*sin(2*c) - 40*b^2*d^2*sin(2*c) + 16*d^4*sin(2*c))*sin(b*x + a + 2*c) + 18*(9*b^4*sin(2*c) - 40*b^2*d^2*sin(2*c) + 16*d^4*sin(2*c))*sin(b*x + a - 2*c))/(9*b^5*cos(2*c)^2 + 9*b^5*sin(2*c)^2 + 16*(b*cos(2*c)^2 + b*sin(2*c)^2)*d^4 - 40*(b^3*cos(2*c)^2 + b^3*sin(2*c)^2)*d^2)","B",0
226,1,2612,0,0.540062," ","integrate(cos(d*x+c)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) - b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) + 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left({\left(3 \, b + d\right)} x + 3 \, a + 4 \, c\right) + 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) - b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) + 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left({\left(3 \, b + d\right)} x + 3 \, a - 2 \, c\right) + 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) + b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) - 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(3 \, b - d\right)} x - 3 \, a + 4 \, c\right) + 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) + b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) - 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(3 \, b - d\right)} x - 3 \, a - 2 \, c\right) - 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) + 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) - 3 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) - 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) + 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) - 3 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a\right) + {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left(3 \, {\left(b + d\right)} x + 3 \, a + 6 \, c\right) + {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left(3 \, {\left(b + d\right)} x + 3 \, a\right) - 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a + 4 \, c\right) - 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a - 2 \, c\right) - 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a + 4 \, c\right) - 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a - 2 \, c\right) + {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left(-3 \, {\left(b - d\right)} x - 3 \, a + 6 \, c\right) + {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left(-3 \, {\left(b - d\right)} x - 3 \, a\right) - 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) - 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) + 3 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) - 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) - 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) + 3 \, d^{5} \cos\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a\right) + 9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) - b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) + 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left({\left(3 \, b + d\right)} x + 3 \, a + 4 \, c\right) - 9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) - b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) + 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left({\left(3 \, b + d\right)} x + 3 \, a - 2 \, c\right) + 9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) + b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) - 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(3 \, b - d\right)} x - 3 \, a + 4 \, c\right) - 9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) + b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) - 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(3 \, b - d\right)} x - 3 \, a - 2 \, c\right) - 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) + 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) - 3 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) + 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) + 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) - 3 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a\right) + {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left(3 \, {\left(b + d\right)} x + 3 \, a + 6 \, c\right) - {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left(3 \, {\left(b + d\right)} x + 3 \, a\right) - 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a + 4 \, c\right) + 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a - 2 \, c\right) - 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a + 4 \, c\right) + 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a - 2 \, c\right) + {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left(-3 \, {\left(b - d\right)} x - 3 \, a + 6 \, c\right) - {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left(-3 \, {\left(b - d\right)} x - 3 \, a\right) - 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) - 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) + 3 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) + 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) - 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) + 3 \, d^{5} \sin\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a\right)}{192 \, {\left(9 \, b^{6} \cos\left(3 \, c\right)^{2} + 9 \, b^{6} \sin\left(3 \, c\right)^{2} - 9 \, {\left(\cos\left(3 \, c\right)^{2} + \sin\left(3 \, c\right)^{2}\right)} d^{6} + 91 \, {\left(b^{2} \cos\left(3 \, c\right)^{2} + b^{2} \sin\left(3 \, c\right)^{2}\right)} d^{4} - 91 \, {\left(b^{4} \cos\left(3 \, c\right)^{2} + b^{4} \sin\left(3 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"1/192*(9*(3*b^5*cos(3*c) - b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) + 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*cos((3*b + d)*x + 3*a + 4*c) + 9*(3*b^5*cos(3*c) - b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) + 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*cos((3*b + d)*x + 3*a - 2*c) + 9*(3*b^5*cos(3*c) + b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) - 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*cos(-(3*b - d)*x - 3*a + 4*c) + 9*(3*b^5*cos(3*c) + b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) - 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*cos(-(3*b - d)*x - 3*a - 2*c) - 9*(9*b^5*cos(3*c) - 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) + 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) - 3*d^5*cos(3*c))*cos((b + 3*d)*x + a + 6*c) - 9*(9*b^5*cos(3*c) - 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) + 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) - 3*d^5*cos(3*c))*cos((b + 3*d)*x + a) + (9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*cos(3*(b + d)*x + 3*a + 6*c) + (9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*cos(3*(b + d)*x + 3*a) - 27*(9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*cos((b + d)*x + a + 4*c) - 27*(9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*cos((b + d)*x + a - 2*c) - 27*(9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*cos(-(b - d)*x - a + 4*c) - 27*(9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*cos(-(b - d)*x - a - 2*c) + (9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*cos(-3*(b - d)*x - 3*a + 6*c) + (9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*cos(-3*(b - d)*x - 3*a) - 9*(9*b^5*cos(3*c) + 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) - 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) + 3*d^5*cos(3*c))*cos(-(b - 3*d)*x - a + 6*c) - 9*(9*b^5*cos(3*c) + 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) - 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) + 3*d^5*cos(3*c))*cos(-(b - 3*d)*x - a) + 9*(3*b^5*sin(3*c) - b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) + 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*sin((3*b + d)*x + 3*a + 4*c) - 9*(3*b^5*sin(3*c) - b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) + 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*sin((3*b + d)*x + 3*a - 2*c) + 9*(3*b^5*sin(3*c) + b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) - 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*sin(-(3*b - d)*x - 3*a + 4*c) - 9*(3*b^5*sin(3*c) + b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) - 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*sin(-(3*b - d)*x - 3*a - 2*c) - 9*(9*b^5*sin(3*c) - 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) + 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) - 3*d^5*sin(3*c))*sin((b + 3*d)*x + a + 6*c) + 9*(9*b^5*sin(3*c) - 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) + 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) - 3*d^5*sin(3*c))*sin((b + 3*d)*x + a) + (9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*sin(3*(b + d)*x + 3*a + 6*c) - (9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*sin(3*(b + d)*x + 3*a) - 27*(9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*sin((b + d)*x + a + 4*c) + 27*(9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*sin((b + d)*x + a - 2*c) - 27*(9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*sin(-(b - d)*x - a + 4*c) + 27*(9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*sin(-(b - d)*x - a - 2*c) + (9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*sin(-3*(b - d)*x - 3*a + 6*c) - (9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*sin(-3*(b - d)*x - 3*a) - 9*(9*b^5*sin(3*c) + 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) - 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) + 3*d^5*sin(3*c))*sin(-(b - 3*d)*x - a + 6*c) + 9*(9*b^5*sin(3*c) + 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) - 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) + 3*d^5*sin(3*c))*sin(-(b - 3*d)*x - a))/(9*b^6*cos(3*c)^2 + 9*b^6*sin(3*c)^2 - 9*(cos(3*c)^2 + sin(3*c)^2)*d^6 + 91*(b^2*cos(3*c)^2 + b^2*sin(3*c)^2)*d^4 - 91*(b^4*cos(3*c)^2 + b^4*sin(3*c)^2)*d^2)","B",0
227,1,106,0,0.358723," ","integrate(cos(b*x+a)/sin(b*x+c),x, algorithm=""maxima"")","\frac{2 \, b x \sin\left(-a + c\right) + \cos\left(-a + c\right) \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + \cos\left(-a + c\right) \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*sin(-a + c) + cos(-a + c)*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) + cos(-a + c)*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2))/b","B",0
228,1,450,0,0.376322," ","integrate(cos(b*x+a)/sin(b*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, c\right)\right)} \cos\left(2 \, b x + a + 2 \, c\right) - {\left(\cos\left(2 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 2 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \sin\left(-a + c\right) + \sin\left(2 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 2 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) \sin\left(-a + c\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(-a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + {\left(\cos\left(2 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 2 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \sin\left(-a + c\right) + \sin\left(2 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 2 \, \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) \sin\left(-a + c\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(-a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - 2 \, {\left(\cos\left(b x + 2 \, a\right) + \cos\left(b x + 2 \, c\right)\right)} \sin\left(2 \, b x + a + 2 \, c\right) - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, c\right) + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(a\right)}{2 \, {\left(b \cos\left(2 \, b x + a + 2 \, c\right)^{2} - 2 \, b \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) + b \sin\left(2 \, b x + a + 2 \, c\right)^{2} - 2 \, b \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b\right)}}"," ",0,"1/2*(2*(sin(b*x + 2*a) + sin(b*x + 2*c))*cos(2*b*x + a + 2*c) - (cos(2*b*x + a + 2*c)^2*sin(-a + c) - 2*cos(2*b*x + a + 2*c)*cos(a)*sin(-a + c) + sin(2*b*x + a + 2*c)^2*sin(-a + c) - 2*sin(2*b*x + a + 2*c)*sin(a)*sin(-a + c) + (cos(a)^2 + sin(a)^2)*sin(-a + c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) + (cos(2*b*x + a + 2*c)^2*sin(-a + c) - 2*cos(2*b*x + a + 2*c)*cos(a)*sin(-a + c) + sin(2*b*x + a + 2*c)^2*sin(-a + c) - 2*sin(2*b*x + a + 2*c)*sin(a)*sin(-a + c) + (cos(a)^2 + sin(a)^2)*sin(-a + c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2) - 2*(cos(b*x + 2*a) + cos(b*x + 2*c))*sin(2*b*x + a + 2*c) - 2*cos(a)*sin(b*x + 2*a) - 2*cos(a)*sin(b*x + 2*c) + 2*cos(b*x + 2*a)*sin(a) + 2*cos(b*x + 2*c)*sin(a))/(b*cos(2*b*x + a + 2*c)^2 - 2*b*cos(2*b*x + a + 2*c)*cos(a) + b*sin(2*b*x + a + 2*c)^2 - 2*b*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*b)","B",0
229,1,395,0,0.344743," ","integrate(cos(b*x+a)/sin(b*x+c)^3,x, algorithm=""maxima"")","\frac{{\left(2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - \cos\left(2 \, a\right) + \cos\left(2 \, c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - \cos\left(2 \, a\right) + \cos\left(2 \, c\right)\right)} \cos\left(2 \, b x + a + 3 \, c\right) - {\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(a + c\right) + 2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) \cos\left(a + c\right) + {\left(2 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - \sin\left(2 \, a\right) + \sin\left(2 \, c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right) - 2 \, {\left(2 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - \sin\left(2 \, a\right) + \sin\left(2 \, c\right)\right)} \sin\left(2 \, b x + a + 3 \, c\right) - {\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(a + c\right) + 2 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) \sin\left(a + c\right)}{b \cos\left(4 \, b x + a + 5 \, c\right)^{2} + 4 \, b \cos\left(2 \, b x + a + 3 \, c\right)^{2} - 4 \, b \cos\left(2 \, b x + a + 3 \, c\right) \cos\left(a + c\right) + b \cos\left(a + c\right)^{2} + b \sin\left(4 \, b x + a + 5 \, c\right)^{2} + 4 \, b \sin\left(2 \, b x + a + 3 \, c\right)^{2} - 4 \, b \sin\left(2 \, b x + a + 3 \, c\right) \sin\left(a + c\right) + b \sin\left(a + c\right)^{2} - 2 \, {\left(2 \, b \cos\left(2 \, b x + a + 3 \, c\right) - b \cos\left(a + c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) - 2 \, {\left(2 \, b \sin\left(2 \, b x + a + 3 \, c\right) - b \sin\left(a + c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right)}"," ",0,"((2*cos(2*b*x + 2*a + 2*c) - cos(2*a) + cos(2*c))*cos(4*b*x + a + 5*c) - 2*(2*cos(2*b*x + 2*a + 2*c) - cos(2*a) + cos(2*c))*cos(2*b*x + a + 3*c) - (cos(2*a) - cos(2*c))*cos(a + c) + 2*cos(2*b*x + 2*a + 2*c)*cos(a + c) + (2*sin(2*b*x + 2*a + 2*c) - sin(2*a) + sin(2*c))*sin(4*b*x + a + 5*c) - 2*(2*sin(2*b*x + 2*a + 2*c) - sin(2*a) + sin(2*c))*sin(2*b*x + a + 3*c) - (sin(2*a) - sin(2*c))*sin(a + c) + 2*sin(2*b*x + 2*a + 2*c)*sin(a + c))/(b*cos(4*b*x + a + 5*c)^2 + 4*b*cos(2*b*x + a + 3*c)^2 - 4*b*cos(2*b*x + a + 3*c)*cos(a + c) + b*cos(a + c)^2 + b*sin(4*b*x + a + 5*c)^2 + 4*b*sin(2*b*x + a + 3*c)^2 - 4*b*sin(2*b*x + a + 3*c)*sin(a + c) + b*sin(a + c)^2 - 2*(2*b*cos(2*b*x + a + 3*c) - b*cos(a + c))*cos(4*b*x + a + 5*c) - 2*(2*b*sin(2*b*x + a + 3*c) - b*sin(a + c))*sin(4*b*x + a + 5*c))","B",0
230,1,1027,0,0.545766," ","integrate(sin(b*x+a)*tan(b*x+c)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\sin\left(5 \, b x + a + 4 \, c\right) + 2 \, \sin\left(3 \, b x + a + 2 \, c\right) + \sin\left(b x + a\right)\right)} \cos\left(6 \, b x + 2 \, a + 4 \, c\right) - 2 \, {\left(5 \, \sin\left(4 \, b x + 2 \, a + 2 \, c\right) - 2 \, \sin\left(4 \, b x + 4 \, c\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right) - 5 \, \sin\left(2 \, b x + 2 \, c\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) + 10 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) + \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 2 \, a + 2 \, c\right) - 4 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) + \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, c\right) - 4 \, {\left(2 \, \sin\left(2 \, b x + 2 \, a\right) - 5 \, \sin\left(2 \, b x + 2 \, c\right)\right)} \cos\left(3 \, b x + a + 2 \, c\right) - 3 \, {\left(\cos\left(5 \, b x + a + 4 \, c\right)^{2} \cos\left(-a + c\right) + 4 \, \cos\left(3 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) + 4 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \cos\left(-a + c\right) + \cos\left(b x + a\right)^{2} \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right)^{2} + 4 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + \cos\left(-a + c\right) \sin\left(b x + a\right)^{2} + 2 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) + \cos\left(b x + a\right) \cos\left(-a + c\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) + 2 \, {\left(2 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right) + \cos\left(-a + c\right) \sin\left(b x + a\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right)\right)} \log\left(\frac{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} - 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} - 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}\right) - 2 \, {\left(\cos\left(5 \, b x + a + 4 \, c\right) + 2 \, \cos\left(3 \, b x + a + 2 \, c\right) + \cos\left(b x + a\right)\right)} \sin\left(6 \, b x + 2 \, a + 4 \, c\right) + 2 \, {\left(5 \, \cos\left(4 \, b x + 2 \, a + 2 \, c\right) - 2 \, \cos\left(4 \, b x + 4 \, c\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 5 \, \cos\left(2 \, b x + 2 \, c\right) - 1\right)} \sin\left(5 \, b x + a + 4 \, c\right) - 10 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) + \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 2 \, a + 2 \, c\right) + 4 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) + \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, c\right) + 4 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 5 \, \cos\left(2 \, b x + 2 \, c\right) - 1\right)} \sin\left(3 \, b x + a + 2 \, c\right) - 4 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) + 10 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, c\right) + 4 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 10 \, \cos\left(2 \, b x + 2 \, c\right) \sin\left(b x + a\right) - 2 \, \sin\left(b x + a\right)}{4 \, {\left(b \cos\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, b \cos\left(3 \, b x + a + 2 \, c\right)^{2} + 4 \, b \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) + b \cos\left(b x + a\right)^{2} + b \sin\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, b \sin\left(3 \, b x + a + 2 \, c\right)^{2} + 4 \, b \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + b \sin\left(b x + a\right)^{2} + 2 \, {\left(2 \, b \cos\left(3 \, b x + a + 2 \, c\right) + b \cos\left(b x + a\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) + 2 \, {\left(2 \, b \sin\left(3 \, b x + a + 2 \, c\right) + b \sin\left(b x + a\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right)\right)}}"," ",0,"-1/4*(2*(sin(5*b*x + a + 4*c) + 2*sin(3*b*x + a + 2*c) + sin(b*x + a))*cos(6*b*x + 2*a + 4*c) - 2*(5*sin(4*b*x + 2*a + 2*c) - 2*sin(4*b*x + 4*c) + 2*sin(2*b*x + 2*a) - 5*sin(2*b*x + 2*c))*cos(5*b*x + a + 4*c) + 10*(2*sin(3*b*x + a + 2*c) + sin(b*x + a))*cos(4*b*x + 2*a + 2*c) - 4*(2*sin(3*b*x + a + 2*c) + sin(b*x + a))*cos(4*b*x + 4*c) - 4*(2*sin(2*b*x + 2*a) - 5*sin(2*b*x + 2*c))*cos(3*b*x + a + 2*c) - 3*(cos(5*b*x + a + 4*c)^2*cos(-a + c) + 4*cos(3*b*x + a + 2*c)^2*cos(-a + c) + 4*cos(3*b*x + a + 2*c)*cos(b*x + a)*cos(-a + c) + cos(b*x + a)^2*cos(-a + c) + cos(-a + c)*sin(5*b*x + a + 4*c)^2 + 4*cos(-a + c)*sin(3*b*x + a + 2*c)^2 + 4*cos(-a + c)*sin(3*b*x + a + 2*c)*sin(b*x + a) + cos(-a + c)*sin(b*x + a)^2 + 2*(2*cos(3*b*x + a + 2*c)*cos(-a + c) + cos(b*x + a)*cos(-a + c))*cos(5*b*x + a + 4*c) + 2*(2*cos(-a + c)*sin(3*b*x + a + 2*c) + cos(-a + c)*sin(b*x + a))*sin(5*b*x + a + 4*c))*log((cos(b*x + 2*c)^2 + cos(c)^2 - 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 + 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)/(cos(b*x + 2*c)^2 + cos(c)^2 + 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 - 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)) - 2*(cos(5*b*x + a + 4*c) + 2*cos(3*b*x + a + 2*c) + cos(b*x + a))*sin(6*b*x + 2*a + 4*c) + 2*(5*cos(4*b*x + 2*a + 2*c) - 2*cos(4*b*x + 4*c) + 2*cos(2*b*x + 2*a) - 5*cos(2*b*x + 2*c) - 1)*sin(5*b*x + a + 4*c) - 10*(2*cos(3*b*x + a + 2*c) + cos(b*x + a))*sin(4*b*x + 2*a + 2*c) + 4*(2*cos(3*b*x + a + 2*c) + cos(b*x + a))*sin(4*b*x + 4*c) + 4*(2*cos(2*b*x + 2*a) - 5*cos(2*b*x + 2*c) - 1)*sin(3*b*x + a + 2*c) - 4*cos(b*x + a)*sin(2*b*x + 2*a) + 10*cos(b*x + a)*sin(2*b*x + 2*c) + 4*cos(2*b*x + 2*a)*sin(b*x + a) - 10*cos(2*b*x + 2*c)*sin(b*x + a) - 2*sin(b*x + a))/(b*cos(5*b*x + a + 4*c)^2 + 4*b*cos(3*b*x + a + 2*c)^2 + 4*b*cos(3*b*x + a + 2*c)*cos(b*x + a) + b*cos(b*x + a)^2 + b*sin(5*b*x + a + 4*c)^2 + 4*b*sin(3*b*x + a + 2*c)^2 + 4*b*sin(3*b*x + a + 2*c)*sin(b*x + a) + b*sin(b*x + a)^2 + 2*(2*b*cos(3*b*x + a + 2*c) + b*cos(b*x + a))*cos(5*b*x + a + 4*c) + 2*(2*b*sin(3*b*x + a + 2*c) + b*sin(b*x + a))*sin(5*b*x + a + 4*c))","B",0
231,1,520,0,0.530422," ","integrate(sin(b*x+a)*tan(b*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(\cos\left(3 \, b x + a + 2 \, c\right) + \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 2 \, a + 2 \, c\right) + {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, c\right) + 1\right)} \cos\left(3 \, b x + a + 2 \, c\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 3 \, \cos\left(2 \, b x + 2 \, c\right) \cos\left(b x + a\right) + {\left(\cos\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) + 2 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \sin\left(-a + c\right) + \cos\left(b x + a\right)^{2} \sin\left(-a + c\right) + \sin\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) + 2 \, \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) \sin\left(-a + c\right) + \sin\left(b x + a\right)^{2} \sin\left(-a + c\right)\right)} \log\left(\frac{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} - 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} - 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}\right) + {\left(\sin\left(3 \, b x + a + 2 \, c\right) + \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 2 \, a + 2 \, c\right) + 3 \, {\left(\sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, c\right)\right)} \sin\left(3 \, b x + a + 2 \, c\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 3 \, \sin\left(2 \, b x + 2 \, c\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)}{2 \, {\left(b \cos\left(3 \, b x + a + 2 \, c\right)^{2} + 2 \, b \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) + b \cos\left(b x + a\right)^{2} + b \sin\left(3 \, b x + a + 2 \, c\right)^{2} + 2 \, b \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + b \sin\left(b x + a\right)^{2}\right)}}"," ",0,"1/2*((cos(3*b*x + a + 2*c) + cos(b*x + a))*cos(4*b*x + 2*a + 2*c) + (3*cos(2*b*x + 2*a) + 3*cos(2*b*x + 2*c) + 1)*cos(3*b*x + a + 2*c) + 3*cos(2*b*x + 2*a)*cos(b*x + a) + 3*cos(2*b*x + 2*c)*cos(b*x + a) + (cos(3*b*x + a + 2*c)^2*sin(-a + c) + 2*cos(3*b*x + a + 2*c)*cos(b*x + a)*sin(-a + c) + cos(b*x + a)^2*sin(-a + c) + sin(3*b*x + a + 2*c)^2*sin(-a + c) + 2*sin(3*b*x + a + 2*c)*sin(b*x + a)*sin(-a + c) + sin(b*x + a)^2*sin(-a + c))*log((cos(b*x + 2*c)^2 + cos(c)^2 - 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 + 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)/(cos(b*x + 2*c)^2 + cos(c)^2 + 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 - 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)) + (sin(3*b*x + a + 2*c) + sin(b*x + a))*sin(4*b*x + 2*a + 2*c) + 3*(sin(2*b*x + 2*a) + sin(2*b*x + 2*c))*sin(3*b*x + a + 2*c) + 3*sin(2*b*x + 2*a)*sin(b*x + a) + 3*sin(2*b*x + 2*c)*sin(b*x + a) + cos(b*x + a))/(b*cos(3*b*x + a + 2*c)^2 + 2*b*cos(3*b*x + a + 2*c)*cos(b*x + a) + b*cos(b*x + a)^2 + b*sin(3*b*x + a + 2*c)^2 + 2*b*sin(3*b*x + a + 2*c)*sin(b*x + a) + b*sin(b*x + a)^2)","B",0
232,1,131,0,0.515164," ","integrate(sin(b*x+a)*tan(b*x+c),x, algorithm=""maxima"")","-\frac{\cos\left(-a + c\right) \log\left(\frac{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} - 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} - 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}\right) + 2 \, \sin\left(b x + a\right)}{2 \, b}"," ",0,"-1/2*(cos(-a + c)*log((cos(b*x + 2*c)^2 + cos(c)^2 - 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 + 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)/(cos(b*x + 2*c)^2 + cos(c)^2 + 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 - 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)) + 2*sin(b*x + a))/b","B",0
233,1,105,0,0.350939," ","integrate(cot(b*x+c)*sin(b*x+a),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) \sin\left(-a + c\right) - \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) \sin\left(-a + c\right) + 2 \, \sin\left(b x + a\right)}{2 \, b}"," ",0,"1/2*(log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2)*sin(-a + c) - log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2)*sin(-a + c) + 2*sin(b*x + a))/b","B",0
234,1,612,0,0.371323," ","integrate(cot(b*x+c)^2*sin(b*x+a),x, algorithm=""maxima"")","\frac{{\left(\cos\left(3 \, b x + a + 2 \, c\right) - \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 2 \, a + 2 \, c\right) - {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, c\right) + 1\right)} \cos\left(3 \, b x + a + 2 \, c\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) - 3 \, \cos\left(2 \, b x + 2 \, c\right) \cos\left(b x + a\right) - {\left(\cos\left(3 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) - 2 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \cos\left(-a + c\right) + \cos\left(b x + a\right)^{2} \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right)^{2} - 2 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + \cos\left(-a + c\right) \sin\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + {\left(\cos\left(3 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) - 2 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \cos\left(-a + c\right) + \cos\left(b x + a\right)^{2} \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right)^{2} - 2 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + \cos\left(-a + c\right) \sin\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + {\left(\sin\left(3 \, b x + a + 2 \, c\right) - \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 2 \, a + 2 \, c\right) - 3 \, {\left(\sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, c\right)\right)} \sin\left(3 \, b x + a + 2 \, c\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 3 \, \sin\left(2 \, b x + 2 \, c\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)}{2 \, {\left(b \cos\left(3 \, b x + a + 2 \, c\right)^{2} - 2 \, b \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) + b \cos\left(b x + a\right)^{2} + b \sin\left(3 \, b x + a + 2 \, c\right)^{2} - 2 \, b \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + b \sin\left(b x + a\right)^{2}\right)}}"," ",0,"1/2*((cos(3*b*x + a + 2*c) - cos(b*x + a))*cos(4*b*x + 2*a + 2*c) - (3*cos(2*b*x + 2*a) - 3*cos(2*b*x + 2*c) + 1)*cos(3*b*x + a + 2*c) + 3*cos(2*b*x + 2*a)*cos(b*x + a) - 3*cos(2*b*x + 2*c)*cos(b*x + a) - (cos(3*b*x + a + 2*c)^2*cos(-a + c) - 2*cos(3*b*x + a + 2*c)*cos(b*x + a)*cos(-a + c) + cos(b*x + a)^2*cos(-a + c) + cos(-a + c)*sin(3*b*x + a + 2*c)^2 - 2*cos(-a + c)*sin(3*b*x + a + 2*c)*sin(b*x + a) + cos(-a + c)*sin(b*x + a)^2)*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) + (cos(3*b*x + a + 2*c)^2*cos(-a + c) - 2*cos(3*b*x + a + 2*c)*cos(b*x + a)*cos(-a + c) + cos(b*x + a)^2*cos(-a + c) + cos(-a + c)*sin(3*b*x + a + 2*c)^2 - 2*cos(-a + c)*sin(3*b*x + a + 2*c)*sin(b*x + a) + cos(-a + c)*sin(b*x + a)^2)*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2) + (sin(3*b*x + a + 2*c) - sin(b*x + a))*sin(4*b*x + 2*a + 2*c) - 3*(sin(2*b*x + 2*a) - sin(2*b*x + 2*c))*sin(3*b*x + a + 2*c) + 3*sin(2*b*x + 2*a)*sin(b*x + a) - 3*sin(2*b*x + 2*c)*sin(b*x + a) + cos(b*x + a))/(b*cos(3*b*x + a + 2*c)^2 - 2*b*cos(3*b*x + a + 2*c)*cos(b*x + a) + b*cos(b*x + a)^2 + b*sin(3*b*x + a + 2*c)^2 - 2*b*sin(3*b*x + a + 2*c)*sin(b*x + a) + b*sin(b*x + a)^2)","B",0
235,1,1254,0,0.396459," ","integrate(cot(b*x+c)^3*sin(b*x+a),x, algorithm=""maxima"")","\frac{2 \, {\left(\sin\left(5 \, b x + a + 4 \, c\right) - 2 \, \sin\left(3 \, b x + a + 2 \, c\right) + \sin\left(b x + a\right)\right)} \cos\left(6 \, b x + 2 \, a + 4 \, c\right) + 2 \, {\left(5 \, \sin\left(4 \, b x + 2 \, a + 2 \, c\right) + 2 \, \sin\left(4 \, b x + 4 \, c\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right) - 5 \, \sin\left(2 \, b x + 2 \, c\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) + 10 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) - \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 2 \, a + 2 \, c\right) + 4 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) - \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, c\right) + 4 \, {\left(2 \, \sin\left(2 \, b x + 2 \, a\right) + 5 \, \sin\left(2 \, b x + 2 \, c\right)\right)} \cos\left(3 \, b x + a + 2 \, c\right) - 3 \, {\left(\cos\left(5 \, b x + a + 4 \, c\right)^{2} \sin\left(-a + c\right) + 4 \, \cos\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 4 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \sin\left(-a + c\right) + \cos\left(b x + a\right)^{2} \sin\left(-a + c\right) + \sin\left(5 \, b x + a + 4 \, c\right)^{2} \sin\left(-a + c\right) + 4 \, \sin\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 4 \, \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) \sin\left(-a + c\right) + \sin\left(b x + a\right)^{2} \sin\left(-a + c\right) - 2 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) - \cos\left(b x + a\right) \sin\left(-a + c\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) - 2 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) - \sin\left(b x + a\right) \sin\left(-a + c\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + 3 \, {\left(\cos\left(5 \, b x + a + 4 \, c\right)^{2} \sin\left(-a + c\right) + 4 \, \cos\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 4 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \sin\left(-a + c\right) + \cos\left(b x + a\right)^{2} \sin\left(-a + c\right) + \sin\left(5 \, b x + a + 4 \, c\right)^{2} \sin\left(-a + c\right) + 4 \, \sin\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 4 \, \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) \sin\left(-a + c\right) + \sin\left(b x + a\right)^{2} \sin\left(-a + c\right) - 2 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) - \cos\left(b x + a\right) \sin\left(-a + c\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) - 2 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) - \sin\left(b x + a\right) \sin\left(-a + c\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - 2 \, {\left(\cos\left(5 \, b x + a + 4 \, c\right) - 2 \, \cos\left(3 \, b x + a + 2 \, c\right) + \cos\left(b x + a\right)\right)} \sin\left(6 \, b x + 2 \, a + 4 \, c\right) - 2 \, {\left(5 \, \cos\left(4 \, b x + 2 \, a + 2 \, c\right) + 2 \, \cos\left(4 \, b x + 4 \, c\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) - 5 \, \cos\left(2 \, b x + 2 \, c\right) + 1\right)} \sin\left(5 \, b x + a + 4 \, c\right) - 10 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) - \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 2 \, a + 2 \, c\right) - 4 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) - \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, c\right) - 4 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 5 \, \cos\left(2 \, b x + 2 \, c\right) - 1\right)} \sin\left(3 \, b x + a + 2 \, c\right) - 4 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 10 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, c\right) + 4 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 10 \, \cos\left(2 \, b x + 2 \, c\right) \sin\left(b x + a\right) - 2 \, \sin\left(b x + a\right)}{4 \, {\left(b \cos\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, b \cos\left(3 \, b x + a + 2 \, c\right)^{2} - 4 \, b \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) + b \cos\left(b x + a\right)^{2} + b \sin\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, b \sin\left(3 \, b x + a + 2 \, c\right)^{2} - 4 \, b \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + b \sin\left(b x + a\right)^{2} - 2 \, {\left(2 \, b \cos\left(3 \, b x + a + 2 \, c\right) - b \cos\left(b x + a\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) - 2 \, {\left(2 \, b \sin\left(3 \, b x + a + 2 \, c\right) - b \sin\left(b x + a\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right)\right)}}"," ",0,"1/4*(2*(sin(5*b*x + a + 4*c) - 2*sin(3*b*x + a + 2*c) + sin(b*x + a))*cos(6*b*x + 2*a + 4*c) + 2*(5*sin(4*b*x + 2*a + 2*c) + 2*sin(4*b*x + 4*c) - 2*sin(2*b*x + 2*a) - 5*sin(2*b*x + 2*c))*cos(5*b*x + a + 4*c) + 10*(2*sin(3*b*x + a + 2*c) - sin(b*x + a))*cos(4*b*x + 2*a + 2*c) + 4*(2*sin(3*b*x + a + 2*c) - sin(b*x + a))*cos(4*b*x + 4*c) + 4*(2*sin(2*b*x + 2*a) + 5*sin(2*b*x + 2*c))*cos(3*b*x + a + 2*c) - 3*(cos(5*b*x + a + 4*c)^2*sin(-a + c) + 4*cos(3*b*x + a + 2*c)^2*sin(-a + c) - 4*cos(3*b*x + a + 2*c)*cos(b*x + a)*sin(-a + c) + cos(b*x + a)^2*sin(-a + c) + sin(5*b*x + a + 4*c)^2*sin(-a + c) + 4*sin(3*b*x + a + 2*c)^2*sin(-a + c) - 4*sin(3*b*x + a + 2*c)*sin(b*x + a)*sin(-a + c) + sin(b*x + a)^2*sin(-a + c) - 2*(2*cos(3*b*x + a + 2*c)*sin(-a + c) - cos(b*x + a)*sin(-a + c))*cos(5*b*x + a + 4*c) - 2*(2*sin(3*b*x + a + 2*c)*sin(-a + c) - sin(b*x + a)*sin(-a + c))*sin(5*b*x + a + 4*c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) + 3*(cos(5*b*x + a + 4*c)^2*sin(-a + c) + 4*cos(3*b*x + a + 2*c)^2*sin(-a + c) - 4*cos(3*b*x + a + 2*c)*cos(b*x + a)*sin(-a + c) + cos(b*x + a)^2*sin(-a + c) + sin(5*b*x + a + 4*c)^2*sin(-a + c) + 4*sin(3*b*x + a + 2*c)^2*sin(-a + c) - 4*sin(3*b*x + a + 2*c)*sin(b*x + a)*sin(-a + c) + sin(b*x + a)^2*sin(-a + c) - 2*(2*cos(3*b*x + a + 2*c)*sin(-a + c) - cos(b*x + a)*sin(-a + c))*cos(5*b*x + a + 4*c) - 2*(2*sin(3*b*x + a + 2*c)*sin(-a + c) - sin(b*x + a)*sin(-a + c))*sin(5*b*x + a + 4*c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2) - 2*(cos(5*b*x + a + 4*c) - 2*cos(3*b*x + a + 2*c) + cos(b*x + a))*sin(6*b*x + 2*a + 4*c) - 2*(5*cos(4*b*x + 2*a + 2*c) + 2*cos(4*b*x + 4*c) - 2*cos(2*b*x + 2*a) - 5*cos(2*b*x + 2*c) + 1)*sin(5*b*x + a + 4*c) - 10*(2*cos(3*b*x + a + 2*c) - cos(b*x + a))*sin(4*b*x + 2*a + 2*c) - 4*(2*cos(3*b*x + a + 2*c) - cos(b*x + a))*sin(4*b*x + 4*c) - 4*(2*cos(2*b*x + 2*a) + 5*cos(2*b*x + 2*c) - 1)*sin(3*b*x + a + 2*c) - 4*cos(b*x + a)*sin(2*b*x + 2*a) - 10*cos(b*x + a)*sin(2*b*x + 2*c) + 4*cos(2*b*x + 2*a)*sin(b*x + a) + 10*cos(2*b*x + 2*c)*sin(b*x + a) - 2*sin(b*x + a))/(b*cos(5*b*x + a + 4*c)^2 + 4*b*cos(3*b*x + a + 2*c)^2 - 4*b*cos(3*b*x + a + 2*c)*cos(b*x + a) + b*cos(b*x + a)^2 + b*sin(5*b*x + a + 4*c)^2 + 4*b*sin(3*b*x + a + 2*c)^2 - 4*b*sin(3*b*x + a + 2*c)*sin(b*x + a) + b*sin(b*x + a)^2 - 2*(2*b*cos(3*b*x + a + 2*c) - b*cos(b*x + a))*cos(5*b*x + a + 4*c) - 2*(2*b*sin(3*b*x + a + 2*c) - b*sin(b*x + a))*sin(5*b*x + a + 4*c))","B",0
236,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(d*x+c),x, algorithm=""maxima"")","\int \sin\left(b x + a\right) \tan\left(d x + c\right)\,{d x}"," ",0,"integrate(sin(b*x + a)*tan(d*x + c), x)","F",0
237,0,0,0,0.000000," ","integrate(cot(d*x+c)*sin(b*x+a),x, algorithm=""maxima"")","\int \cot\left(d x + c\right) \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(cot(d*x + c)*sin(b*x + a), x)","F",0
238,1,914,0,0.404656," ","integrate(cos(b*x+a)*cos(d*x+c)^3,x, algorithm=""maxima"")","-\frac{{\left(b^{3} \sin\left(3 \, c\right) - 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) + 3 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) - {\left(b^{3} \sin\left(3 \, c\right) - 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) + 3 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a\right) + 3 \, {\left(b^{3} \sin\left(3 \, c\right) - b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) + 9 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a + 4 \, c\right) - 3 \, {\left(b^{3} \sin\left(3 \, c\right) - b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) + 9 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a - 2 \, c\right) - 3 \, {\left(b^{3} \sin\left(3 \, c\right) + b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) - 9 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a + 4 \, c\right) + 3 \, {\left(b^{3} \sin\left(3 \, c\right) + b^{2} d \sin\left(3 \, c\right) - 9 \, b d^{2} \sin\left(3 \, c\right) - 9 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a - 2 \, c\right) - {\left(b^{3} \sin\left(3 \, c\right) + 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) - 3 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) + {\left(b^{3} \sin\left(3 \, c\right) + 3 \, b^{2} d \sin\left(3 \, c\right) - b d^{2} \sin\left(3 \, c\right) - 3 \, d^{3} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a\right) - {\left(b^{3} \cos\left(3 \, c\right) - 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) + 3 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) - {\left(b^{3} \cos\left(3 \, c\right) - 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) + 3 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a\right) - 3 \, {\left(b^{3} \cos\left(3 \, c\right) - b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) + 9 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a + 4 \, c\right) - 3 \, {\left(b^{3} \cos\left(3 \, c\right) - b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) + 9 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a - 2 \, c\right) + 3 \, {\left(b^{3} \cos\left(3 \, c\right) + b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) - 9 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a + 4 \, c\right) + 3 \, {\left(b^{3} \cos\left(3 \, c\right) + b^{2} d \cos\left(3 \, c\right) - 9 \, b d^{2} \cos\left(3 \, c\right) - 9 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a - 2 \, c\right) + {\left(b^{3} \cos\left(3 \, c\right) + 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) - 3 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) + {\left(b^{3} \cos\left(3 \, c\right) + 3 \, b^{2} d \cos\left(3 \, c\right) - b d^{2} \cos\left(3 \, c\right) - 3 \, d^{3} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a\right)}{16 \, {\left(b^{4} \cos\left(3 \, c\right)^{2} + b^{4} \sin\left(3 \, c\right)^{2} + 9 \, {\left(\cos\left(3 \, c\right)^{2} + \sin\left(3 \, c\right)^{2}\right)} d^{4} - 10 \, {\left(b^{2} \cos\left(3 \, c\right)^{2} + b^{2} \sin\left(3 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"-1/16*((b^3*sin(3*c) - 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) + 3*d^3*sin(3*c))*cos((b + 3*d)*x + a + 6*c) - (b^3*sin(3*c) - 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) + 3*d^3*sin(3*c))*cos((b + 3*d)*x + a) + 3*(b^3*sin(3*c) - b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) + 9*d^3*sin(3*c))*cos((b + d)*x + a + 4*c) - 3*(b^3*sin(3*c) - b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) + 9*d^3*sin(3*c))*cos((b + d)*x + a - 2*c) - 3*(b^3*sin(3*c) + b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) - 9*d^3*sin(3*c))*cos(-(b - d)*x - a + 4*c) + 3*(b^3*sin(3*c) + b^2*d*sin(3*c) - 9*b*d^2*sin(3*c) - 9*d^3*sin(3*c))*cos(-(b - d)*x - a - 2*c) - (b^3*sin(3*c) + 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) - 3*d^3*sin(3*c))*cos(-(b - 3*d)*x - a + 6*c) + (b^3*sin(3*c) + 3*b^2*d*sin(3*c) - b*d^2*sin(3*c) - 3*d^3*sin(3*c))*cos(-(b - 3*d)*x - a) - (b^3*cos(3*c) - 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) + 3*d^3*cos(3*c))*sin((b + 3*d)*x + a + 6*c) - (b^3*cos(3*c) - 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) + 3*d^3*cos(3*c))*sin((b + 3*d)*x + a) - 3*(b^3*cos(3*c) - b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) + 9*d^3*cos(3*c))*sin((b + d)*x + a + 4*c) - 3*(b^3*cos(3*c) - b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) + 9*d^3*cos(3*c))*sin((b + d)*x + a - 2*c) + 3*(b^3*cos(3*c) + b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) - 9*d^3*cos(3*c))*sin(-(b - d)*x - a + 4*c) + 3*(b^3*cos(3*c) + b^2*d*cos(3*c) - 9*b*d^2*cos(3*c) - 9*d^3*cos(3*c))*sin(-(b - d)*x - a - 2*c) + (b^3*cos(3*c) + 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) - 3*d^3*cos(3*c))*sin(-(b - 3*d)*x - a + 6*c) + (b^3*cos(3*c) + 3*b^2*d*cos(3*c) - b*d^2*cos(3*c) - 3*d^3*cos(3*c))*sin(-(b - 3*d)*x - a))/(b^4*cos(3*c)^2 + b^4*sin(3*c)^2 + 9*(cos(3*c)^2 + sin(3*c)^2)*d^4 - 10*(b^2*cos(3*c)^2 + b^2*sin(3*c)^2)*d^2)","B",0
239,1,416,0,0.371670," ","integrate(cos(b*x+a)*cos(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{2} \sin\left(2 \, c\right) - 2 \, b d \sin\left(2 \, c\right)\right)} \cos\left({\left(b + 2 \, d\right)} x + a + 4 \, c\right) - {\left(b^{2} \sin\left(2 \, c\right) - 2 \, b d \sin\left(2 \, c\right)\right)} \cos\left({\left(b + 2 \, d\right)} x + a\right) - {\left(b^{2} \sin\left(2 \, c\right) + 2 \, b d \sin\left(2 \, c\right)\right)} \cos\left(-{\left(b - 2 \, d\right)} x - a + 4 \, c\right) + {\left(b^{2} \sin\left(2 \, c\right) + 2 \, b d \sin\left(2 \, c\right)\right)} \cos\left(-{\left(b - 2 \, d\right)} x - a\right) + 2 \, {\left(b^{2} \sin\left(2 \, c\right) - 4 \, d^{2} \sin\left(2 \, c\right)\right)} \cos\left(b x + a + 2 \, c\right) - 2 \, {\left(b^{2} \sin\left(2 \, c\right) - 4 \, d^{2} \sin\left(2 \, c\right)\right)} \cos\left(b x + a - 2 \, c\right) - {\left(b^{2} \cos\left(2 \, c\right) - 2 \, b d \cos\left(2 \, c\right)\right)} \sin\left({\left(b + 2 \, d\right)} x + a + 4 \, c\right) - {\left(b^{2} \cos\left(2 \, c\right) - 2 \, b d \cos\left(2 \, c\right)\right)} \sin\left({\left(b + 2 \, d\right)} x + a\right) + {\left(b^{2} \cos\left(2 \, c\right) + 2 \, b d \cos\left(2 \, c\right)\right)} \sin\left(-{\left(b - 2 \, d\right)} x - a + 4 \, c\right) + {\left(b^{2} \cos\left(2 \, c\right) + 2 \, b d \cos\left(2 \, c\right)\right)} \sin\left(-{\left(b - 2 \, d\right)} x - a\right) - 2 \, {\left(b^{2} \cos\left(2 \, c\right) - 4 \, d^{2} \cos\left(2 \, c\right)\right)} \sin\left(b x + a + 2 \, c\right) - 2 \, {\left(b^{2} \cos\left(2 \, c\right) - 4 \, d^{2} \cos\left(2 \, c\right)\right)} \sin\left(b x + a - 2 \, c\right)}{8 \, {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2} - 4 \, {\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"-1/8*((b^2*sin(2*c) - 2*b*d*sin(2*c))*cos((b + 2*d)*x + a + 4*c) - (b^2*sin(2*c) - 2*b*d*sin(2*c))*cos((b + 2*d)*x + a) - (b^2*sin(2*c) + 2*b*d*sin(2*c))*cos(-(b - 2*d)*x - a + 4*c) + (b^2*sin(2*c) + 2*b*d*sin(2*c))*cos(-(b - 2*d)*x - a) + 2*(b^2*sin(2*c) - 4*d^2*sin(2*c))*cos(b*x + a + 2*c) - 2*(b^2*sin(2*c) - 4*d^2*sin(2*c))*cos(b*x + a - 2*c) - (b^2*cos(2*c) - 2*b*d*cos(2*c))*sin((b + 2*d)*x + a + 4*c) - (b^2*cos(2*c) - 2*b*d*cos(2*c))*sin((b + 2*d)*x + a) + (b^2*cos(2*c) + 2*b*d*cos(2*c))*sin(-(b - 2*d)*x - a + 4*c) + (b^2*cos(2*c) + 2*b*d*cos(2*c))*sin(-(b - 2*d)*x - a) - 2*(b^2*cos(2*c) - 4*d^2*cos(2*c))*sin(b*x + a + 2*c) - 2*(b^2*cos(2*c) - 4*d^2*cos(2*c))*sin(b*x + a - 2*c))/(b^3*cos(2*c)^2 + b^3*sin(2*c)^2 - 4*(b*cos(2*c)^2 + b*sin(2*c)^2)*d^2)","B",0
240,1,40,0,0.332744," ","integrate(cos(b*x+a)*cos(d*x+c),x, algorithm=""maxima"")","\frac{\sin\left(b x + d x + a + c\right)}{2 \, {\left(b + d\right)}} - \frac{\sin\left(-b x + d x - a + c\right)}{2 \, {\left(b - d\right)}}"," ",0,"1/2*sin(b*x + d*x + a + c)/(b + d) - 1/2*sin(-b*x + d*x - a + c)/(b - d)","A",0
241,1,74,0,0.342816," ","integrate(cos(b*x+a)*sec(b*x+c),x, algorithm=""maxima"")","\frac{2 \, b x \cos\left(-a + c\right) - \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, c\right) + \cos\left(2 \, c\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, c\right) + \sin\left(2 \, c\right)^{2}\right) \sin\left(-a + c\right)}{2 \, b}"," ",0,"1/2*(2*b*x*cos(-a + c) - log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*c) + cos(2*c)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*c) + sin(2*c)^2)*sin(-a + c))/b","B",0
242,1,391,0,0.524359," ","integrate(cos(b*x+a)*sec(b*x+c)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\sin\left(b x + 2 \, a\right) - \sin\left(b x + 2 \, c\right)\right)} \cos\left(2 \, b x + a + 2 \, c\right) + {\left(\cos\left(2 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) + 2 \, \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right)^{2} + 2 \, \cos\left(-a + c\right) \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(-a + c\right)\right)} \log\left(\frac{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} - 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} - 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}\right) - 2 \, {\left(\cos\left(b x + 2 \, a\right) - \cos\left(b x + 2 \, c\right)\right)} \sin\left(2 \, b x + a + 2 \, c\right) + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, c\right) - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(a\right)}{2 \, {\left(b \cos\left(2 \, b x + a + 2 \, c\right)^{2} + 2 \, b \cos\left(2 \, b x + a + 2 \, c\right) \cos\left(a\right) + b \sin\left(2 \, b x + a + 2 \, c\right)^{2} + 2 \, b \sin\left(2 \, b x + a + 2 \, c\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b\right)}}"," ",0,"-1/2*(2*(sin(b*x + 2*a) - sin(b*x + 2*c))*cos(2*b*x + a + 2*c) + (cos(2*b*x + a + 2*c)^2*cos(-a + c) + 2*cos(2*b*x + a + 2*c)*cos(a)*cos(-a + c) + cos(-a + c)*sin(2*b*x + a + 2*c)^2 + 2*cos(-a + c)*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*cos(-a + c))*log((cos(b*x + 2*c)^2 + cos(c)^2 - 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 + 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)/(cos(b*x + 2*c)^2 + cos(c)^2 + 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 - 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)) - 2*(cos(b*x + 2*a) - cos(b*x + 2*c))*sin(2*b*x + a + 2*c) + 2*cos(a)*sin(b*x + 2*a) - 2*cos(a)*sin(b*x + 2*c) - 2*cos(b*x + 2*a)*sin(a) + 2*cos(b*x + 2*c)*sin(a))/(b*cos(2*b*x + a + 2*c)^2 + 2*b*cos(2*b*x + a + 2*c)*cos(a) + b*sin(2*b*x + a + 2*c)^2 + 2*b*sin(2*b*x + a + 2*c)*sin(a) + (cos(a)^2 + sin(a)^2)*b)","B",0
243,1,382,0,0.333191," ","integrate(cos(b*x+a)*sec(b*x+c)^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) + \sin\left(2 \, a\right) + \sin\left(2 \, c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) + 2 \, {\left(2 \, \sin\left(2 \, b x + 2 \, a + 2 \, c\right) + \sin\left(2 \, a\right) + \sin\left(2 \, c\right)\right)} \cos\left(2 \, b x + a + 3 \, c\right) + {\left(\sin\left(2 \, a\right) + \sin\left(2 \, c\right)\right)} \cos\left(a + c\right) - {\left(2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) + \cos\left(2 \, a\right) + \cos\left(2 \, c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right) + 2 \, \cos\left(a + c\right) \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - 2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) + \cos\left(2 \, a\right) + \cos\left(2 \, c\right)\right)} \sin\left(2 \, b x + a + 3 \, c\right) - {\left(\cos\left(2 \, a\right) + \cos\left(2 \, c\right)\right)} \sin\left(a + c\right) - 2 \, \cos\left(2 \, b x + 2 \, a + 2 \, c\right) \sin\left(a + c\right)}{b \cos\left(4 \, b x + a + 5 \, c\right)^{2} + 4 \, b \cos\left(2 \, b x + a + 3 \, c\right)^{2} + 4 \, b \cos\left(2 \, b x + a + 3 \, c\right) \cos\left(a + c\right) + b \cos\left(a + c\right)^{2} + b \sin\left(4 \, b x + a + 5 \, c\right)^{2} + 4 \, b \sin\left(2 \, b x + a + 3 \, c\right)^{2} + 4 \, b \sin\left(2 \, b x + a + 3 \, c\right) \sin\left(a + c\right) + b \sin\left(a + c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, b x + a + 3 \, c\right) + b \cos\left(a + c\right)\right)} \cos\left(4 \, b x + a + 5 \, c\right) + 2 \, {\left(2 \, b \sin\left(2 \, b x + a + 3 \, c\right) + b \sin\left(a + c\right)\right)} \sin\left(4 \, b x + a + 5 \, c\right)}"," ",0,"-((2*sin(2*b*x + 2*a + 2*c) + sin(2*a) + sin(2*c))*cos(4*b*x + a + 5*c) + 2*(2*sin(2*b*x + 2*a + 2*c) + sin(2*a) + sin(2*c))*cos(2*b*x + a + 3*c) + (sin(2*a) + sin(2*c))*cos(a + c) - (2*cos(2*b*x + 2*a + 2*c) + cos(2*a) + cos(2*c))*sin(4*b*x + a + 5*c) + 2*cos(a + c)*sin(2*b*x + 2*a + 2*c) - 2*(2*cos(2*b*x + 2*a + 2*c) + cos(2*a) + cos(2*c))*sin(2*b*x + a + 3*c) - (cos(2*a) + cos(2*c))*sin(a + c) - 2*cos(2*b*x + 2*a + 2*c)*sin(a + c))/(b*cos(4*b*x + a + 5*c)^2 + 4*b*cos(2*b*x + a + 3*c)^2 + 4*b*cos(2*b*x + a + 3*c)*cos(a + c) + b*cos(a + c)^2 + b*sin(4*b*x + a + 5*c)^2 + 4*b*sin(2*b*x + a + 3*c)^2 + 4*b*sin(2*b*x + a + 3*c)*sin(a + c) + b*sin(a + c)^2 + 2*(2*b*cos(2*b*x + a + 3*c) + b*cos(a + c))*cos(4*b*x + a + 5*c) + 2*(2*b*sin(2*b*x + a + 3*c) + b*sin(a + c))*sin(4*b*x + a + 5*c))","B",0
244,1,1362,0,0.426380," ","integrate(cos(b*x+a)^2*cos(d*x+c)^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) + 3 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a + 6 \, c\right) - 3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) + 3 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a\right) + 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + d\right)} x + 2 \, a + 4 \, c\right) - 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) - 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left({\left(2 \, b + d\right)} x + 2 \, a - 2 \, c\right) - 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) - 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - d\right)} x - 2 \, a + 4 \, c\right) + 9 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 4 \, b^{2} d^{2} \sin\left(3 \, c\right) - 18 \, b d^{3} \sin\left(3 \, c\right) - 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - d\right)} x - 2 \, a - 2 \, c\right) - 3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) - 3 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a + 6 \, c\right) + 3 \, {\left(8 \, b^{3} d \sin\left(3 \, c\right) + 12 \, b^{2} d^{2} \sin\left(3 \, c\right) - 2 \, b d^{3} \sin\left(3 \, c\right) - 3 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a\right) - 2 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(3 \, d x\right) + 2 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(3 \, d x + 6 \, c\right) + 18 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(d x + 4 \, c\right) - 18 \, {\left(16 \, b^{4} \sin\left(3 \, c\right) - 40 \, b^{2} d^{2} \sin\left(3 \, c\right) + 9 \, d^{4} \sin\left(3 \, c\right)\right)} \cos\left(d x - 2 \, c\right) - 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) + 3 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a + 6 \, c\right) - 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) + 3 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + 3 \, d\right)} x + 2 \, a\right) - 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + d\right)} x + 2 \, a + 4 \, c\right) - 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) - 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left({\left(2 \, b + d\right)} x + 2 \, a - 2 \, c\right) + 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) - 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - d\right)} x - 2 \, a + 4 \, c\right) + 9 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 4 \, b^{2} d^{2} \cos\left(3 \, c\right) - 18 \, b d^{3} \cos\left(3 \, c\right) - 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - d\right)} x - 2 \, a - 2 \, c\right) + 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) - 3 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a + 6 \, c\right) + 3 \, {\left(8 \, b^{3} d \cos\left(3 \, c\right) + 12 \, b^{2} d^{2} \cos\left(3 \, c\right) - 2 \, b d^{3} \cos\left(3 \, c\right) - 3 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(2 \, b - 3 \, d\right)} x - 2 \, a\right) - 2 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(3 \, d x\right) - 2 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(3 \, d x + 6 \, c\right) - 18 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(d x + 4 \, c\right) - 18 \, {\left(16 \, b^{4} \cos\left(3 \, c\right) - 40 \, b^{2} d^{2} \cos\left(3 \, c\right) + 9 \, d^{4} \cos\left(3 \, c\right)\right)} \sin\left(d x - 2 \, c\right)}{96 \, {\left(9 \, {\left(\cos\left(3 \, c\right)^{2} + \sin\left(3 \, c\right)^{2}\right)} d^{5} - 40 \, {\left(b^{2} \cos\left(3 \, c\right)^{2} + b^{2} \sin\left(3 \, c\right)^{2}\right)} d^{3} + 16 \, {\left(b^{4} \cos\left(3 \, c\right)^{2} + b^{4} \sin\left(3 \, c\right)^{2}\right)} d\right)}}"," ",0,"-1/96*(3*(8*b^3*d*sin(3*c) - 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) + 3*d^4*sin(3*c))*cos((2*b + 3*d)*x + 2*a + 6*c) - 3*(8*b^3*d*sin(3*c) - 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) + 3*d^4*sin(3*c))*cos((2*b + 3*d)*x + 2*a) + 9*(8*b^3*d*sin(3*c) - 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) + 9*d^4*sin(3*c))*cos((2*b + d)*x + 2*a + 4*c) - 9*(8*b^3*d*sin(3*c) - 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) + 9*d^4*sin(3*c))*cos((2*b + d)*x + 2*a - 2*c) - 9*(8*b^3*d*sin(3*c) + 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) - 9*d^4*sin(3*c))*cos(-(2*b - d)*x - 2*a + 4*c) + 9*(8*b^3*d*sin(3*c) + 4*b^2*d^2*sin(3*c) - 18*b*d^3*sin(3*c) - 9*d^4*sin(3*c))*cos(-(2*b - d)*x - 2*a - 2*c) - 3*(8*b^3*d*sin(3*c) + 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) - 3*d^4*sin(3*c))*cos(-(2*b - 3*d)*x - 2*a + 6*c) + 3*(8*b^3*d*sin(3*c) + 12*b^2*d^2*sin(3*c) - 2*b*d^3*sin(3*c) - 3*d^4*sin(3*c))*cos(-(2*b - 3*d)*x - 2*a) - 2*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*cos(3*d*x) + 2*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*cos(3*d*x + 6*c) + 18*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*cos(d*x + 4*c) - 18*(16*b^4*sin(3*c) - 40*b^2*d^2*sin(3*c) + 9*d^4*sin(3*c))*cos(d*x - 2*c) - 3*(8*b^3*d*cos(3*c) - 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) + 3*d^4*cos(3*c))*sin((2*b + 3*d)*x + 2*a + 6*c) - 3*(8*b^3*d*cos(3*c) - 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) + 3*d^4*cos(3*c))*sin((2*b + 3*d)*x + 2*a) - 9*(8*b^3*d*cos(3*c) - 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) + 9*d^4*cos(3*c))*sin((2*b + d)*x + 2*a + 4*c) - 9*(8*b^3*d*cos(3*c) - 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) + 9*d^4*cos(3*c))*sin((2*b + d)*x + 2*a - 2*c) + 9*(8*b^3*d*cos(3*c) + 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) - 9*d^4*cos(3*c))*sin(-(2*b - d)*x - 2*a + 4*c) + 9*(8*b^3*d*cos(3*c) + 4*b^2*d^2*cos(3*c) - 18*b*d^3*cos(3*c) - 9*d^4*cos(3*c))*sin(-(2*b - d)*x - 2*a - 2*c) + 3*(8*b^3*d*cos(3*c) + 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) - 3*d^4*cos(3*c))*sin(-(2*b - 3*d)*x - 2*a + 6*c) + 3*(8*b^3*d*cos(3*c) + 12*b^2*d^2*cos(3*c) - 2*b*d^3*cos(3*c) - 3*d^4*cos(3*c))*sin(-(2*b - 3*d)*x - 2*a) - 2*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*sin(3*d*x) - 2*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*sin(3*d*x + 6*c) - 18*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*sin(d*x + 4*c) - 18*(16*b^4*cos(3*c) - 40*b^2*d^2*cos(3*c) + 9*d^4*cos(3*c))*sin(d*x - 2*c))/(9*(cos(3*c)^2 + sin(3*c)^2)*d^5 - 40*(b^2*cos(3*c)^2 + b^2*sin(3*c)^2)*d^3 + 16*(b^4*cos(3*c)^2 + b^4*sin(3*c)^2)*d)","B",0
245,1,620,0,0.371100," ","integrate(cos(b*x+a)^2*cos(d*x+c)^2,x, algorithm=""maxima"")","\frac{8 \, {\left({\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{3} - {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2}\right)} d\right)} x + {\left(b^{2} d \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, {\left(b + d\right)} x + 2 \, a + 4 \, c\right) - {\left(b^{2} d \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, {\left(b + d\right)} x + 2 \, a\right) - {\left(b^{2} d \sin\left(2 \, c\right) + b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(-2 \, {\left(b - d\right)} x - 2 \, a + 4 \, c\right) + {\left(b^{2} d \sin\left(2 \, c\right) + b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(-2 \, {\left(b - d\right)} x - 2 \, a\right) + 2 \, {\left(b^{2} d \sin\left(2 \, c\right) - d^{3} \sin\left(2 \, c\right)\right)} \cos\left(2 \, b x + 2 \, a + 2 \, c\right) - 2 \, {\left(b^{2} d \sin\left(2 \, c\right) - d^{3} \sin\left(2 \, c\right)\right)} \cos\left(2 \, b x + 2 \, a - 2 \, c\right) - 2 \, {\left(b^{3} \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x\right) + 2 \, {\left(b^{3} \sin\left(2 \, c\right) - b d^{2} \sin\left(2 \, c\right)\right)} \cos\left(2 \, d x + 4 \, c\right) - {\left(b^{2} d \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, {\left(b + d\right)} x + 2 \, a + 4 \, c\right) - {\left(b^{2} d \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, {\left(b + d\right)} x + 2 \, a\right) + {\left(b^{2} d \cos\left(2 \, c\right) + b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(-2 \, {\left(b - d\right)} x - 2 \, a + 4 \, c\right) + {\left(b^{2} d \cos\left(2 \, c\right) + b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(-2 \, {\left(b - d\right)} x - 2 \, a\right) - 2 \, {\left(b^{2} d \cos\left(2 \, c\right) - d^{3} \cos\left(2 \, c\right)\right)} \sin\left(2 \, b x + 2 \, a + 2 \, c\right) - 2 \, {\left(b^{2} d \cos\left(2 \, c\right) - d^{3} \cos\left(2 \, c\right)\right)} \sin\left(2 \, b x + 2 \, a - 2 \, c\right) - 2 \, {\left(b^{3} \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, d x\right) - 2 \, {\left(b^{3} \cos\left(2 \, c\right) - b d^{2} \cos\left(2 \, c\right)\right)} \sin\left(2 \, d x + 4 \, c\right)}{32 \, {\left({\left(b \cos\left(2 \, c\right)^{2} + b \sin\left(2 \, c\right)^{2}\right)} d^{3} - {\left(b^{3} \cos\left(2 \, c\right)^{2} + b^{3} \sin\left(2 \, c\right)^{2}\right)} d\right)}}"," ",0,"1/32*(8*((b*cos(2*c)^2 + b*sin(2*c)^2)*d^3 - (b^3*cos(2*c)^2 + b^3*sin(2*c)^2)*d)*x + (b^2*d*sin(2*c) - b*d^2*sin(2*c))*cos(2*(b + d)*x + 2*a + 4*c) - (b^2*d*sin(2*c) - b*d^2*sin(2*c))*cos(2*(b + d)*x + 2*a) - (b^2*d*sin(2*c) + b*d^2*sin(2*c))*cos(-2*(b - d)*x - 2*a + 4*c) + (b^2*d*sin(2*c) + b*d^2*sin(2*c))*cos(-2*(b - d)*x - 2*a) + 2*(b^2*d*sin(2*c) - d^3*sin(2*c))*cos(2*b*x + 2*a + 2*c) - 2*(b^2*d*sin(2*c) - d^3*sin(2*c))*cos(2*b*x + 2*a - 2*c) - 2*(b^3*sin(2*c) - b*d^2*sin(2*c))*cos(2*d*x) + 2*(b^3*sin(2*c) - b*d^2*sin(2*c))*cos(2*d*x + 4*c) - (b^2*d*cos(2*c) - b*d^2*cos(2*c))*sin(2*(b + d)*x + 2*a + 4*c) - (b^2*d*cos(2*c) - b*d^2*cos(2*c))*sin(2*(b + d)*x + 2*a) + (b^2*d*cos(2*c) + b*d^2*cos(2*c))*sin(-2*(b - d)*x - 2*a + 4*c) + (b^2*d*cos(2*c) + b*d^2*cos(2*c))*sin(-2*(b - d)*x - 2*a) - 2*(b^2*d*cos(2*c) - d^3*cos(2*c))*sin(2*b*x + 2*a + 2*c) - 2*(b^2*d*cos(2*c) - d^3*cos(2*c))*sin(2*b*x + 2*a - 2*c) - 2*(b^3*cos(2*c) - b*d^2*cos(2*c))*sin(2*d*x) - 2*(b^3*cos(2*c) - b*d^2*cos(2*c))*sin(2*d*x + 4*c))/((b*cos(2*c)^2 + b*sin(2*c)^2)*d^3 - (b^3*cos(2*c)^2 + b^3*sin(2*c)^2)*d)","B",0
246,1,2614,0,0.581740," ","integrate(cos(b*x+a)^3*cos(d*x+c)^3,x, algorithm=""maxima"")","-\frac{9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) - b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) + 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(3 \, b + d\right)} x + 3 \, a + 4 \, c\right) - 9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) - b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) + 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(3 \, b + d\right)} x + 3 \, a - 2 \, c\right) - 9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) + b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) - 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(3 \, b - d\right)} x - 3 \, a + 4 \, c\right) + 9 \, {\left(3 \, b^{5} \sin\left(3 \, c\right) + b^{4} d \sin\left(3 \, c\right) - 30 \, b^{3} d^{2} \sin\left(3 \, c\right) - 10 \, b^{2} d^{3} \sin\left(3 \, c\right) + 27 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(3 \, b - d\right)} x - 3 \, a - 2 \, c\right) + 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) + 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) - 3 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) - 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) + 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) - 3 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + 3 \, d\right)} x + a\right) + {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(3 \, {\left(b + d\right)} x + 3 \, a + 6 \, c\right) - {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(3 \, {\left(b + d\right)} x + 3 \, a\right) + 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a + 4 \, c\right) - 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) - 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) + 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) - 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left({\left(b + d\right)} x + a - 2 \, c\right) - 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a + 4 \, c\right) + 27 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - d\right)} x - a - 2 \, c\right) - {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-3 \, {\left(b - d\right)} x - 3 \, a + 6 \, c\right) + {\left(9 \, b^{5} \sin\left(3 \, c\right) + 9 \, b^{4} d \sin\left(3 \, c\right) - 82 \, b^{3} d^{2} \sin\left(3 \, c\right) - 82 \, b^{2} d^{3} \sin\left(3 \, c\right) + 9 \, b d^{4} \sin\left(3 \, c\right) + 9 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-3 \, {\left(b - d\right)} x - 3 \, a\right) - 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) - 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) + 3 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) + 9 \, {\left(9 \, b^{5} \sin\left(3 \, c\right) + 27 \, b^{4} d \sin\left(3 \, c\right) - 10 \, b^{3} d^{2} \sin\left(3 \, c\right) - 30 \, b^{2} d^{3} \sin\left(3 \, c\right) + b d^{4} \sin\left(3 \, c\right) + 3 \, d^{5} \sin\left(3 \, c\right)\right)} \cos\left(-{\left(b - 3 \, d\right)} x - a\right) - 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) - b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) + 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(3 \, b + d\right)} x + 3 \, a + 4 \, c\right) - 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) - b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) + 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(3 \, b + d\right)} x + 3 \, a - 2 \, c\right) + 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) + b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) - 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(3 \, b - d\right)} x - 3 \, a + 4 \, c\right) + 9 \, {\left(3 \, b^{5} \cos\left(3 \, c\right) + b^{4} d \cos\left(3 \, c\right) - 30 \, b^{3} d^{2} \cos\left(3 \, c\right) - 10 \, b^{2} d^{3} \cos\left(3 \, c\right) + 27 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(3 \, b - d\right)} x - 3 \, a - 2 \, c\right) - 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) + 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) - 3 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a + 6 \, c\right) - 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) + 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) - 3 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + 3 \, d\right)} x + a\right) - {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(3 \, {\left(b + d\right)} x + 3 \, a + 6 \, c\right) - {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(3 \, {\left(b + d\right)} x + 3 \, a\right) - 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a + 4 \, c\right) - 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) - 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) + 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) - 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left({\left(b + d\right)} x + a - 2 \, c\right) + 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a + 4 \, c\right) + 27 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - d\right)} x - a - 2 \, c\right) + {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-3 \, {\left(b - d\right)} x - 3 \, a + 6 \, c\right) + {\left(9 \, b^{5} \cos\left(3 \, c\right) + 9 \, b^{4} d \cos\left(3 \, c\right) - 82 \, b^{3} d^{2} \cos\left(3 \, c\right) - 82 \, b^{2} d^{3} \cos\left(3 \, c\right) + 9 \, b d^{4} \cos\left(3 \, c\right) + 9 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-3 \, {\left(b - d\right)} x - 3 \, a\right) + 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) - 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) + 3 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a + 6 \, c\right) + 9 \, {\left(9 \, b^{5} \cos\left(3 \, c\right) + 27 \, b^{4} d \cos\left(3 \, c\right) - 10 \, b^{3} d^{2} \cos\left(3 \, c\right) - 30 \, b^{2} d^{3} \cos\left(3 \, c\right) + b d^{4} \cos\left(3 \, c\right) + 3 \, d^{5} \cos\left(3 \, c\right)\right)} \sin\left(-{\left(b - 3 \, d\right)} x - a\right)}{192 \, {\left(9 \, b^{6} \cos\left(3 \, c\right)^{2} + 9 \, b^{6} \sin\left(3 \, c\right)^{2} - 9 \, {\left(\cos\left(3 \, c\right)^{2} + \sin\left(3 \, c\right)^{2}\right)} d^{6} + 91 \, {\left(b^{2} \cos\left(3 \, c\right)^{2} + b^{2} \sin\left(3 \, c\right)^{2}\right)} d^{4} - 91 \, {\left(b^{4} \cos\left(3 \, c\right)^{2} + b^{4} \sin\left(3 \, c\right)^{2}\right)} d^{2}\right)}}"," ",0,"-1/192*(9*(3*b^5*sin(3*c) - b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) + 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos((3*b + d)*x + 3*a + 4*c) - 9*(3*b^5*sin(3*c) - b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) + 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos((3*b + d)*x + 3*a - 2*c) - 9*(3*b^5*sin(3*c) + b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) - 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-(3*b - d)*x - 3*a + 4*c) + 9*(3*b^5*sin(3*c) + b^4*d*sin(3*c) - 30*b^3*d^2*sin(3*c) - 10*b^2*d^3*sin(3*c) + 27*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-(3*b - d)*x - 3*a - 2*c) + 9*(9*b^5*sin(3*c) - 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) + 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) - 3*d^5*sin(3*c))*cos((b + 3*d)*x + a + 6*c) - 9*(9*b^5*sin(3*c) - 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) + 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) - 3*d^5*sin(3*c))*cos((b + 3*d)*x + a) + (9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos(3*(b + d)*x + 3*a + 6*c) - (9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos(3*(b + d)*x + 3*a) + 27*(9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos((b + d)*x + a + 4*c) - 27*(9*b^5*sin(3*c) - 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) + 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) - 9*d^5*sin(3*c))*cos((b + d)*x + a - 2*c) - 27*(9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-(b - d)*x - a + 4*c) + 27*(9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-(b - d)*x - a - 2*c) - (9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-3*(b - d)*x - 3*a + 6*c) + (9*b^5*sin(3*c) + 9*b^4*d*sin(3*c) - 82*b^3*d^2*sin(3*c) - 82*b^2*d^3*sin(3*c) + 9*b*d^4*sin(3*c) + 9*d^5*sin(3*c))*cos(-3*(b - d)*x - 3*a) - 9*(9*b^5*sin(3*c) + 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) - 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) + 3*d^5*sin(3*c))*cos(-(b - 3*d)*x - a + 6*c) + 9*(9*b^5*sin(3*c) + 27*b^4*d*sin(3*c) - 10*b^3*d^2*sin(3*c) - 30*b^2*d^3*sin(3*c) + b*d^4*sin(3*c) + 3*d^5*sin(3*c))*cos(-(b - 3*d)*x - a) - 9*(3*b^5*cos(3*c) - b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) + 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin((3*b + d)*x + 3*a + 4*c) - 9*(3*b^5*cos(3*c) - b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) + 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin((3*b + d)*x + 3*a - 2*c) + 9*(3*b^5*cos(3*c) + b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) - 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-(3*b - d)*x - 3*a + 4*c) + 9*(3*b^5*cos(3*c) + b^4*d*cos(3*c) - 30*b^3*d^2*cos(3*c) - 10*b^2*d^3*cos(3*c) + 27*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-(3*b - d)*x - 3*a - 2*c) - 9*(9*b^5*cos(3*c) - 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) + 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) - 3*d^5*cos(3*c))*sin((b + 3*d)*x + a + 6*c) - 9*(9*b^5*cos(3*c) - 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) + 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) - 3*d^5*cos(3*c))*sin((b + 3*d)*x + a) - (9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin(3*(b + d)*x + 3*a + 6*c) - (9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin(3*(b + d)*x + 3*a) - 27*(9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin((b + d)*x + a + 4*c) - 27*(9*b^5*cos(3*c) - 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) + 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) - 9*d^5*cos(3*c))*sin((b + d)*x + a - 2*c) + 27*(9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-(b - d)*x - a + 4*c) + 27*(9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-(b - d)*x - a - 2*c) + (9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-3*(b - d)*x - 3*a + 6*c) + (9*b^5*cos(3*c) + 9*b^4*d*cos(3*c) - 82*b^3*d^2*cos(3*c) - 82*b^2*d^3*cos(3*c) + 9*b*d^4*cos(3*c) + 9*d^5*cos(3*c))*sin(-3*(b - d)*x - 3*a) + 9*(9*b^5*cos(3*c) + 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) - 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) + 3*d^5*cos(3*c))*sin(-(b - 3*d)*x - a + 6*c) + 9*(9*b^5*cos(3*c) + 27*b^4*d*cos(3*c) - 10*b^3*d^2*cos(3*c) - 30*b^2*d^3*cos(3*c) + b*d^4*cos(3*c) + 3*d^5*cos(3*c))*sin(-(b - 3*d)*x - a))/(9*b^6*cos(3*c)^2 + 9*b^6*sin(3*c)^2 - 9*(cos(3*c)^2 + sin(3*c)^2)*d^6 + 91*(b^2*cos(3*c)^2 + b^2*sin(3*c)^2)*d^4 - 91*(b^4*cos(3*c)^2 + b^4*sin(3*c)^2)*d^2)","B",0
247,1,1027,0,0.541658," ","integrate(cos(b*x+a)*tan(b*x+c)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(5 \, b x + a + 4 \, c\right) + 2 \, \cos\left(3 \, b x + a + 2 \, c\right) + \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 2 \, a + 4 \, c\right) + 2 \, {\left(5 \, \cos\left(4 \, b x + 2 \, a + 2 \, c\right) + 2 \, \cos\left(4 \, b x + 4 \, c\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 5 \, \cos\left(2 \, b x + 2 \, c\right) + 1\right)} \cos\left(5 \, b x + a + 4 \, c\right) + 10 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) + \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 2 \, a + 2 \, c\right) + 4 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) + \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, c\right) + 4 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 5 \, \cos\left(2 \, b x + 2 \, c\right) + 1\right)} \cos\left(3 \, b x + a + 2 \, c\right) + 4 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 10 \, \cos\left(2 \, b x + 2 \, c\right) \cos\left(b x + a\right) + 3 \, {\left(\cos\left(5 \, b x + a + 4 \, c\right)^{2} \sin\left(-a + c\right) + 4 \, \cos\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) + 4 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \sin\left(-a + c\right) + \cos\left(b x + a\right)^{2} \sin\left(-a + c\right) + \sin\left(5 \, b x + a + 4 \, c\right)^{2} \sin\left(-a + c\right) + 4 \, \sin\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) + 4 \, \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) \sin\left(-a + c\right) + \sin\left(b x + a\right)^{2} \sin\left(-a + c\right) + 2 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \cos\left(b x + a\right) \sin\left(-a + c\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) + 2 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(-a + c\right) + \sin\left(b x + a\right) \sin\left(-a + c\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right)\right)} \log\left(\frac{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} - 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} - 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}\right) + 2 \, {\left(\sin\left(5 \, b x + a + 4 \, c\right) + 2 \, \sin\left(3 \, b x + a + 2 \, c\right) + \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 2 \, a + 4 \, c\right) + 2 \, {\left(5 \, \sin\left(4 \, b x + 2 \, a + 2 \, c\right) + 2 \, \sin\left(4 \, b x + 4 \, c\right) + 2 \, \sin\left(2 \, b x + 2 \, a\right) + 5 \, \sin\left(2 \, b x + 2 \, c\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right) + 10 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) + \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 2 \, a + 2 \, c\right) + 4 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) + \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, c\right) + 4 \, {\left(2 \, \sin\left(2 \, b x + 2 \, a\right) + 5 \, \sin\left(2 \, b x + 2 \, c\right)\right)} \sin\left(3 \, b x + a + 2 \, c\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 10 \, \sin\left(2 \, b x + 2 \, c\right) \sin\left(b x + a\right) + 2 \, \cos\left(b x + a\right)}{4 \, {\left(b \cos\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, b \cos\left(3 \, b x + a + 2 \, c\right)^{2} + 4 \, b \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) + b \cos\left(b x + a\right)^{2} + b \sin\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, b \sin\left(3 \, b x + a + 2 \, c\right)^{2} + 4 \, b \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + b \sin\left(b x + a\right)^{2} + 2 \, {\left(2 \, b \cos\left(3 \, b x + a + 2 \, c\right) + b \cos\left(b x + a\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) + 2 \, {\left(2 \, b \sin\left(3 \, b x + a + 2 \, c\right) + b \sin\left(b x + a\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right)\right)}}"," ",0,"1/4*(2*(cos(5*b*x + a + 4*c) + 2*cos(3*b*x + a + 2*c) + cos(b*x + a))*cos(6*b*x + 2*a + 4*c) + 2*(5*cos(4*b*x + 2*a + 2*c) + 2*cos(4*b*x + 4*c) + 2*cos(2*b*x + 2*a) + 5*cos(2*b*x + 2*c) + 1)*cos(5*b*x + a + 4*c) + 10*(2*cos(3*b*x + a + 2*c) + cos(b*x + a))*cos(4*b*x + 2*a + 2*c) + 4*(2*cos(3*b*x + a + 2*c) + cos(b*x + a))*cos(4*b*x + 4*c) + 4*(2*cos(2*b*x + 2*a) + 5*cos(2*b*x + 2*c) + 1)*cos(3*b*x + a + 2*c) + 4*cos(2*b*x + 2*a)*cos(b*x + a) + 10*cos(2*b*x + 2*c)*cos(b*x + a) + 3*(cos(5*b*x + a + 4*c)^2*sin(-a + c) + 4*cos(3*b*x + a + 2*c)^2*sin(-a + c) + 4*cos(3*b*x + a + 2*c)*cos(b*x + a)*sin(-a + c) + cos(b*x + a)^2*sin(-a + c) + sin(5*b*x + a + 4*c)^2*sin(-a + c) + 4*sin(3*b*x + a + 2*c)^2*sin(-a + c) + 4*sin(3*b*x + a + 2*c)*sin(b*x + a)*sin(-a + c) + sin(b*x + a)^2*sin(-a + c) + 2*(2*cos(3*b*x + a + 2*c)*sin(-a + c) + cos(b*x + a)*sin(-a + c))*cos(5*b*x + a + 4*c) + 2*(2*sin(3*b*x + a + 2*c)*sin(-a + c) + sin(b*x + a)*sin(-a + c))*sin(5*b*x + a + 4*c))*log((cos(b*x + 2*c)^2 + cos(c)^2 - 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 + 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)/(cos(b*x + 2*c)^2 + cos(c)^2 + 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 - 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)) + 2*(sin(5*b*x + a + 4*c) + 2*sin(3*b*x + a + 2*c) + sin(b*x + a))*sin(6*b*x + 2*a + 4*c) + 2*(5*sin(4*b*x + 2*a + 2*c) + 2*sin(4*b*x + 4*c) + 2*sin(2*b*x + 2*a) + 5*sin(2*b*x + 2*c))*sin(5*b*x + a + 4*c) + 10*(2*sin(3*b*x + a + 2*c) + sin(b*x + a))*sin(4*b*x + 2*a + 2*c) + 4*(2*sin(3*b*x + a + 2*c) + sin(b*x + a))*sin(4*b*x + 4*c) + 4*(2*sin(2*b*x + 2*a) + 5*sin(2*b*x + 2*c))*sin(3*b*x + a + 2*c) + 4*sin(2*b*x + 2*a)*sin(b*x + a) + 10*sin(2*b*x + 2*c)*sin(b*x + a) + 2*cos(b*x + a))/(b*cos(5*b*x + a + 4*c)^2 + 4*b*cos(3*b*x + a + 2*c)^2 + 4*b*cos(3*b*x + a + 2*c)*cos(b*x + a) + b*cos(b*x + a)^2 + b*sin(5*b*x + a + 4*c)^2 + 4*b*sin(3*b*x + a + 2*c)^2 + 4*b*sin(3*b*x + a + 2*c)*sin(b*x + a) + b*sin(b*x + a)^2 + 2*(2*b*cos(3*b*x + a + 2*c) + b*cos(b*x + a))*cos(5*b*x + a + 4*c) + 2*(2*b*sin(3*b*x + a + 2*c) + b*sin(b*x + a))*sin(5*b*x + a + 4*c))","B",0
248,1,526,0,0.519567," ","integrate(cos(b*x+a)*tan(b*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(\sin\left(3 \, b x + a + 2 \, c\right) + \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 2 \, a + 2 \, c\right) - 3 \, {\left(\sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, c\right)\right)} \cos\left(3 \, b x + a + 2 \, c\right) - {\left(\cos\left(3 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) + 2 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \cos\left(-a + c\right) + \cos\left(b x + a\right)^{2} \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right)^{2} + 2 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + \cos\left(-a + c\right) \sin\left(b x + a\right)^{2}\right)} \log\left(\frac{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} - 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} - 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}\right) - {\left(\cos\left(3 \, b x + a + 2 \, c\right) + \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 2 \, a + 2 \, c\right) + {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) - 3 \, \cos\left(2 \, b x + 2 \, c\right) - 1\right)} \sin\left(3 \, b x + a + 2 \, c\right) - 3 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) + 3 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, c\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 3 \, \cos\left(2 \, b x + 2 \, c\right) \sin\left(b x + a\right) - \sin\left(b x + a\right)}{2 \, {\left(b \cos\left(3 \, b x + a + 2 \, c\right)^{2} + 2 \, b \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) + b \cos\left(b x + a\right)^{2} + b \sin\left(3 \, b x + a + 2 \, c\right)^{2} + 2 \, b \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + b \sin\left(b x + a\right)^{2}\right)}}"," ",0,"1/2*((sin(3*b*x + a + 2*c) + sin(b*x + a))*cos(4*b*x + 2*a + 2*c) - 3*(sin(2*b*x + 2*a) - sin(2*b*x + 2*c))*cos(3*b*x + a + 2*c) - (cos(3*b*x + a + 2*c)^2*cos(-a + c) + 2*cos(3*b*x + a + 2*c)*cos(b*x + a)*cos(-a + c) + cos(b*x + a)^2*cos(-a + c) + cos(-a + c)*sin(3*b*x + a + 2*c)^2 + 2*cos(-a + c)*sin(3*b*x + a + 2*c)*sin(b*x + a) + cos(-a + c)*sin(b*x + a)^2)*log((cos(b*x + 2*c)^2 + cos(c)^2 - 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 + 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)/(cos(b*x + 2*c)^2 + cos(c)^2 + 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 - 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)) - (cos(3*b*x + a + 2*c) + cos(b*x + a))*sin(4*b*x + 2*a + 2*c) + (3*cos(2*b*x + 2*a) - 3*cos(2*b*x + 2*c) - 1)*sin(3*b*x + a + 2*c) - 3*cos(b*x + a)*sin(2*b*x + 2*a) + 3*cos(b*x + a)*sin(2*b*x + 2*c) + 3*cos(2*b*x + 2*a)*sin(b*x + a) - 3*cos(2*b*x + 2*c)*sin(b*x + a) - sin(b*x + a))/(b*cos(3*b*x + a + 2*c)^2 + 2*b*cos(3*b*x + a + 2*c)*cos(b*x + a) + b*cos(b*x + a)^2 + b*sin(3*b*x + a + 2*c)^2 + 2*b*sin(3*b*x + a + 2*c)*sin(b*x + a) + b*sin(b*x + a)^2)","B",0
249,1,131,0,0.509882," ","integrate(cos(b*x+a)*tan(b*x+c),x, algorithm=""maxima"")","-\frac{\log\left(\frac{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} - 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} + 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}{\cos\left(b x + 2 \, c\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(b x + 2 \, c\right) + \sin\left(b x + 2 \, c\right)^{2} - 2 \, \cos\left(b x + 2 \, c\right) \sin\left(c\right) + \sin\left(c\right)^{2}}\right) \sin\left(-a + c\right) + 2 \, \cos\left(b x + a\right)}{2 \, b}"," ",0,"-1/2*(log((cos(b*x + 2*c)^2 + cos(c)^2 - 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 + 2*cos(b*x + 2*c)*sin(c) + sin(c)^2)/(cos(b*x + 2*c)^2 + cos(c)^2 + 2*cos(c)*sin(b*x + 2*c) + sin(b*x + 2*c)^2 - 2*cos(b*x + 2*c)*sin(c) + sin(c)^2))*sin(-a + c) + 2*cos(b*x + a))/b","B",0
250,1,105,0,0.345657," ","integrate(cos(b*x+a)*cot(b*x+c),x, algorithm=""maxima"")","-\frac{\cos\left(-a + c\right) \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - \cos\left(-a + c\right) \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - 2 \, \cos\left(b x + a\right)}{2 \, b}"," ",0,"-1/2*(cos(-a + c)*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) - cos(-a + c)*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2) - 2*cos(b*x + a))/b","B",0
251,1,613,0,0.359355," ","integrate(cos(b*x+a)*cot(b*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(\sin\left(3 \, b x + a + 2 \, c\right) - \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 2 \, a + 2 \, c\right) + 3 \, {\left(\sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, c\right)\right)} \cos\left(3 \, b x + a + 2 \, c\right) - {\left(\cos\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 2 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \sin\left(-a + c\right) + \cos\left(b x + a\right)^{2} \sin\left(-a + c\right) + \sin\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 2 \, \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) \sin\left(-a + c\right) + \sin\left(b x + a\right)^{2} \sin\left(-a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + {\left(\cos\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 2 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \sin\left(-a + c\right) + \cos\left(b x + a\right)^{2} \sin\left(-a + c\right) + \sin\left(3 \, b x + a + 2 \, c\right)^{2} \sin\left(-a + c\right) - 2 \, \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) \sin\left(-a + c\right) + \sin\left(b x + a\right)^{2} \sin\left(-a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - {\left(\cos\left(3 \, b x + a + 2 \, c\right) - \cos\left(b x + a\right)\right)} \sin\left(4 \, b x + 2 \, a + 2 \, c\right) - {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, c\right) - 1\right)} \sin\left(3 \, b x + a + 2 \, c\right) - 3 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 3 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, c\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 3 \, \cos\left(2 \, b x + 2 \, c\right) \sin\left(b x + a\right) - \sin\left(b x + a\right)}{2 \, {\left(b \cos\left(3 \, b x + a + 2 \, c\right)^{2} - 2 \, b \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) + b \cos\left(b x + a\right)^{2} + b \sin\left(3 \, b x + a + 2 \, c\right)^{2} - 2 \, b \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + b \sin\left(b x + a\right)^{2}\right)}}"," ",0,"1/2*((sin(3*b*x + a + 2*c) - sin(b*x + a))*cos(4*b*x + 2*a + 2*c) + 3*(sin(2*b*x + 2*a) + sin(2*b*x + 2*c))*cos(3*b*x + a + 2*c) - (cos(3*b*x + a + 2*c)^2*sin(-a + c) - 2*cos(3*b*x + a + 2*c)*cos(b*x + a)*sin(-a + c) + cos(b*x + a)^2*sin(-a + c) + sin(3*b*x + a + 2*c)^2*sin(-a + c) - 2*sin(3*b*x + a + 2*c)*sin(b*x + a)*sin(-a + c) + sin(b*x + a)^2*sin(-a + c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) + (cos(3*b*x + a + 2*c)^2*sin(-a + c) - 2*cos(3*b*x + a + 2*c)*cos(b*x + a)*sin(-a + c) + cos(b*x + a)^2*sin(-a + c) + sin(3*b*x + a + 2*c)^2*sin(-a + c) - 2*sin(3*b*x + a + 2*c)*sin(b*x + a)*sin(-a + c) + sin(b*x + a)^2*sin(-a + c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2) - (cos(3*b*x + a + 2*c) - cos(b*x + a))*sin(4*b*x + 2*a + 2*c) - (3*cos(2*b*x + 2*a) + 3*cos(2*b*x + 2*c) - 1)*sin(3*b*x + a + 2*c) - 3*cos(b*x + a)*sin(2*b*x + 2*a) - 3*cos(b*x + a)*sin(2*b*x + 2*c) + 3*cos(2*b*x + 2*a)*sin(b*x + a) + 3*cos(2*b*x + 2*c)*sin(b*x + a) - sin(b*x + a))/(b*cos(3*b*x + a + 2*c)^2 - 2*b*cos(3*b*x + a + 2*c)*cos(b*x + a) + b*cos(b*x + a)^2 + b*sin(3*b*x + a + 2*c)^2 - 2*b*sin(3*b*x + a + 2*c)*sin(b*x + a) + b*sin(b*x + a)^2)","B",0
252,1,1254,0,0.403928," ","integrate(cos(b*x+a)*cot(b*x+c)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(5 \, b x + a + 4 \, c\right) - 2 \, \cos\left(3 \, b x + a + 2 \, c\right) + \cos\left(b x + a\right)\right)} \cos\left(6 \, b x + 2 \, a + 4 \, c\right) - 2 \, {\left(5 \, \cos\left(4 \, b x + 2 \, a + 2 \, c\right) - 2 \, \cos\left(4 \, b x + 4 \, c\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 5 \, \cos\left(2 \, b x + 2 \, c\right) - 1\right)} \cos\left(5 \, b x + a + 4 \, c\right) + 10 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) - \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 2 \, a + 2 \, c\right) - 4 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) - \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, c\right) - 4 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 5 \, \cos\left(2 \, b x + 2 \, c\right) + 1\right)} \cos\left(3 \, b x + a + 2 \, c\right) + 4 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) - 10 \, \cos\left(2 \, b x + 2 \, c\right) \cos\left(b x + a\right) - 3 \, {\left(\cos\left(5 \, b x + a + 4 \, c\right)^{2} \cos\left(-a + c\right) + 4 \, \cos\left(3 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) - 4 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \cos\left(-a + c\right) + \cos\left(b x + a\right)^{2} \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right)^{2} - 4 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + \cos\left(-a + c\right) \sin\left(b x + a\right)^{2} - 2 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) - \cos\left(b x + a\right) \cos\left(-a + c\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) - 2 \, {\left(2 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right) - \cos\left(-a + c\right) \sin\left(b x + a\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + 3 \, {\left(\cos\left(5 \, b x + a + 4 \, c\right)^{2} \cos\left(-a + c\right) + 4 \, \cos\left(3 \, b x + a + 2 \, c\right)^{2} \cos\left(-a + c\right) - 4 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) \cos\left(-a + c\right) + \cos\left(b x + a\right)^{2} \cos\left(-a + c\right) + \cos\left(-a + c\right) \sin\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right)^{2} - 4 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + \cos\left(-a + c\right) \sin\left(b x + a\right)^{2} - 2 \, {\left(2 \, \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(-a + c\right) - \cos\left(b x + a\right) \cos\left(-a + c\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) - 2 \, {\left(2 \, \cos\left(-a + c\right) \sin\left(3 \, b x + a + 2 \, c\right) - \cos\left(-a + c\right) \sin\left(b x + a\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + 2 \, {\left(\sin\left(5 \, b x + a + 4 \, c\right) - 2 \, \sin\left(3 \, b x + a + 2 \, c\right) + \sin\left(b x + a\right)\right)} \sin\left(6 \, b x + 2 \, a + 4 \, c\right) - 2 \, {\left(5 \, \sin\left(4 \, b x + 2 \, a + 2 \, c\right) - 2 \, \sin\left(4 \, b x + 4 \, c\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right) + 5 \, \sin\left(2 \, b x + 2 \, c\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right) + 10 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) - \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 2 \, a + 2 \, c\right) - 4 \, {\left(2 \, \sin\left(3 \, b x + a + 2 \, c\right) - \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, c\right) - 4 \, {\left(2 \, \sin\left(2 \, b x + 2 \, a\right) - 5 \, \sin\left(2 \, b x + 2 \, c\right)\right)} \sin\left(3 \, b x + a + 2 \, c\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) - 10 \, \sin\left(2 \, b x + 2 \, c\right) \sin\left(b x + a\right) + 2 \, \cos\left(b x + a\right)}{4 \, {\left(b \cos\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, b \cos\left(3 \, b x + a + 2 \, c\right)^{2} - 4 \, b \cos\left(3 \, b x + a + 2 \, c\right) \cos\left(b x + a\right) + b \cos\left(b x + a\right)^{2} + b \sin\left(5 \, b x + a + 4 \, c\right)^{2} + 4 \, b \sin\left(3 \, b x + a + 2 \, c\right)^{2} - 4 \, b \sin\left(3 \, b x + a + 2 \, c\right) \sin\left(b x + a\right) + b \sin\left(b x + a\right)^{2} - 2 \, {\left(2 \, b \cos\left(3 \, b x + a + 2 \, c\right) - b \cos\left(b x + a\right)\right)} \cos\left(5 \, b x + a + 4 \, c\right) - 2 \, {\left(2 \, b \sin\left(3 \, b x + a + 2 \, c\right) - b \sin\left(b x + a\right)\right)} \sin\left(5 \, b x + a + 4 \, c\right)\right)}}"," ",0,"-1/4*(2*(cos(5*b*x + a + 4*c) - 2*cos(3*b*x + a + 2*c) + cos(b*x + a))*cos(6*b*x + 2*a + 4*c) - 2*(5*cos(4*b*x + 2*a + 2*c) - 2*cos(4*b*x + 4*c) - 2*cos(2*b*x + 2*a) + 5*cos(2*b*x + 2*c) - 1)*cos(5*b*x + a + 4*c) + 10*(2*cos(3*b*x + a + 2*c) - cos(b*x + a))*cos(4*b*x + 2*a + 2*c) - 4*(2*cos(3*b*x + a + 2*c) - cos(b*x + a))*cos(4*b*x + 4*c) - 4*(2*cos(2*b*x + 2*a) - 5*cos(2*b*x + 2*c) + 1)*cos(3*b*x + a + 2*c) + 4*cos(2*b*x + 2*a)*cos(b*x + a) - 10*cos(2*b*x + 2*c)*cos(b*x + a) - 3*(cos(5*b*x + a + 4*c)^2*cos(-a + c) + 4*cos(3*b*x + a + 2*c)^2*cos(-a + c) - 4*cos(3*b*x + a + 2*c)*cos(b*x + a)*cos(-a + c) + cos(b*x + a)^2*cos(-a + c) + cos(-a + c)*sin(5*b*x + a + 4*c)^2 + 4*cos(-a + c)*sin(3*b*x + a + 2*c)^2 - 4*cos(-a + c)*sin(3*b*x + a + 2*c)*sin(b*x + a) + cos(-a + c)*sin(b*x + a)^2 - 2*(2*cos(3*b*x + a + 2*c)*cos(-a + c) - cos(b*x + a)*cos(-a + c))*cos(5*b*x + a + 4*c) - 2*(2*cos(-a + c)*sin(3*b*x + a + 2*c) - cos(-a + c)*sin(b*x + a))*sin(5*b*x + a + 4*c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) + 3*(cos(5*b*x + a + 4*c)^2*cos(-a + c) + 4*cos(3*b*x + a + 2*c)^2*cos(-a + c) - 4*cos(3*b*x + a + 2*c)*cos(b*x + a)*cos(-a + c) + cos(b*x + a)^2*cos(-a + c) + cos(-a + c)*sin(5*b*x + a + 4*c)^2 + 4*cos(-a + c)*sin(3*b*x + a + 2*c)^2 - 4*cos(-a + c)*sin(3*b*x + a + 2*c)*sin(b*x + a) + cos(-a + c)*sin(b*x + a)^2 - 2*(2*cos(3*b*x + a + 2*c)*cos(-a + c) - cos(b*x + a)*cos(-a + c))*cos(5*b*x + a + 4*c) - 2*(2*cos(-a + c)*sin(3*b*x + a + 2*c) - cos(-a + c)*sin(b*x + a))*sin(5*b*x + a + 4*c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2) + 2*(sin(5*b*x + a + 4*c) - 2*sin(3*b*x + a + 2*c) + sin(b*x + a))*sin(6*b*x + 2*a + 4*c) - 2*(5*sin(4*b*x + 2*a + 2*c) - 2*sin(4*b*x + 4*c) - 2*sin(2*b*x + 2*a) + 5*sin(2*b*x + 2*c))*sin(5*b*x + a + 4*c) + 10*(2*sin(3*b*x + a + 2*c) - sin(b*x + a))*sin(4*b*x + 2*a + 2*c) - 4*(2*sin(3*b*x + a + 2*c) - sin(b*x + a))*sin(4*b*x + 4*c) - 4*(2*sin(2*b*x + 2*a) - 5*sin(2*b*x + 2*c))*sin(3*b*x + a + 2*c) + 4*sin(2*b*x + 2*a)*sin(b*x + a) - 10*sin(2*b*x + 2*c)*sin(b*x + a) + 2*cos(b*x + a))/(b*cos(5*b*x + a + 4*c)^2 + 4*b*cos(3*b*x + a + 2*c)^2 - 4*b*cos(3*b*x + a + 2*c)*cos(b*x + a) + b*cos(b*x + a)^2 + b*sin(5*b*x + a + 4*c)^2 + 4*b*sin(3*b*x + a + 2*c)^2 - 4*b*sin(3*b*x + a + 2*c)*sin(b*x + a) + b*sin(b*x + a)^2 - 2*(2*b*cos(3*b*x + a + 2*c) - b*cos(b*x + a))*cos(5*b*x + a + 4*c) - 2*(2*b*sin(3*b*x + a + 2*c) - b*sin(b*x + a))*sin(5*b*x + a + 4*c))","B",0
253,0,0,0,0.000000," ","integrate(cos(b*x+a)*tan(d*x+c),x, algorithm=""maxima"")","\int \cos\left(b x + a\right) \tan\left(d x + c\right)\,{d x}"," ",0,"integrate(cos(b*x + a)*tan(d*x + c), x)","F",0
254,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(d*x+c),x, algorithm=""maxima"")","\int \cos\left(b x + a\right) \cot\left(d x + c\right)\,{d x}"," ",0,"integrate(cos(b*x + a)*cot(d*x + c), x)","F",0
