1,0,0,131,0.353000," ","int((d*x+c)^m*cos(b*x+a)*sin(b*x+a),x)","\int \left(d x +c \right)^{m} \cos \left(b x +a \right) \sin \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)*sin(b*x+a),x)","F"
2,1,853,142,0.056000," ","int((d*x+c)^4*cos(b*x+a)*sin(b*x+a),x)","\frac{\frac{d^{4} \left(-\frac{\left(b x +a \right)^{4} \left(\cos^{2}\left(b x +a \right)\right)}{2}+2 \left(b x +a \right)^{3} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{3 \left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{2}-3 \left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{3 \left(b x +a \right)^{2}}{4}+\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{4}-\frac{3 \left(b x +a \right)^{4}}{4}\right)}{b^{4}}-\frac{4 a \,d^{4} \left(-\frac{\left(b x +a \right)^{3} \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{3 \left(b x +a \right)^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{2}+\frac{3 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{4}-\frac{3 \cos \left(b x +a \right) \sin \left(b x +a \right)}{8}-\frac{3 b x}{8}-\frac{3 a}{8}-\frac{\left(b x +a \right)^{3}}{2}\right)}{b^{4}}+\frac{4 c \,d^{3} \left(-\frac{\left(b x +a \right)^{3} \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{3 \left(b x +a \right)^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{2}+\frac{3 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{4}-\frac{3 \cos \left(b x +a \right) \sin \left(b x +a \right)}{8}-\frac{3 b x}{8}-\frac{3 a}{8}-\frac{\left(b x +a \right)^{3}}{2}\right)}{b^{3}}+\frac{6 a^{2} d^{4} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{2}+\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b^{4}}-\frac{12 a c \,d^{3} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{2}+\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{2}+\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b^{2}}-\frac{4 a^{3} d^{4} \left(-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{b x}{4}+\frac{a}{4}\right)}{b^{4}}+\frac{12 a^{2} c \,d^{3} \left(-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{b x}{4}+\frac{a}{4}\right)}{b^{3}}-\frac{12 a \,c^{2} d^{2} \left(-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{b x}{4}+\frac{a}{4}\right)}{b^{2}}+\frac{4 c^{3} d \left(-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{b x}{4}+\frac{a}{4}\right)}{b}-\frac{a^{4} d^{4} \left(\cos^{2}\left(b x +a \right)\right)}{2 b^{4}}+\frac{2 a^{3} c \,d^{3} \left(\cos^{2}\left(b x +a \right)\right)}{b^{3}}-\frac{3 a^{2} c^{2} d^{2} \left(\cos^{2}\left(b x +a \right)\right)}{b^{2}}+\frac{2 a \,c^{3} d \left(\cos^{2}\left(b x +a \right)\right)}{b}-\frac{c^{4} \left(\cos^{2}\left(b x +a \right)\right)}{2}}{b}"," ",0,"1/b*(1/b^4*d^4*(-1/2*(b*x+a)^4*cos(b*x+a)^2+2*(b*x+a)^3*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/2*(b*x+a)^2*cos(b*x+a)^2-3*(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/4*(b*x+a)^2+3/4*sin(b*x+a)^2-3/4*(b*x+a)^4)-4/b^4*a*d^4*(-1/2*(b*x+a)^3*cos(b*x+a)^2+3/2*(b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/4*(b*x+a)*cos(b*x+a)^2-3/8*cos(b*x+a)*sin(b*x+a)-3/8*b*x-3/8*a-1/2*(b*x+a)^3)+4/b^3*c*d^3*(-1/2*(b*x+a)^3*cos(b*x+a)^2+3/2*(b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/4*(b*x+a)*cos(b*x+a)^2-3/8*cos(b*x+a)*sin(b*x+a)-3/8*b*x-3/8*a-1/2*(b*x+a)^3)+6/b^4*a^2*d^4*(-1/2*(b*x+a)^2*cos(b*x+a)^2+(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)-12/b^3*a*c*d^3*(-1/2*(b*x+a)^2*cos(b*x+a)^2+(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+6/b^2*c^2*d^2*(-1/2*(b*x+a)^2*cos(b*x+a)^2+(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)-4/b^4*a^3*d^4*(-1/2*(b*x+a)*cos(b*x+a)^2+1/4*cos(b*x+a)*sin(b*x+a)+1/4*b*x+1/4*a)+12/b^3*a^2*c*d^3*(-1/2*(b*x+a)*cos(b*x+a)^2+1/4*cos(b*x+a)*sin(b*x+a)+1/4*b*x+1/4*a)-12/b^2*a*c^2*d^2*(-1/2*(b*x+a)*cos(b*x+a)^2+1/4*cos(b*x+a)*sin(b*x+a)+1/4*b*x+1/4*a)+4/b*c^3*d*(-1/2*(b*x+a)*cos(b*x+a)^2+1/4*cos(b*x+a)*sin(b*x+a)+1/4*b*x+1/4*a)-1/2/b^4*a^4*d^4*cos(b*x+a)^2+2/b^3*a^3*c*d^3*cos(b*x+a)^2-3/b^2*a^2*c^2*d^2*cos(b*x+a)^2+2/b*a*c^3*d*cos(b*x+a)^2-1/2*c^4*cos(b*x+a)^2)","B"
3,1,466,108,0.009000," ","int((d*x+c)^3*cos(b*x+a)*sin(b*x+a),x)","\frac{\frac{d^{3} \left(-\frac{\left(b x +a \right)^{3} \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{3 \left(b x +a \right)^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{2}+\frac{3 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{4}-\frac{3 \cos \left(b x +a \right) \sin \left(b x +a \right)}{8}-\frac{3 b x}{8}-\frac{3 a}{8}-\frac{\left(b x +a \right)^{3}}{2}\right)}{b^{3}}-\frac{3 a \,d^{3} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{2}+\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b^{3}}+\frac{3 c \,d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{2}+\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{b x}{4}+\frac{a}{4}\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{b x}{4}+\frac{a}{4}\right)}{b^{2}}+\frac{3 c^{2} d \left(-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{b x}{4}+\frac{a}{4}\right)}{b}+\frac{a^{3} d^{3} \left(\cos^{2}\left(b x +a \right)\right)}{2 b^{3}}-\frac{3 a^{2} c \,d^{2} \left(\cos^{2}\left(b x +a \right)\right)}{2 b^{2}}+\frac{3 a \,c^{2} d \left(\cos^{2}\left(b x +a \right)\right)}{2 b}-\frac{c^{3} \left(\cos^{2}\left(b x +a \right)\right)}{2}}{b}"," ",0,"1/b*(1/b^3*d^3*(-1/2*(b*x+a)^3*cos(b*x+a)^2+3/2*(b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/4*(b*x+a)*cos(b*x+a)^2-3/8*cos(b*x+a)*sin(b*x+a)-3/8*b*x-3/8*a-1/2*(b*x+a)^3)-3/b^3*a*d^3*(-1/2*(b*x+a)^2*cos(b*x+a)^2+(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+3/b^2*c*d^2*(-1/2*(b*x+a)^2*cos(b*x+a)^2+(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+3/b^3*a^2*d^3*(-1/2*(b*x+a)*cos(b*x+a)^2+1/4*cos(b*x+a)*sin(b*x+a)+1/4*b*x+1/4*a)-6/b^2*a*c*d^2*(-1/2*(b*x+a)*cos(b*x+a)^2+1/4*cos(b*x+a)*sin(b*x+a)+1/4*b*x+1/4*a)+3/b*c^2*d*(-1/2*(b*x+a)*cos(b*x+a)^2+1/4*cos(b*x+a)*sin(b*x+a)+1/4*b*x+1/4*a)+1/2/b^3*a^3*d^3*cos(b*x+a)^2-3/2/b^2*a^2*c*d^2*cos(b*x+a)^2+3/2/b*a*c^2*d*cos(b*x+a)^2-1/2*c^3*cos(b*x+a)^2)","B"
4,1,215,79,0.007000," ","int((d*x+c)^2*cos(b*x+a)*sin(b*x+a),x)","\frac{\frac{d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{2}+\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b^{2}}-\frac{2 a \,d^{2} \left(-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{b x}{4}+\frac{a}{4}\right)}{b^{2}}+\frac{2 c d \left(-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{b x}{4}+\frac{a}{4}\right)}{b}-\frac{a^{2} d^{2} \left(\cos^{2}\left(b x +a \right)\right)}{2 b^{2}}+\frac{a c d \left(\cos^{2}\left(b x +a \right)\right)}{b}-\frac{c^{2} \left(\cos^{2}\left(b x +a \right)\right)}{2}}{b}"," ",0,"1/b*(1/b^2*d^2*(-1/2*(b*x+a)^2*cos(b*x+a)^2+(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)-2/b^2*a*d^2*(-1/2*(b*x+a)*cos(b*x+a)^2+1/4*cos(b*x+a)*sin(b*x+a)+1/4*b*x+1/4*a)+2/b*c*d*(-1/2*(b*x+a)*cos(b*x+a)^2+1/4*cos(b*x+a)*sin(b*x+a)+1/4*b*x+1/4*a)-1/2/b^2*a^2*d^2*cos(b*x+a)^2+1/b*a*c*d*cos(b*x+a)^2-1/2*c^2*cos(b*x+a)^2)","B"
5,1,74,44,0.007000," ","int((d*x+c)*cos(b*x+a)*sin(b*x+a),x)","\frac{\frac{d \left(-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{b x}{4}+\frac{a}{4}\right)}{b}+\frac{d a \left(\cos^{2}\left(b x +a \right)\right)}{2 b}-\frac{c \left(\cos^{2}\left(b x +a \right)\right)}{2}}{b}"," ",0,"1/b*(1/b*d*(-1/2*(b*x+a)*cos(b*x+a)^2+1/4*cos(b*x+a)*sin(b*x+a)+1/4*b*x+1/4*a)+1/2/b*d*a*cos(b*x+a)^2-1/2*c*cos(b*x+a)^2)","A"
6,1,84,61,0.017000," ","int(cos(b*x+a)*sin(b*x+a)/(d*x+c),x)","\frac{\Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{2 d}-\frac{\Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{2 d}"," ",0,"1/2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-1/2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d","A"
7,1,124,83,0.010000," ","int(cos(b*x+a)*sin(b*x+a)/(d*x+c)^2,x)","\frac{b \left(-\frac{2 \sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{4 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{4 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}}{d}\right)}{4}"," ",0,"1/4*b*(-2*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d+2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d)/d)","A"
8,1,162,110,0.012000," ","int(cos(b*x+a)*sin(b*x+a)/(d*x+c)^3,x)","\frac{b^{2} \left(-\frac{\sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{2 \cos \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{2 \left(\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}-\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}\right)}{d}}{d}\right)}{4}"," ",0,"1/4*b^2*(-sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d+(-2*cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d-2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d)/d)/d)","A"
9,1,200,134,0.010000," ","int(cos(b*x+a)*sin(b*x+a)/(d*x+c)^4,x)","\frac{b^{3} \left(-\frac{2 \sin \left(2 b x +2 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{2 \cos \left(2 b x +2 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{2 \left(-\frac{2 \sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{4 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{4 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}}{d}\right)}{3 d}}{d}\right)}{4}"," ",0,"1/4*b^3*(-2/3*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^3/d+2/3*(-cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d-(-2*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d+2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d)/d)/d)/d)","A"
10,1,7,6,0.022000," ","int(cos(x)*sin(x)/x,x)","\frac{\Si \left(2 x \right)}{2}"," ",0,"1/2*Si(2*x)","A"
11,1,15,14,0.018000," ","int(cos(x)*sin(x)/x^2,x)","\Ci \left(2 x \right)-\frac{\sin \left(2 x \right)}{2 x}"," ",0,"Ci(2*x)-1/2*sin(2*x)/x","A"
12,1,26,25,0.017000," ","int(cos(x)*sin(x)/x^3,x)","-\frac{\cos \left(2 x \right)}{2 x}-\Si \left(2 x \right)-\frac{\sin \left(2 x \right)}{4 x^{2}}"," ",0,"-1/2*cos(2*x)/x-Si(2*x)-1/4*sin(2*x)/x^2","A"
13,0,0,251,0.348000," ","int((d*x+c)^m*cos(b*x+a)*sin(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \cos \left(b x +a \right) \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)*sin(b*x+a)^2,x)","F"
14,1,835,187,0.091000," ","int((d*x+c)^4*cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\frac{d^{4} \left(\frac{\left(b x +a \right)^{4} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{4 \left(b x +a \right)^{3} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{8 \left(b x +a \right)^{2} \sin \left(b x +a \right)}{3}+\frac{160 \sin \left(b x +a \right)}{27}-\frac{16 \left(b x +a \right) \cos \left(b x +a \right)}{3}-\frac{4 \left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{9}-\frac{8 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{27}+\frac{8 \left(\sin^{3}\left(b x +a \right)\right)}{81}\right)}{b^{4}}-\frac{4 a \,d^{4} \left(\frac{\left(b x +a \right)^{3} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}-\frac{4 \cos \left(b x +a \right)}{3}-\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{3}-\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{9}-\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{27}\right)}{b^{4}}+\frac{4 c \,d^{3} \left(\frac{\left(b x +a \right)^{3} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}-\frac{4 \cos \left(b x +a \right)}{3}-\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{3}-\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{9}-\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{27}\right)}{b^{3}}+\frac{6 a^{2} d^{4} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{27}-\frac{4 \sin \left(b x +a \right)}{9}\right)}{b^{4}}-\frac{12 a c \,d^{3} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{27}-\frac{4 \sin \left(b x +a \right)}{9}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{27}-\frac{4 \sin \left(b x +a \right)}{9}\right)}{b^{2}}-\frac{4 a^{3} d^{4} \left(\frac{\left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}\right)}{b^{4}}+\frac{12 a^{2} c \,d^{3} \left(\frac{\left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}\right)}{b^{3}}-\frac{12 a \,c^{2} d^{2} \left(\frac{\left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}\right)}{b^{2}}+\frac{4 c^{3} d \left(\frac{\left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}\right)}{b}+\frac{a^{4} d^{4} \left(\sin^{3}\left(b x +a \right)\right)}{3 b^{4}}-\frac{4 a^{3} c \,d^{3} \left(\sin^{3}\left(b x +a \right)\right)}{3 b^{3}}+\frac{2 a^{2} c^{2} d^{2} \left(\sin^{3}\left(b x +a \right)\right)}{b^{2}}-\frac{4 a \,c^{3} d \left(\sin^{3}\left(b x +a \right)\right)}{3 b}+\frac{c^{4} \left(\sin^{3}\left(b x +a \right)\right)}{3}}{b}"," ",0,"1/b*(1/b^4*d^4*(1/3*(b*x+a)^4*sin(b*x+a)^3+4/9*(b*x+a)^3*(2+sin(b*x+a)^2)*cos(b*x+a)-8/3*(b*x+a)^2*sin(b*x+a)+160/27*sin(b*x+a)-16/3*(b*x+a)*cos(b*x+a)-4/9*(b*x+a)^2*sin(b*x+a)^3-8/27*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+8/81*sin(b*x+a)^3)-4/b^4*a*d^4*(1/3*(b*x+a)^3*sin(b*x+a)^3+1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)-4/3*cos(b*x+a)-4/3*(b*x+a)*sin(b*x+a)-2/9*(b*x+a)*sin(b*x+a)^3-2/27*(2+sin(b*x+a)^2)*cos(b*x+a))+4/b^3*c*d^3*(1/3*(b*x+a)^3*sin(b*x+a)^3+1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)-4/3*cos(b*x+a)-4/3*(b*x+a)*sin(b*x+a)-2/9*(b*x+a)*sin(b*x+a)^3-2/27*(2+sin(b*x+a)^2)*cos(b*x+a))+6/b^4*a^2*d^4*(1/3*(b*x+a)^2*sin(b*x+a)^3+2/9*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)-2/27*sin(b*x+a)^3-4/9*sin(b*x+a))-12/b^3*a*c*d^3*(1/3*(b*x+a)^2*sin(b*x+a)^3+2/9*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)-2/27*sin(b*x+a)^3-4/9*sin(b*x+a))+6/b^2*c^2*d^2*(1/3*(b*x+a)^2*sin(b*x+a)^3+2/9*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)-2/27*sin(b*x+a)^3-4/9*sin(b*x+a))-4/b^4*a^3*d^4*(1/3*(b*x+a)*sin(b*x+a)^3+1/9*(2+sin(b*x+a)^2)*cos(b*x+a))+12/b^3*a^2*c*d^3*(1/3*(b*x+a)*sin(b*x+a)^3+1/9*(2+sin(b*x+a)^2)*cos(b*x+a))-12/b^2*a*c^2*d^2*(1/3*(b*x+a)*sin(b*x+a)^3+1/9*(2+sin(b*x+a)^2)*cos(b*x+a))+4/b*c^3*d*(1/3*(b*x+a)*sin(b*x+a)^3+1/9*(2+sin(b*x+a)^2)*cos(b*x+a))+1/3/b^4*a^4*d^4*sin(b*x+a)^3-4/3/b^3*a^3*c*d^3*sin(b*x+a)^3+2/b^2*a^2*c^2*d^2*sin(b*x+a)^3-4/3/b*a*c^3*d*sin(b*x+a)^3+1/3*c^4*sin(b*x+a)^3)","B"
15,1,447,137,0.011000," ","int((d*x+c)^3*cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\frac{d^{3} \left(\frac{\left(b x +a \right)^{3} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}-\frac{4 \cos \left(b x +a \right)}{3}-\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{3}-\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{9}-\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{27}\right)}{b^{3}}-\frac{3 a \,d^{3} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{27}-\frac{4 \sin \left(b x +a \right)}{9}\right)}{b^{3}}+\frac{3 c \,d^{2} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{27}-\frac{4 \sin \left(b x +a \right)}{9}\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(\frac{\left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(\frac{\left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}\right)}{b^{2}}+\frac{3 c^{2} d \left(\frac{\left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}\right)}{b}-\frac{a^{3} d^{3} \left(\sin^{3}\left(b x +a \right)\right)}{3 b^{3}}+\frac{a^{2} c \,d^{2} \left(\sin^{3}\left(b x +a \right)\right)}{b^{2}}-\frac{a \,c^{2} d \left(\sin^{3}\left(b x +a \right)\right)}{b}+\frac{c^{3} \left(\sin^{3}\left(b x +a \right)\right)}{3}}{b}"," ",0,"1/b*(1/b^3*d^3*(1/3*(b*x+a)^3*sin(b*x+a)^3+1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)-4/3*cos(b*x+a)-4/3*(b*x+a)*sin(b*x+a)-2/9*(b*x+a)*sin(b*x+a)^3-2/27*(2+sin(b*x+a)^2)*cos(b*x+a))-3/b^3*a*d^3*(1/3*(b*x+a)^2*sin(b*x+a)^3+2/9*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)-2/27*sin(b*x+a)^3-4/9*sin(b*x+a))+3/b^2*c*d^2*(1/3*(b*x+a)^2*sin(b*x+a)^3+2/9*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)-2/27*sin(b*x+a)^3-4/9*sin(b*x+a))+3/b^3*a^2*d^3*(1/3*(b*x+a)*sin(b*x+a)^3+1/9*(2+sin(b*x+a)^2)*cos(b*x+a))-6/b^2*a*c*d^2*(1/3*(b*x+a)*sin(b*x+a)^3+1/9*(2+sin(b*x+a)^2)*cos(b*x+a))+3/b*c^2*d*(1/3*(b*x+a)*sin(b*x+a)^3+1/9*(2+sin(b*x+a)^2)*cos(b*x+a))-1/3/b^3*a^3*d^3*sin(b*x+a)^3+1/b^2*a^2*c*d^2*sin(b*x+a)^3-1/b*a*c^2*d*sin(b*x+a)^3+1/3*c^3*sin(b*x+a)^3)","B"
16,1,204,93,0.010000," ","int((d*x+c)^2*cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\frac{d^{2} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{27}-\frac{4 \sin \left(b x +a \right)}{9}\right)}{b^{2}}-\frac{2 a \,d^{2} \left(\frac{\left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}\right)}{b^{2}}+\frac{2 c d \left(\frac{\left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}\right)}{b}+\frac{a^{2} d^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3 b^{2}}-\frac{2 a c d \left(\sin^{3}\left(b x +a \right)\right)}{3 b}+\frac{c^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3}}{b}"," ",0,"1/b*(1/b^2*d^2*(1/3*(b*x+a)^2*sin(b*x+a)^3+2/9*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)-2/27*sin(b*x+a)^3-4/9*sin(b*x+a))-2/b^2*a*d^2*(1/3*(b*x+a)*sin(b*x+a)^3+1/9*(2+sin(b*x+a)^2)*cos(b*x+a))+2/b*c*d*(1/3*(b*x+a)*sin(b*x+a)^3+1/9*(2+sin(b*x+a)^2)*cos(b*x+a))+1/3/b^2*a^2*d^2*sin(b*x+a)^3-2/3/b*a*c*d*sin(b*x+a)^3+1/3*c^2*sin(b*x+a)^3)","B"
17,1,71,45,0.009000," ","int((d*x+c)*cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\frac{d \left(\frac{\left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}\right)}{b}-\frac{d a \left(\sin^{3}\left(b x +a \right)\right)}{3 b}+\frac{c \left(\sin^{3}\left(b x +a \right)\right)}{3}}{b}"," ",0,"1/b*(1/b*d*(1/3*(b*x+a)*sin(b*x+a)^3+1/9*(2+sin(b*x+a)^2)*cos(b*x+a))-1/3/b*d*a*sin(b*x+a)^3+1/3*c*sin(b*x+a)^3)","A"
18,1,166,113,0.012000," ","int(cos(b*x+a)*sin(b*x+a)^2/(d*x+c),x)","\frac{\frac{b \left(\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}+\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}\right)}{4}-\frac{b \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}+\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{12}}{b}"," ",0,"1/b*(1/4*b*(Si(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)-1/12*b*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d+3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d))","A"
19,1,242,156,0.013000," ","int(cos(b*x+a)*sin(b*x+a)^2/(d*x+c)^2,x)","\frac{\frac{b^{2} \left(-\frac{\cos \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}}{d}\right)}{4}-\frac{b^{2} \left(-\frac{3 \cos \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{3 \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}-\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{d}\right)}{12}}{b}"," ",0,"1/b*(1/4*b^2*(-cos(b*x+a)/((b*x+a)*d-d*a+c*b)/d-(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d)/d)-1/12*b^2*(-3*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d-3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d-3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d)/d))","A"
20,1,311,205,0.015000," ","int(cos(b*x+a)*sin(b*x+a)^2/(d*x+c)^3,x)","\frac{\frac{b^{3} \left(-\frac{\cos \left(b x +a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{-\frac{\sin \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}+\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}}{d}}{2 d}\right)}{4}-\frac{b^{3} \left(-\frac{3 \cos \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{3 \left(-\frac{3 \sin \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{9 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}+\frac{9 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}}{d}\right)}{2 d}\right)}{12}}{b}"," ",0,"1/b*(1/4*b^3*(-1/2*cos(b*x+a)/((b*x+a)*d-d*a+c*b)^2/d-1/2*(-sin(b*x+a)/((b*x+a)*d-d*a+c*b)/d+(Si(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)/d)/d)-1/12*b^3*(-3/2*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^2/d-3/2*(-3*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d+3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d+3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d)/d)/d))","A"
21,1,384,250,0.012000," ","int(cos(b*x+a)*sin(b*x+a)^2/(d*x+c)^4,x)","\frac{\frac{b^{4} \left(-\frac{\cos \left(b x +a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}-\frac{-\frac{\sin \left(b x +a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{\cos \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}}{d}}{2 d}}{3 d}\right)}{4}-\frac{b^{4} \left(-\frac{\cos \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{3} d}-\frac{-\frac{3 \sin \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{9 \cos \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right) d}-\frac{9 \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}-\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{2 d}}{d}}{d}\right)}{12}}{b}"," ",0,"1/b*(1/4*b^4*(-1/3*cos(b*x+a)/((b*x+a)*d-d*a+c*b)^3/d-1/3*(-1/2*sin(b*x+a)/((b*x+a)*d-d*a+c*b)^2/d+1/2*(-cos(b*x+a)/((b*x+a)*d-d*a+c*b)/d-(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d)/d)/d)/d)-1/12*b^4*(-cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^3/d-(-3/2*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^2/d+3/2*(-3*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d-3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d-3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d)/d)/d)/d))","A"
22,0,0,263,0.241000," ","int((d*x+c)^m*cos(b*x+a)*sin(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \cos \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)*sin(b*x+a)^3,x)","F"
23,1,1143,236,0.120000," ","int((d*x+c)^4*cos(b*x+a)*sin(b*x+a)^3,x)","\frac{\frac{d^{4} \left(\frac{\left(b x +a \right)^{4} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\left(b x +a \right)^{3} \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{3 \left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{16}+\frac{3 \left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{8}+\frac{27 \left(b x +a \right)^{2}}{128}+\frac{3 \left(\sin^{4}\left(b x +a \right)\right)}{128}+\frac{45 \left(\sin^{2}\left(b x +a \right)\right)}{128}+\frac{9 \left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{16}-\frac{9 \left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{8}+\frac{9 \left(b x +a \right)^{4}}{32}\right)}{b^{4}}-\frac{4 a \,d^{4} \left(\frac{\left(b x +a \right)^{3} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{3 \left(b x +a \right)^{2} \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{4}-\frac{3 \left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{128}-\frac{27 b x}{256}-\frac{27 a}{256}+\frac{9 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{32}-\frac{9 \cos \left(b x +a \right) \sin \left(b x +a \right)}{64}+\frac{3 \left(b x +a \right)^{3}}{16}\right)}{b^{4}}+\frac{4 c \,d^{3} \left(\frac{\left(b x +a \right)^{3} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{3 \left(b x +a \right)^{2} \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{4}-\frac{3 \left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{128}-\frac{27 b x}{256}-\frac{27 a}{256}+\frac{9 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{32}-\frac{9 \cos \left(b x +a \right) \sin \left(b x +a \right)}{64}+\frac{3 \left(b x +a \right)^{3}}{16}\right)}{b^{3}}+\frac{6 a^{2} d^{4} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}+\frac{3 \left(b x +a \right)^{2}}{32}-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{32}\right)}{b^{4}}-\frac{12 a c \,d^{3} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}+\frac{3 \left(b x +a \right)^{2}}{32}-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{32}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}+\frac{3 \left(b x +a \right)^{2}}{32}-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{32}\right)}{b^{2}}-\frac{4 a^{3} d^{4} \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{3 b x}{32}-\frac{3 a}{32}\right)}{b^{4}}+\frac{12 a^{2} c \,d^{3} \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{3 b x}{32}-\frac{3 a}{32}\right)}{b^{3}}-\frac{12 a \,c^{2} d^{2} \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{3 b x}{32}-\frac{3 a}{32}\right)}{b^{2}}+\frac{4 c^{3} d \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{3 b x}{32}-\frac{3 a}{32}\right)}{b}+\frac{a^{4} d^{4} \left(\sin^{4}\left(b x +a \right)\right)}{4 b^{4}}-\frac{a^{3} c \,d^{3} \left(\sin^{4}\left(b x +a \right)\right)}{b^{3}}+\frac{3 a^{2} c^{2} d^{2} \left(\sin^{4}\left(b x +a \right)\right)}{2 b^{2}}-\frac{a \,c^{3} d \left(\sin^{4}\left(b x +a \right)\right)}{b}+\frac{c^{4} \left(\sin^{4}\left(b x +a \right)\right)}{4}}{b}"," ",0,"1/b*(1/b^4*d^4*(1/4*(b*x+a)^4*sin(b*x+a)^4-(b*x+a)^3*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-3/16*(b*x+a)^2*sin(b*x+a)^4+3/8*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+27/128*(b*x+a)^2+3/128*sin(b*x+a)^4+45/128*sin(b*x+a)^2+9/16*(b*x+a)^2*cos(b*x+a)^2-9/8*(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+9/32*(b*x+a)^4)-4/b^4*a*d^4*(1/4*(b*x+a)^3*sin(b*x+a)^4-3/4*(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-3/32*(b*x+a)*sin(b*x+a)^4-3/128*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-27/256*b*x-27/256*a+9/32*(b*x+a)*cos(b*x+a)^2-9/64*cos(b*x+a)*sin(b*x+a)+3/16*(b*x+a)^3)+4/b^3*c*d^3*(1/4*(b*x+a)^3*sin(b*x+a)^4-3/4*(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-3/32*(b*x+a)*sin(b*x+a)^4-3/128*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-27/256*b*x-27/256*a+9/32*(b*x+a)*cos(b*x+a)^2-9/64*cos(b*x+a)*sin(b*x+a)+3/16*(b*x+a)^3)+6/b^4*a^2*d^4*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+3/32*(b*x+a)^2-1/32*sin(b*x+a)^4-3/32*sin(b*x+a)^2)-12/b^3*a*c*d^3*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+3/32*(b*x+a)^2-1/32*sin(b*x+a)^4-3/32*sin(b*x+a)^2)+6/b^2*c^2*d^2*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+3/32*(b*x+a)^2-1/32*sin(b*x+a)^4-3/32*sin(b*x+a)^2)-4/b^4*a^3*d^4*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/32*b*x-3/32*a)+12/b^3*a^2*c*d^3*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/32*b*x-3/32*a)-12/b^2*a*c^2*d^2*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/32*b*x-3/32*a)+4/b*c^3*d*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/32*b*x-3/32*a)+1/4/b^4*a^4*d^4*sin(b*x+a)^4-1/b^3*a^3*c*d^3*sin(b*x+a)^4+3/2/b^2*a^2*c^2*d^2*sin(b*x+a)^4-1/b*a*c^3*d*sin(b*x+a)^4+1/4*c^4*sin(b*x+a)^4)","B"
24,1,594,178,0.019000," ","int((d*x+c)^3*cos(b*x+a)*sin(b*x+a)^3,x)","\frac{\frac{d^{3} \left(\frac{\left(b x +a \right)^{3} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{3 \left(b x +a \right)^{2} \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{4}-\frac{3 \left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{128}-\frac{27 b x}{256}-\frac{27 a}{256}+\frac{9 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{32}-\frac{9 \cos \left(b x +a \right) \sin \left(b x +a \right)}{64}+\frac{3 \left(b x +a \right)^{3}}{16}\right)}{b^{3}}-\frac{3 a \,d^{3} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}+\frac{3 \left(b x +a \right)^{2}}{32}-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{32}\right)}{b^{3}}+\frac{3 c \,d^{2} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}+\frac{3 \left(b x +a \right)^{2}}{32}-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{32}\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{3 b x}{32}-\frac{3 a}{32}\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{3 b x}{32}-\frac{3 a}{32}\right)}{b^{2}}+\frac{3 c^{2} d \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{3 b x}{32}-\frac{3 a}{32}\right)}{b}-\frac{a^{3} d^{3} \left(\sin^{4}\left(b x +a \right)\right)}{4 b^{3}}+\frac{3 a^{2} c \,d^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4 b^{2}}-\frac{3 a \,c^{2} d \left(\sin^{4}\left(b x +a \right)\right)}{4 b}+\frac{c^{3} \left(\sin^{4}\left(b x +a \right)\right)}{4}}{b}"," ",0,"1/b*(1/b^3*d^3*(1/4*(b*x+a)^3*sin(b*x+a)^4-3/4*(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-3/32*(b*x+a)*sin(b*x+a)^4-3/128*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-27/256*b*x-27/256*a+9/32*(b*x+a)*cos(b*x+a)^2-9/64*cos(b*x+a)*sin(b*x+a)+3/16*(b*x+a)^3)-3/b^3*a*d^3*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+3/32*(b*x+a)^2-1/32*sin(b*x+a)^4-3/32*sin(b*x+a)^2)+3/b^2*c*d^2*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+3/32*(b*x+a)^2-1/32*sin(b*x+a)^4-3/32*sin(b*x+a)^2)+3/b^3*a^2*d^3*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/32*b*x-3/32*a)-6/b^2*a*c*d^2*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/32*b*x-3/32*a)+3/b*c^2*d*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/32*b*x-3/32*a)-1/4/b^3*a^3*d^3*sin(b*x+a)^4+3/4/b^2*a^2*c*d^2*sin(b*x+a)^4-3/4/b*a*c^2*d*sin(b*x+a)^4+1/4*c^3*sin(b*x+a)^4)","B"
25,1,260,120,0.019000," ","int((d*x+c)^2*cos(b*x+a)*sin(b*x+a)^3,x)","\frac{\frac{d^{2} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}+\frac{3 \left(b x +a \right)^{2}}{32}-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{32}\right)}{b^{2}}-\frac{2 a \,d^{2} \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{3 b x}{32}-\frac{3 a}{32}\right)}{b^{2}}+\frac{2 c d \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{3 b x}{32}-\frac{3 a}{32}\right)}{b}+\frac{a^{2} d^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4 b^{2}}-\frac{a c d \left(\sin^{4}\left(b x +a \right)\right)}{2 b}+\frac{c^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4}}{b}"," ",0,"1/b*(1/b^2*d^2*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+3/32*(b*x+a)^2-1/32*sin(b*x+a)^4-3/32*sin(b*x+a)^2)-2/b^2*a*d^2*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/32*b*x-3/32*a)+2/b*c*d*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/32*b*x-3/32*a)+1/4/b^2*a^2*d^2*sin(b*x+a)^4-1/2/b*a*c*d*sin(b*x+a)^4+1/4*c^2*sin(b*x+a)^4)","B"
26,1,85,64,0.017000," ","int((d*x+c)*cos(b*x+a)*sin(b*x+a)^3,x)","\frac{\frac{d \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{3 b x}{32}-\frac{3 a}{32}\right)}{b}-\frac{d a \left(\sin^{4}\left(b x +a \right)\right)}{4 b}+\frac{c \left(\sin^{4}\left(b x +a \right)\right)}{4}}{b}"," ",0,"1/b*(1/b*d*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/32*b*x-3/32*a)-1/4/b*d*a*sin(b*x+a)^4+1/4*c*sin(b*x+a)^4)","A"
27,1,178,121,0.019000," ","int(cos(b*x+a)*sin(b*x+a)^3/(d*x+c),x)","\frac{-\frac{b \left(\frac{4 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}-\frac{4 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}\right)}{32}+\frac{b \left(\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}-\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}\right)}{8}}{b}"," ",0,"1/b*(-1/32*b*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d-4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d)+1/8*b*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d))","A"
28,1,256,167,0.023000," ","int(cos(b*x+a)*sin(b*x+a)^3/(d*x+c)^2,x)","\frac{-\frac{b^{2} \left(-\frac{4 \sin \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{16 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}+\frac{16 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}}{d}\right)}{32}+\frac{b^{2} \left(-\frac{2 \sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{4 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{4 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}}{d}\right)}{8}}{b}"," ",0,"1/b*(-1/32*b^2*(-4*sin(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)/d+4*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d+4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d)/d)+1/8*b^2*(-2*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d+2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d)/d))","A"
29,1,329,217,0.022000," ","int(cos(b*x+a)*sin(b*x+a)^3/(d*x+c)^3,x)","\frac{-\frac{b^{3} \left(-\frac{2 \sin \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{8 \cos \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{8 \left(\frac{4 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}-\frac{4 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}\right)}{d}}{d}\right)}{32}+\frac{b^{3} \left(-\frac{\sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{2 \cos \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{2 \left(\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}-\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}\right)}{d}}{d}\right)}{8}}{b}"," ",0,"1/b*(-1/32*b^3*(-2*sin(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)^2/d+2*(-4*cos(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)/d-4*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d-4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d)/d)/d)+1/8*b^3*(-sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d+(-2*cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d-2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d)/d)/d))","A"
30,1,404,267,0.023000," ","int(cos(b*x+a)*sin(b*x+a)^3/(d*x+c)^4,x)","\frac{-\frac{b^{4} \left(-\frac{4 \sin \left(4 b x +4 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{8 \cos \left(4 b x +4 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{8 \left(-\frac{4 \sin \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{16 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}+\frac{16 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}}{d}\right)}{3 d}}{d}\right)}{32}+\frac{b^{4} \left(-\frac{2 \sin \left(2 b x +2 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{2 \cos \left(2 b x +2 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{2 \left(-\frac{2 \sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{4 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{4 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}}{d}\right)}{3 d}}{d}\right)}{8}}{b}"," ",0,"1/b*(-1/32*b^4*(-4/3*sin(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)^3/d+4/3*(-2*cos(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)^2/d-2*(-4*sin(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)/d+4*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d+4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d)/d)/d)/d)+1/8*b^4*(-2/3*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^3/d+2/3*(-cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d-(-2*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d+2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d)/d)/d)/d))","A"
31,0,0,16,0.160000," ","int((d*x+c)^m*cos(b*x+a)*csc(b*x+a),x)","\int \left(d x +c \right)^{m} \cos \left(b x +a \right) \csc \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)*csc(b*x+a),x)","F"
32,1,1150,134,0.172000," ","int((d*x+c)^4*cos(b*x+a)*csc(b*x+a),x)","\frac{d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{5}}-\frac{2 d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{d^{4} a^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{8 i d^{4} a^{5}}{5 b^{5}}-i c \,d^{3} x^{4}-2 i c^{2} d^{2} x^{3}-2 i c^{3} d \,x^{2}+\frac{12 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 c^{2} d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{12 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{4}}{b}+\frac{d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{4}}{b}+i c^{4} x -\frac{2 c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{i d^{4} x^{5}}{5}-\frac{24 d^{4} \polylog \left(5, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 d^{4} \polylog \left(5, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{8 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{8 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{12 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{4 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{4 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{24 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{4 i c^{3} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 i c^{3} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{24 c \,d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 c \,d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 i c \,d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{4 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{24 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{4 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{4 c^{3} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{6 c^{2} d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{6 c^{2} d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{2 i d^{4} a^{4} x}{b^{4}}-\frac{4 i c^{3} d \,a^{2}}{b^{2}}+\frac{8 i c^{2} d^{2} a^{3}}{b^{3}}-\frac{6 i c \,d^{3} a^{4}}{b^{4}}-\frac{8 i c \,d^{3} a^{3} x}{b^{3}}+\frac{12 i c^{2} d^{2} a^{2} x}{b^{2}}-\frac{8 i c^{3} d a x}{b}-\frac{12 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{12 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c^{2} d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c \,d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}"," ",0,"1/b^5*d^4*a^4*ln(exp(I*(b*x+a))-1)-2/b^5*d^4*a^4*ln(exp(I*(b*x+a)))+12/b^3*c^2*d^2*polylog(3,-exp(I*(b*x+a)))+12/b^3*c^2*d^2*polylog(3,exp(I*(b*x+a)))-1/b^5*d^4*a^4*ln(1-exp(I*(b*x+a)))+12/b^3*d^4*polylog(3,exp(I*(b*x+a)))*x^2+12/b^3*d^4*polylog(3,-exp(I*(b*x+a)))*x^2+8/5*I/b^5*d^4*a^5-I*c*d^3*x^4-2*I*c^2*d^2*x^3-2*I*c^3*d*x^2-24*d^4*polylog(5,-exp(I*(b*x+a)))/b^5-24*d^4*polylog(5,exp(I*(b*x+a)))/b^5+I*c^4*x-2/b*c^4*ln(exp(I*(b*x+a)))+1/b*c^4*ln(exp(I*(b*x+a))+1)+1/b*c^4*ln(exp(I*(b*x+a))-1)-1/5*I*d^4*x^5+4/b*c^3*d*ln(exp(I*(b*x+a))+1)*x+4/b*c^3*d*ln(1-exp(I*(b*x+a)))*x+4/b^2*c^3*d*ln(1-exp(I*(b*x+a)))*a+6/b*c^2*d^2*ln(exp(I*(b*x+a))+1)*x^2+24/b^3*c*d^3*polylog(3,-exp(I*(b*x+a)))*x-6/b^3*c^2*d^2*a^2*ln(1-exp(I*(b*x+a)))+6/b*c^2*d^2*ln(1-exp(I*(b*x+a)))*x^2+24/b^3*c*d^3*polylog(3,exp(I*(b*x+a)))*x+24*I/b^4*c*d^3*polylog(4,-exp(I*(b*x+a)))+24*I/b^4*c*d^3*polylog(4,exp(I*(b*x+a)))+2*I/b^4*d^4*a^4*x-4*I/b^2*c^3*d*a^2+8*I/b^3*c^2*d^2*a^3-6*I/b^4*c*d^3*a^4-4*I/b^2*d^4*polylog(2,exp(I*(b*x+a)))*x^3+24*I/b^4*d^4*polylog(4,exp(I*(b*x+a)))*x-4*I/b^2*d^4*polylog(2,-exp(I*(b*x+a)))*x^3+24*I/b^4*d^4*polylog(4,-exp(I*(b*x+a)))*x-4*I/b^2*c^3*d*polylog(2,-exp(I*(b*x+a)))-4*I/b^2*c^3*d*polylog(2,exp(I*(b*x+a)))+8/b^2*c^3*d*a*ln(exp(I*(b*x+a)))-4/b^4*c*d^3*a^3*ln(exp(I*(b*x+a))-1)+8/b^4*c*d^3*a^3*ln(exp(I*(b*x+a)))+6/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a))-1)-12/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a)))-4/b^2*c^3*d*a*ln(exp(I*(b*x+a))-1)+1/b*d^4*ln(1-exp(I*(b*x+a)))*x^4+1/b*d^4*ln(exp(I*(b*x+a))+1)*x^4-8*I/b^3*c*d^3*a^3*x+12*I/b^2*c^2*d^2*a^2*x-8*I/b*c^3*d*a*x-12*I/b^2*c*d^3*polylog(2,-exp(I*(b*x+a)))*x^2-12*I/b^2*c^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-12*I/b^2*c^2*d^2*polylog(2,exp(I*(b*x+a)))*x-12*I/b^2*c*d^3*polylog(2,exp(I*(b*x+a)))*x^2+4/b*c*d^3*ln(exp(I*(b*x+a))+1)*x^3+4/b*c*d^3*ln(1-exp(I*(b*x+a)))*x^3+4/b^4*c*d^3*ln(1-exp(I*(b*x+a)))*a^3","B"
33,1,783,108,0.095000," ","int((d*x+c)^3*cos(b*x+a)*csc(b*x+a),x)","\frac{6 i c \,d^{2} a^{2} x}{b^{2}}-\frac{6 i c^{2} d a x}{b}-\frac{6 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{6 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{2 d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i a^{4} d^{3}}{2 b^{4}}-i c \,d^{2} x^{3}-\frac{3 i c^{2} d \,x^{2}}{2}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{6 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+i c^{3} x -\frac{i d^{3} x^{4}}{4}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{2 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{6 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i c^{2} d \,a^{2}}{b^{2}}-\frac{2 i a^{3} d^{3} x}{b^{3}}+\frac{4 i c \,d^{2} a^{3}}{b^{3}}-\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{3 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{6 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"6*I/b^2*c*d^2*a^2*x-6*I/b^2*c*d^2*polylog(2,exp(I*(b*x+a)))*x-6*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x-6*I/b*c^2*d*a*x+6*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4+I*c^3*x-1/b^4*d^3*a^3*ln(exp(I*(b*x+a))-1)+2/b^4*d^3*a^3*ln(exp(I*(b*x+a)))+6/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+6/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))+6/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x+6/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x-3/2*I/b^4*a^4*d^3+6*I/b^4*d^3*polylog(4,-exp(I*(b*x+a)))-I*c*d^2*x^3-3/2*I*c^2*d*x^2-1/4*I*d^3*x^4+1/b*c^3*ln(exp(I*(b*x+a))-1)+1/b*c^3*ln(exp(I*(b*x+a))+1)-2/b*c^3*ln(exp(I*(b*x+a)))+3/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))-1)-6/b^3*c*d^2*a^2*ln(exp(I*(b*x+a)))-3*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))-3*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-3*I/b^2*c^2*d*a^2-2*I/b^3*a^3*d^3*x+4*I/b^3*c*d^2*a^3-3*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2-3*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+3/b*c^2*d*ln(exp(I*(b*x+a))+1)*x+3/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+3/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-3/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+3/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2+3/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2-3/b^2*c^2*d*a*ln(exp(I*(b*x+a))-1)+6/b^2*c^2*d*a*ln(exp(I*(b*x+a)))+1/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+1/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3+1/b*d^3*ln(exp(I*(b*x+a))+1)*x^3","B"
34,1,468,81,0.074000," ","int((d*x+c)^2*cos(b*x+a)*csc(b*x+a),x)","\frac{d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{2 d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{4 i d^{2} a^{3}}{3 b^{3}}-i c d \,x^{2}-\frac{4 i c d a x}{b}+i c^{2} x -\frac{2 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{i d^{2} x^{3}}{3}+\frac{2 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{4 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{2 i d^{2} a^{2} x}{b^{2}}-\frac{2 i c d \,a^{2}}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"1/b^3*d^2*a^2*ln(exp(I*(b*x+a))-1)-2/b^3*d^2*a^2*ln(exp(I*(b*x+a)))+1/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-1/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2+1/b*d^2*ln(exp(I*(b*x+a))+1)*x^2+4/3*I/b^3*d^2*a^3-I*c*d*x^2-4*I/b*c*d*a*x+2*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+2*d^2*polylog(3,exp(I*(b*x+a)))/b^3+I*c^2*x-2/b*c^2*ln(exp(I*(b*x+a)))+1/b*c^2*ln(exp(I*(b*x+a))-1)+1/b*c^2*ln(exp(I*(b*x+a))+1)-1/3*I*d^2*x^3+2/b*c*d*ln(1-exp(I*(b*x+a)))*x+2/b^2*c*d*ln(1-exp(I*(b*x+a)))*a+2/b*c*d*ln(exp(I*(b*x+a))+1)*x+4/b^2*c*d*a*ln(exp(I*(b*x+a)))-2/b^2*c*d*a*ln(exp(I*(b*x+a))-1)+2*I/b^2*d^2*a^2*x-2*I/b^2*c*d*a^2-2*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-2*I/b^2*d^2*polylog(2,exp(I*(b*x+a)))*x-2*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))-2*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))","B"
35,1,215,55,0.073000," ","int((d*x+c)*cos(b*x+a)*csc(b*x+a),x)","-\frac{i d \,x^{2}}{2}+i c x +\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{2 c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{2 i d a x}{b}-\frac{i d \,a^{2}}{b^{2}}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{i d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{i d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{2 d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"-1/2*I*d*x^2+I*c*x+1/b*c*ln(exp(I*(b*x+a))-1)+1/b*c*ln(exp(I*(b*x+a))+1)-2/b*c*ln(exp(I*(b*x+a)))-2*I/b*d*a*x-I/b^2*d*a^2+1/b*d*ln(exp(I*(b*x+a))+1)*x-I*d*polylog(2,-exp(I*(b*x+a)))/b^2+1/b*d*ln(1-exp(I*(b*x+a)))*x+1/b^2*d*ln(1-exp(I*(b*x+a)))*a-I*d*polylog(2,exp(I*(b*x+a)))/b^2-1/b^2*d*a*ln(exp(I*(b*x+a))-1)+2/b^2*d*a*ln(exp(I*(b*x+a)))","B"
36,0,0,16,0.174000," ","int(cos(b*x+a)*csc(b*x+a)/(d*x+c),x)","\int \frac{\cos \left(b x +a \right) \csc \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(cos(b*x+a)*csc(b*x+a)/(d*x+c),x)","F"
37,0,0,16,0.200000," ","int(cos(b*x+a)*csc(b*x+a)/(d*x+c)^2,x)","\int \frac{\cos \left(b x +a \right) \csc \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(cos(b*x+a)*csc(b*x+a)/(d*x+c)^2,x)","F"
38,0,0,22,0.080000," ","int((d*x+c)^m*cos(b*x+a)*csc(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \cos \left(b x +a \right) \left(\csc^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)*csc(b*x+a)^2,x)","F"
39,1,716,190,0.125000," ","int((d*x+c)^4*cos(b*x+a)*csc(b*x+a)^2,x)","\frac{8 d^{4} a^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 d^{3} c \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 d^{3} c \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{8 d \,c^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{24 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{24 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{24 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{24 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{4 d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{4 d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{5}}-\frac{4 d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b^{2}}-\frac{4 d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{3}}{b^{5}}+\frac{24 i d^{3} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{24 i d^{3} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{2 i \left(d^{4} x^{4}+4 c \,d^{3} x^{3}+6 c^{2} d^{2} x^{2}+4 c^{3} d x +c^{4}\right) {\mathrm e}^{i \left(b x +a \right)}}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}-\frac{24 d^{3} c \,a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 d^{2} c^{2} a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{12 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{12 i d^{2} c^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{12 i d^{2} c^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{2} c^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{12 d^{2} c^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{12 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}-\frac{12 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{3}}+\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}-\frac{12 d^{3} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}+\frac{12 d^{3} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{b^{4}}"," ",0,"8/b^5*d^4*a^3*arctanh(exp(I*(b*x+a)))-24/b^4*d^3*c*polylog(3,-exp(I*(b*x+a)))+24/b^4*d^3*c*polylog(3,exp(I*(b*x+a)))-8/b^2*d*c^3*arctanh(exp(I*(b*x+a)))-24/b^4*d^4*polylog(3,-exp(I*(b*x+a)))*x+24/b^4*d^4*polylog(3,exp(I*(b*x+a)))*x-24*I*d^4*polylog(4,-exp(I*(b*x+a)))/b^5+24*I/b^3*d^3*c*polylog(2,-exp(I*(b*x+a)))*x-24*I/b^3*d^3*c*polylog(2,exp(I*(b*x+a)))*x+24*I*d^4*polylog(4,exp(I*(b*x+a)))/b^5-2*I*(d^4*x^4+4*c*d^3*x^3+6*c^2*d^2*x^2+4*c^3*d*x+c^4)*exp(I*(b*x+a))/b/(exp(2*I*(b*x+a))-1)+12/b^2*d^2*c^2*ln(1-exp(I*(b*x+a)))*x+12/b^3*d^2*c^2*ln(1-exp(I*(b*x+a)))*a-12/b^2*d^2*c^2*ln(exp(I*(b*x+a))+1)*x-12/b^3*d^2*c^2*ln(exp(I*(b*x+a))+1)*a+12/b^2*d^3*c*ln(1-exp(I*(b*x+a)))*x^2-12/b^4*d^3*c*ln(1-exp(I*(b*x+a)))*a^2-12/b^2*d^3*c*ln(exp(I*(b*x+a))+1)*x^2+12/b^4*d^3*c*ln(exp(I*(b*x+a))+1)*a^2+4/b^2*d^4*ln(1-exp(I*(b*x+a)))*x^3+4/b^5*d^4*ln(1-exp(I*(b*x+a)))*a^3-4/b^2*d^4*ln(exp(I*(b*x+a))+1)*x^3-4/b^5*d^4*ln(exp(I*(b*x+a))+1)*a^3-24/b^4*d^3*c*a^2*arctanh(exp(I*(b*x+a)))+24/b^3*d^2*c^2*a*arctanh(exp(I*(b*x+a)))+12*I/b^3*d^4*polylog(2,-exp(I*(b*x+a)))*x^2-12*I/b^3*d^4*polylog(2,exp(I*(b*x+a)))*x^2+12*I/b^3*d^2*c^2*polylog(2,-exp(I*(b*x+a)))-12*I/b^3*d^2*c^2*polylog(2,exp(I*(b*x+a)))","B"
40,1,433,134,0.089000," ","int((d*x+c)^3*cos(b*x+a)*csc(b*x+a)^2,x)","-\frac{6 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{2} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 d^{2} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}-\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{3}}-\frac{6 d \,c^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 d^{3} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{12 d^{2} c a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i d^{2} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{2} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}+\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{b^{4}}-\frac{2 i \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right) {\mathrm e}^{i \left(b x +a \right)}}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}+\frac{6 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}"," ",0,"-6*I/b^3*d^2*c*polylog(2,exp(I*(b*x+a)))+6/b^2*d^2*c*ln(1-exp(I*(b*x+a)))*x+6/b^3*d^2*c*ln(1-exp(I*(b*x+a)))*a-6/b^2*d^2*c*ln(exp(I*(b*x+a))+1)*x-6/b^3*d^2*c*ln(exp(I*(b*x+a))+1)*a-6/b^2*d*c^2*arctanh(exp(I*(b*x+a)))-6/b^4*d^3*a^2*arctanh(exp(I*(b*x+a)))-6*d^3*polylog(3,-exp(I*(b*x+a)))/b^4+6*d^3*polylog(3,exp(I*(b*x+a)))/b^4+12/b^3*d^2*c*a*arctanh(exp(I*(b*x+a)))+6*I/b^3*d^2*c*polylog(2,-exp(I*(b*x+a)))-6*I/b^3*d^3*polylog(2,exp(I*(b*x+a)))*x-3/b^2*d^3*ln(exp(I*(b*x+a))+1)*x^2+3/b^4*d^3*ln(exp(I*(b*x+a))+1)*a^2-2*I*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)*exp(I*(b*x+a))/b/(exp(2*I*(b*x+a))-1)+3/b^2*d^3*ln(1-exp(I*(b*x+a)))*x^2-3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^2+6*I/b^3*d^3*polylog(2,-exp(I*(b*x+a)))*x","B"
41,1,233,82,0.028000," ","int((d*x+c)^2*cos(b*x+a)*csc(b*x+a)^2,x)","-\frac{d^{2} x^{2}}{b \sin \left(b x +a \right)}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}-\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{3}}-\frac{2 i d^{2} \dilog \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 i d^{2} \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{2 a \,d^{2} \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b^{3}}-\frac{2 c d x}{b \sin \left(b x +a \right)}+\frac{2 c d \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b^{2}}-\frac{c^{2}}{b \sin \left(b x +a \right)}"," ",0,"-1/b*d^2/sin(b*x+a)*x^2+2/b^2*d^2*ln(1-exp(I*(b*x+a)))*x+2/b^3*d^2*ln(1-exp(I*(b*x+a)))*a-2/b^2*d^2*ln(exp(I*(b*x+a))+1)*x-2/b^3*d^2*ln(exp(I*(b*x+a))+1)*a-2*I/b^3*d^2*dilog(1-exp(I*(b*x+a)))+2*I/b^3*d^2*dilog(exp(I*(b*x+a))+1)-2/b^3*a*d^2*ln(csc(b*x+a)-cot(b*x+a))-2/b*c*d/sin(b*x+a)*x+2/b^2*c*d*ln(csc(b*x+a)-cot(b*x+a))-1/b*c^2/sin(b*x+a)","B"
42,1,52,30,0.021000," ","int((d*x+c)*cos(b*x+a)*csc(b*x+a)^2,x)","-\frac{d x}{b \sin \left(b x +a \right)}+\frac{d \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b^{2}}-\frac{c}{b \sin \left(b x +a \right)}"," ",0,"-1/b*d/sin(b*x+a)*x+1/b^2*d*ln(csc(b*x+a)-cot(b*x+a))-1/b*c/sin(b*x+a)","A"
43,0,0,22,0.218000," ","int(cos(b*x+a)*csc(b*x+a)^2/(d*x+c),x)","\int \frac{\cos \left(b x +a \right) \left(\csc^{2}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(cos(b*x+a)*csc(b*x+a)^2/(d*x+c),x)","F"
44,0,0,22,0.379000," ","int(cos(b*x+a)*csc(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\cos \left(b x +a \right) \left(\csc^{2}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(cos(b*x+a)*csc(b*x+a)^2/(d*x+c)^2,x)","F"
45,0,0,24,0.099000," ","int((d*x+c)^m*cos(b*x+a)*csc(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \cos \left(b x +a \right) \left(\csc^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)*csc(b*x+a)^3,x)","F"
46,1,716,127,0.133000," ","int((d*x+c)^4*cos(b*x+a)*csc(b*x+a)^3,x)","-\frac{24 i d^{3} c a x}{b^{3}}+\frac{12 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{12 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{6 d^{4} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{5}}-\frac{12 d^{4} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{6 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{6 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{12 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 d^{4} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{6 d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{6 d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{3}}-\frac{4 i d^{4} x^{3}}{b^{2}}+\frac{8 i d^{4} a^{3}}{b^{5}}+\frac{2 b \,d^{4} x^{4} {\mathrm e}^{2 i \left(b x +a \right)}+8 b c \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}+12 b \,c^{2} d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+8 b \,c^{3} d x \,{\mathrm e}^{2 i \left(b x +a \right)}-4 i d^{4} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}+2 b \,c^{4} {\mathrm e}^{2 i \left(b x +a \right)}-12 i c \,d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-12 i c^{2} d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+4 i d^{4} x^{3}-4 i c^{3} d \,{\mathrm e}^{2 i \left(b x +a \right)}+12 i c \,d^{3} x^{2}+12 i c^{2} d^{2} x +4 i c^{3} d}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}+\frac{24 d^{3} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 d^{3} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{12 i d^{4} a^{2} x}{b^{4}}-\frac{12 i d^{3} c \,x^{2}}{b^{2}}-\frac{12 i d^{3} c \,a^{2}}{b^{4}}-\frac{12 i d^{3} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 i d^{3} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{12 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{12 d^{3} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}"," ",0,"-24*I/b^3*d^3*c*a*x+12*d^4*polylog(3,-exp(I*(b*x+a)))/b^5+12*d^4*polylog(3,exp(I*(b*x+a)))/b^5+6/b^5*d^4*a^2*ln(exp(I*(b*x+a))-1)-12/b^5*d^4*a^2*ln(exp(I*(b*x+a)))+6/b^3*d^2*c^2*ln(exp(I*(b*x+a))-1)+6/b^3*d^2*c^2*ln(exp(I*(b*x+a))+1)-12/b^3*d^2*c^2*ln(exp(I*(b*x+a)))-6/b^5*d^4*a^2*ln(1-exp(I*(b*x+a)))+6/b^3*d^4*ln(1-exp(I*(b*x+a)))*x^2+6/b^3*d^4*ln(exp(I*(b*x+a))+1)*x^2-4*I/b^2*d^4*x^3+8*I/b^5*d^4*a^3+2*(b*d^4*x^4*exp(2*I*(b*x+a))+4*b*c*d^3*x^3*exp(2*I*(b*x+a))+6*b*c^2*d^2*x^2*exp(2*I*(b*x+a))+4*b*c^3*d*x*exp(2*I*(b*x+a))-2*I*d^4*x^3*exp(2*I*(b*x+a))+b*c^4*exp(2*I*(b*x+a))-6*I*c*d^3*x^2*exp(2*I*(b*x+a))-6*I*c^2*d^2*x*exp(2*I*(b*x+a))+2*I*d^4*x^3-2*I*c^3*d*exp(2*I*(b*x+a))+6*I*c*d^3*x^2+6*I*c^2*d^2*x+2*I*c^3*d)/b^2/(exp(2*I*(b*x+a))-1)^2+12/b^3*d^3*c*ln(exp(I*(b*x+a))+1)*x+12/b^3*d^3*c*ln(1-exp(I*(b*x+a)))*x+12/b^4*d^3*c*ln(1-exp(I*(b*x+a)))*a+24/b^4*d^3*c*a*ln(exp(I*(b*x+a)))-12/b^4*d^3*c*a*ln(exp(I*(b*x+a))-1)-12*I/b^4*d^3*c*polylog(2,-exp(I*(b*x+a)))-12*I/b^4*d^3*c*polylog(2,exp(I*(b*x+a)))+12*I/b^4*d^4*a^2*x-12*I/b^2*d^3*c*x^2-12*I/b^4*d^3*c*a^2-12*I/b^4*d^4*polylog(2,-exp(I*(b*x+a)))*x-12*I/b^4*d^4*polylog(2,exp(I*(b*x+a)))*x","B"
47,1,409,101,0.105000," ","int((d*x+c)^3*cos(b*x+a)*csc(b*x+a)^3,x)","\frac{2 b \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+6 b c \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+6 b \,c^{2} d x \,{\mathrm e}^{2 i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{2 i \left(b x +a \right)}+3 i d^{3} x^{2}+2 b \,c^{3} {\mathrm e}^{2 i \left(b x +a \right)}+6 i c \,d^{2} x +3 i c^{2} d}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{3 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{3 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i d^{3} x^{2}}{b^{2}}-\frac{6 i d^{3} a x}{b^{3}}-\frac{3 i d^{3} a^{2}}{b^{4}}+\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{6 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"(2*b*d^3*x^3*exp(2*I*(b*x+a))-3*I*d^3*x^2*exp(2*I*(b*x+a))+6*b*c*d^2*x^2*exp(2*I*(b*x+a))-6*I*c*d^2*x*exp(2*I*(b*x+a))+6*b*c^2*d*x*exp(2*I*(b*x+a))-3*I*c^2*d*exp(2*I*(b*x+a))+3*I*d^3*x^2+2*b*c^3*exp(2*I*(b*x+a))+6*I*c*d^2*x+3*I*c^2*d)/b^2/(exp(2*I*(b*x+a))-1)^2+3/b^3*d^2*c*ln(exp(I*(b*x+a))-1)+3/b^3*d^2*c*ln(exp(I*(b*x+a))+1)-6/b^3*d^2*c*ln(exp(I*(b*x+a)))-3*I/b^2*d^3*x^2-6*I/b^3*d^3*a*x-3*I/b^4*d^3*a^2+3/b^3*d^3*ln(exp(I*(b*x+a))+1)*x-3*I/b^4*d^3*polylog(2,-exp(I*(b*x+a)))+3/b^3*d^3*ln(1-exp(I*(b*x+a)))*x+3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a-3*I*d^3*polylog(2,exp(I*(b*x+a)))/b^4-3/b^4*d^3*a*ln(exp(I*(b*x+a))-1)+6/b^4*d^3*a*ln(exp(I*(b*x+a)))","B"
48,1,95,52,0.033000," ","int((d*x+c)^2*cos(b*x+a)*csc(b*x+a)^3,x)","-\frac{d^{2} x^{2}}{2 b \sin \left(b x +a \right)^{2}}-\frac{d^{2} \cot \left(b x +a \right) x}{b^{2}}+\frac{d^{2} \ln \left(\sin \left(b x +a \right)\right)}{b^{3}}-\frac{c d x}{b \sin \left(b x +a \right)^{2}}-\frac{c d \cot \left(b x +a \right)}{b^{2}}-\frac{c^{2}}{2 b \sin \left(b x +a \right)^{2}}"," ",0,"-1/2/b*d^2/sin(b*x+a)^2*x^2-1/b^2*d^2*cot(b*x+a)*x+d^2*ln(sin(b*x+a))/b^3-1/b*c*d/sin(b*x+a)^2*x-1/b^2*c*d*cot(b*x+a)-1/2/b*c^2/sin(b*x+a)^2","A"
49,1,61,31,0.029000," ","int((d*x+c)*cos(b*x+a)*csc(b*x+a)^3,x)","\frac{\frac{d \left(-\frac{b x +a}{2 \sin \left(b x +a \right)^{2}}-\frac{\cot \left(b x +a \right)}{2}\right)}{b}+\frac{d a}{2 b \sin \left(b x +a \right)^{2}}-\frac{c}{2 \sin \left(b x +a \right)^{2}}}{b}"," ",0,"1/b*(1/b*d*(-1/2*(b*x+a)/sin(b*x+a)^2-1/2*cot(b*x+a))+1/2/b*d*a/sin(b*x+a)^2-1/2*c/sin(b*x+a)^2)","A"
50,0,0,24,0.366000," ","int(cos(b*x+a)*csc(b*x+a)^3/(d*x+c),x)","\int \frac{\cos \left(b x +a \right) \left(\csc^{3}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(cos(b*x+a)*csc(b*x+a)^3/(d*x+c),x)","F"
51,0,0,24,0.539000," ","int(cos(b*x+a)*csc(b*x+a)^3/(d*x+c)^2,x)","\int \frac{\cos \left(b x +a \right) \left(\csc^{3}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(cos(b*x+a)*csc(b*x+a)^3/(d*x+c)^2,x)","F"
52,1,234,152,0.028000," ","int((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{4 b}\right)}{4 b}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(5/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+5/8/b*d*(1/4/b*d*(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-3/4/b*d*(-1/4/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
53,1,187,128,0.025000," ","int((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{4 b}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/8/b*d*(1/4/b*d*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
54,1,142,106,0.023000," ","int((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a),x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/16/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
55,1,142,106,0.000000," ","int((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a),x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/16/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
56,1,187,128,0.000000," ","int((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{4 b}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/8/b*d*(1/4/b*d*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
57,1,234,152,0.000000," ","int((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{4 b}\right)}{4 b}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(5/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+5/8/b*d*(1/4/b*d*(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-3/4/b*d*(-1/4/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
58,1,474,310,0.049000," ","int((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}-\frac{5 d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{4 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{5 d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{12 b}}{d}"," ",0,"2/d*(1/8/b*d*(d*x+c)^(5/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-5/8/b*d*(-1/2/b*d*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/2/b*d*(1/2/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/24/b*d*(d*x+c)^(5/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+5/24/b*d*(-1/6/b*d*(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/2/b*d*(1/6/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
59,1,386,265,0.042000," ","int((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{4 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{4 b}}{d}"," ",0,"2/d*(1/8/b*d*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/8/b*d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/24/b*d*(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/8/b*d*(-1/6/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
60,1,294,224,0.042000," ","int((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{72 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(1/8/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/16/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/24/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/144/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
61,1,294,224,0.000000," ","int((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{72 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(1/8/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/16/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/24/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/144/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
62,1,386,265,0.000000," ","int((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{4 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{4 b}}{d}"," ",0,"2/d*(1/8/b*d*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/8/b*d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/24/b*d*(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/8/b*d*(-1/6/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
63,1,474,310,0.000000," ","int((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}-\frac{5 d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{4 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{5 d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{12 b}}{d}"," ",0,"2/d*(1/8/b*d*(d*x+c)^(5/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-5/8/b*d*(-1/2/b*d*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/2/b*d*(1/2/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/24/b*d*(d*x+c)^(5/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+5/24/b*d*(-1/6/b*d*(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/2/b*d*(1/6/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
64,1,470,315,0.039000," ","int((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^3,x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{4 b}\right)}{8 b}+\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}-\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{8 b}\right)}{32 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(5/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+5/16/b*d*(1/4/b*d*(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-3/4/b*d*(-1/4/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))+1/64/b*d*(d*x+c)^(5/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-5/64/b*d*(1/8/b*d*(d*x+c)^(3/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-3/8/b*d*(-1/8/b*d*(d*x+c)^(1/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
65,1,376,267,0.037000," ","int((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^3,x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{8 b}+\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}-\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{32 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/16/b*d*(1/4/b*d*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))+1/64/b*d*(d*x+c)^(3/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-3/64/b*d*(1/8/b*d*(d*x+c)^(1/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
66,1,286,223,0.033000," ","int((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^3,x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{16 b \sqrt{\frac{b}{d}}}+\frac{d \sqrt{d x +c}\, \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{128 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/32/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))+1/64/b*d*(d*x+c)^(1/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-1/256/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
67,1,286,223,0.000000," ","int((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^3,x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{16 b \sqrt{\frac{b}{d}}}+\frac{d \sqrt{d x +c}\, \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{128 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/32/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))+1/64/b*d*(d*x+c)^(1/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-1/256/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
68,1,376,267,0.000000," ","int((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^3,x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{8 b}+\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}-\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{32 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/16/b*d*(1/4/b*d*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))+1/64/b*d*(d*x+c)^(3/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-3/64/b*d*(1/8/b*d*(d*x+c)^(1/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
69,1,470,315,0.000000," ","int((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^3,x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{4 b}\right)}{8 b}+\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}-\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{8 b}\right)}{32 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(5/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+5/16/b*d*(1/4/b*d*(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-3/4/b*d*(-1/4/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))+1/64/b*d*(d*x+c)^(5/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-5/64/b*d*(1/8/b*d*(d*x+c)^(3/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-3/8/b*d*(-1/8/b*d*(d*x+c)^(1/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
70,0,0,247,0.184000," ","int((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a),x)","\int \left(d x +c \right)^{m} \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a),x)","F"
71,1,835,187,0.057000," ","int((d*x+c)^4*cos(b*x+a)^2*sin(b*x+a),x)","\frac{\frac{d^{4} \left(-\frac{\left(b x +a \right)^{4} \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{4 \left(b x +a \right)^{3} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}+\frac{8 \left(b x +a \right)^{2} \cos \left(b x +a \right)}{3}-\frac{160 \cos \left(b x +a \right)}{27}-\frac{16 \left(b x +a \right) \sin \left(b x +a \right)}{3}+\frac{4 \left(b x +a \right)^{2} \left(\cos^{3}\left(b x +a \right)\right)}{9}-\frac{8 \left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{27}-\frac{8 \left(\cos^{3}\left(b x +a \right)\right)}{81}\right)}{b^{4}}-\frac{4 a \,d^{4} \left(-\frac{\left(b x +a \right)^{3} \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(b x +a \right)^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}-\frac{4 \sin \left(b x +a \right)}{3}+\frac{4 \left(b x +a \right) \cos \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{9}-\frac{2 \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{27}\right)}{b^{4}}+\frac{4 c \,d^{3} \left(-\frac{\left(b x +a \right)^{3} \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(b x +a \right)^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}-\frac{4 \sin \left(b x +a \right)}{3}+\frac{4 \left(b x +a \right) \cos \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{9}-\frac{2 \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{27}\right)}{b^{3}}+\frac{6 a^{2} d^{4} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}+\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{27}+\frac{4 \cos \left(b x +a \right)}{9}\right)}{b^{4}}-\frac{12 a c \,d^{3} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}+\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{27}+\frac{4 \cos \left(b x +a \right)}{9}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}+\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{27}+\frac{4 \cos \left(b x +a \right)}{9}\right)}{b^{2}}-\frac{4 a^{3} d^{4} \left(-\frac{\left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}\right)}{b^{4}}+\frac{12 a^{2} c \,d^{3} \left(-\frac{\left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}\right)}{b^{3}}-\frac{12 a \,c^{2} d^{2} \left(-\frac{\left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}\right)}{b^{2}}+\frac{4 c^{3} d \left(-\frac{\left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}\right)}{b}-\frac{a^{4} d^{4} \left(\cos^{3}\left(b x +a \right)\right)}{3 b^{4}}+\frac{4 a^{3} c \,d^{3} \left(\cos^{3}\left(b x +a \right)\right)}{3 b^{3}}-\frac{2 a^{2} c^{2} d^{2} \left(\cos^{3}\left(b x +a \right)\right)}{b^{2}}+\frac{4 a \,c^{3} d \left(\cos^{3}\left(b x +a \right)\right)}{3 b}-\frac{c^{4} \left(\cos^{3}\left(b x +a \right)\right)}{3}}{b}"," ",0,"1/b*(1/b^4*d^4*(-1/3*(b*x+a)^4*cos(b*x+a)^3+4/9*(b*x+a)^3*(2+cos(b*x+a)^2)*sin(b*x+a)+8/3*(b*x+a)^2*cos(b*x+a)-160/27*cos(b*x+a)-16/3*(b*x+a)*sin(b*x+a)+4/9*(b*x+a)^2*cos(b*x+a)^3-8/27*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)-8/81*cos(b*x+a)^3)-4/b^4*a*d^4*(-1/3*(b*x+a)^3*cos(b*x+a)^3+1/3*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)-4/3*sin(b*x+a)+4/3*(b*x+a)*cos(b*x+a)+2/9*(b*x+a)*cos(b*x+a)^3-2/27*(2+cos(b*x+a)^2)*sin(b*x+a))+4/b^3*c*d^3*(-1/3*(b*x+a)^3*cos(b*x+a)^3+1/3*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)-4/3*sin(b*x+a)+4/3*(b*x+a)*cos(b*x+a)+2/9*(b*x+a)*cos(b*x+a)^3-2/27*(2+cos(b*x+a)^2)*sin(b*x+a))+6/b^4*a^2*d^4*(-1/3*(b*x+a)^2*cos(b*x+a)^3+2/9*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+2/27*cos(b*x+a)^3+4/9*cos(b*x+a))-12/b^3*a*c*d^3*(-1/3*(b*x+a)^2*cos(b*x+a)^3+2/9*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+2/27*cos(b*x+a)^3+4/9*cos(b*x+a))+6/b^2*c^2*d^2*(-1/3*(b*x+a)^2*cos(b*x+a)^3+2/9*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+2/27*cos(b*x+a)^3+4/9*cos(b*x+a))-4/b^4*a^3*d^4*(-1/3*(b*x+a)*cos(b*x+a)^3+1/9*(2+cos(b*x+a)^2)*sin(b*x+a))+12/b^3*a^2*c*d^3*(-1/3*(b*x+a)*cos(b*x+a)^3+1/9*(2+cos(b*x+a)^2)*sin(b*x+a))-12/b^2*a*c^2*d^2*(-1/3*(b*x+a)*cos(b*x+a)^3+1/9*(2+cos(b*x+a)^2)*sin(b*x+a))+4/b*c^3*d*(-1/3*(b*x+a)*cos(b*x+a)^3+1/9*(2+cos(b*x+a)^2)*sin(b*x+a))-1/3/b^4*a^4*d^4*cos(b*x+a)^3+4/3/b^3*a^3*c*d^3*cos(b*x+a)^3-2/b^2*a^2*c^2*d^2*cos(b*x+a)^3+4/3/b*a*c^3*d*cos(b*x+a)^3-1/3*c^4*cos(b*x+a)^3)","B"
72,1,447,137,0.010000," ","int((d*x+c)^3*cos(b*x+a)^2*sin(b*x+a),x)","\frac{\frac{d^{3} \left(-\frac{\left(b x +a \right)^{3} \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(b x +a \right)^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}-\frac{4 \sin \left(b x +a \right)}{3}+\frac{4 \left(b x +a \right) \cos \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{9}-\frac{2 \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{27}\right)}{b^{3}}-\frac{3 a \,d^{3} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}+\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{27}+\frac{4 \cos \left(b x +a \right)}{9}\right)}{b^{3}}+\frac{3 c \,d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}+\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{27}+\frac{4 \cos \left(b x +a \right)}{9}\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(-\frac{\left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(-\frac{\left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}\right)}{b^{2}}+\frac{3 c^{2} d \left(-\frac{\left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}\right)}{b}+\frac{a^{3} d^{3} \left(\cos^{3}\left(b x +a \right)\right)}{3 b^{3}}-\frac{a^{2} c \,d^{2} \left(\cos^{3}\left(b x +a \right)\right)}{b^{2}}+\frac{a \,c^{2} d \left(\cos^{3}\left(b x +a \right)\right)}{b}-\frac{c^{3} \left(\cos^{3}\left(b x +a \right)\right)}{3}}{b}"," ",0,"1/b*(1/b^3*d^3*(-1/3*(b*x+a)^3*cos(b*x+a)^3+1/3*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)-4/3*sin(b*x+a)+4/3*(b*x+a)*cos(b*x+a)+2/9*(b*x+a)*cos(b*x+a)^3-2/27*(2+cos(b*x+a)^2)*sin(b*x+a))-3/b^3*a*d^3*(-1/3*(b*x+a)^2*cos(b*x+a)^3+2/9*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+2/27*cos(b*x+a)^3+4/9*cos(b*x+a))+3/b^2*c*d^2*(-1/3*(b*x+a)^2*cos(b*x+a)^3+2/9*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+2/27*cos(b*x+a)^3+4/9*cos(b*x+a))+3/b^3*a^2*d^3*(-1/3*(b*x+a)*cos(b*x+a)^3+1/9*(2+cos(b*x+a)^2)*sin(b*x+a))-6/b^2*a*c*d^2*(-1/3*(b*x+a)*cos(b*x+a)^3+1/9*(2+cos(b*x+a)^2)*sin(b*x+a))+3/b*c^2*d*(-1/3*(b*x+a)*cos(b*x+a)^3+1/9*(2+cos(b*x+a)^2)*sin(b*x+a))+1/3/b^3*a^3*d^3*cos(b*x+a)^3-1/b^2*a^2*c*d^2*cos(b*x+a)^3+1/b*a*c^2*d*cos(b*x+a)^3-1/3*c^3*cos(b*x+a)^3)","B"
73,1,204,93,0.010000," ","int((d*x+c)^2*cos(b*x+a)^2*sin(b*x+a),x)","\frac{\frac{d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}+\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{27}+\frac{4 \cos \left(b x +a \right)}{9}\right)}{b^{2}}-\frac{2 a \,d^{2} \left(-\frac{\left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}\right)}{b^{2}}+\frac{2 c d \left(-\frac{\left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}\right)}{b}-\frac{a^{2} d^{2} \left(\cos^{3}\left(b x +a \right)\right)}{3 b^{2}}+\frac{2 a c d \left(\cos^{3}\left(b x +a \right)\right)}{3 b}-\frac{c^{2} \left(\cos^{3}\left(b x +a \right)\right)}{3}}{b}"," ",0,"1/b*(1/b^2*d^2*(-1/3*(b*x+a)^2*cos(b*x+a)^3+2/9*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+2/27*cos(b*x+a)^3+4/9*cos(b*x+a))-2/b^2*a*d^2*(-1/3*(b*x+a)*cos(b*x+a)^3+1/9*(2+cos(b*x+a)^2)*sin(b*x+a))+2/b*c*d*(-1/3*(b*x+a)*cos(b*x+a)^3+1/9*(2+cos(b*x+a)^2)*sin(b*x+a))-1/3/b^2*a^2*d^2*cos(b*x+a)^3+2/3/b*a*c*d*cos(b*x+a)^3-1/3*c^2*cos(b*x+a)^3)","B"
74,1,71,45,0.010000," ","int((d*x+c)*cos(b*x+a)^2*sin(b*x+a),x)","\frac{\frac{d \left(-\frac{\left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{3}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}\right)}{b}+\frac{d a \left(\cos^{3}\left(b x +a \right)\right)}{3 b}-\frac{c \left(\cos^{3}\left(b x +a \right)\right)}{3}}{b}"," ",0,"1/b*(1/b*d*(-1/3*(b*x+a)*cos(b*x+a)^3+1/9*(2+cos(b*x+a)^2)*sin(b*x+a))+1/3/b*d*a*cos(b*x+a)^3-1/3*c*cos(b*x+a)^3)","A"
75,1,167,113,0.010000," ","int(cos(b*x+a)^2*sin(b*x+a)/(d*x+c),x)","\frac{\frac{b \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}-\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{12}+\frac{b \left(\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}\right)}{4}}{b}"," ",0,"1/b*(1/12*b*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d-3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d)+1/4*b*(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d))","A"
76,1,240,156,0.012000," ","int(cos(b*x+a)^2*sin(b*x+a)/(d*x+c)^2,x)","\frac{\frac{b^{2} \left(-\frac{3 \sin \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{9 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}+\frac{9 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}}{d}\right)}{12}+\frac{b^{2} \left(-\frac{\sin \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}+\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}}{d}\right)}{4}}{b}"," ",0,"1/b*(1/12*b^2*(-3*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d+3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d+3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d)/d)+1/4*b^2*(-sin(b*x+a)/((b*x+a)*d-d*a+c*b)/d+(Si(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)/d))","A"
77,1,313,205,0.013000," ","int(cos(b*x+a)^2*sin(b*x+a)/(d*x+c)^3,x)","\frac{\frac{b^{3} \left(-\frac{3 \sin \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{9 \cos \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right) d}-\frac{9 \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}-\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{2 d}}{d}\right)}{12}+\frac{b^{3} \left(-\frac{\sin \left(b x +a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{\cos \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}}{d}}{2 d}\right)}{4}}{b}"," ",0,"1/b*(1/12*b^3*(-3/2*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^2/d+3/2*(-3*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d-3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d-3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d)/d)/d)+1/4*b^3*(-1/2*sin(b*x+a)/((b*x+a)*d-d*a+c*b)^2/d+1/2*(-cos(b*x+a)/((b*x+a)*d-d*a+c*b)/d-(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d)/d)/d))","A"
78,1,381,250,0.013000," ","int(cos(b*x+a)^2*sin(b*x+a)/(d*x+c)^4,x)","\frac{\frac{b^{4} \left(-\frac{\sin \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{3 \cos \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{3 \left(-\frac{3 \sin \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{9 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}+\frac{9 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}}{d}\right)}{2 d}}{d}\right)}{12}+\frac{b^{4} \left(-\frac{\sin \left(b x +a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{\cos \left(b x +a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{-\frac{\sin \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}+\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}}{d}}{2 d}}{3 d}\right)}{4}}{b}"," ",0,"1/b*(1/12*b^4*(-sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^3/d+(-3/2*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^2/d-3/2*(-3*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d+3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d+3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d)/d)/d)/d)+1/4*b^4*(-1/3*sin(b*x+a)/((b*x+a)*d-d*a+c*b)^3/d+1/3*(-1/2*cos(b*x+a)/((b*x+a)*d-d*a+c*b)^2/d-1/2*(-sin(b*x+a)/((b*x+a)*d-d*a+c*b)/d+(Si(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)/d)/d)/d))","A"
79,0,0,156,0.151000," ","int((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \left(\cos^{2}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a)^2,x)","F"
80,1,1915,119,0.092000," ","int((d*x+c)^4*cos(b*x+a)^2*sin(b*x+a)^2,x)","\text{Expression too large to display}"," ",0,"1/b*(1/b^4*d^4*((b*x+a)^4*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^3*cos(b*x+a)^2+3/4*(b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/32*(b*x+a)*cos(b*x+a)^2-3/64*cos(b*x+a)*sin(b*x+a)-21/256*b*x-21/256*a-7/16*(b*x+a)^3-1/10*(b*x+a)^5-(b*x+a)^4*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/4*(b*x+a)^3*sin(b*x+a)^4+3/4*(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+3/32*(b*x+a)*sin(b*x+a)^4+3/128*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a))-4/b^4*a*d^4*((b*x+a)^3*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-3/16*(b*x+a)^2*cos(b*x+a)^2+3/8*(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-21/128*(b*x+a)^2-3/128*sin(b*x+a)^2-3/32*(b*x+a)^4-(b*x+a)^3*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-3/16*(b*x+a)^2*sin(b*x+a)^4+3/8*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+3/128*sin(b*x+a)^4)+4/b^3*c*d^3*((b*x+a)^3*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-3/16*(b*x+a)^2*cos(b*x+a)^2+3/8*(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-21/128*(b*x+a)^2-3/128*sin(b*x+a)^2-3/32*(b*x+a)^4-(b*x+a)^3*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-3/16*(b*x+a)^2*sin(b*x+a)^4+3/8*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+3/128*sin(b*x+a)^4)+6/b^4*a^2*d^4*((b*x+a)^2*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/8*(b*x+a)*cos(b*x+a)^2+1/16*cos(b*x+a)*sin(b*x+a)+7/64*b*x+7/64*a-1/12*(b*x+a)^3-(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/8*(b*x+a)*sin(b*x+a)^4-1/32*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a))-12/b^3*a*c*d^3*((b*x+a)^2*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/8*(b*x+a)*cos(b*x+a)^2+1/16*cos(b*x+a)*sin(b*x+a)+7/64*b*x+7/64*a-1/12*(b*x+a)^3-(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/8*(b*x+a)*sin(b*x+a)^4-1/32*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a))+6/b^2*c^2*d^2*((b*x+a)^2*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/8*(b*x+a)*cos(b*x+a)^2+1/16*cos(b*x+a)*sin(b*x+a)+7/64*b*x+7/64*a-1/12*(b*x+a)^3-(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/8*(b*x+a)*sin(b*x+a)^4-1/32*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a))-4/b^4*a^3*d^4*((b*x+a)*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/16*(b*x+a)^2+1/16*sin(b*x+a)^2-(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/16*sin(b*x+a)^4)+12/b^3*a^2*c*d^3*((b*x+a)*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/16*(b*x+a)^2+1/16*sin(b*x+a)^2-(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/16*sin(b*x+a)^4)-12/b^2*a*c^2*d^2*((b*x+a)*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/16*(b*x+a)^2+1/16*sin(b*x+a)^2-(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/16*sin(b*x+a)^4)+4/b*c^3*d*((b*x+a)*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/16*(b*x+a)^2+1/16*sin(b*x+a)^2-(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/16*sin(b*x+a)^4)+1/b^4*a^4*d^4*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)-4/b^3*a^3*c*d^3*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)+6/b^2*a^2*c^2*d^2*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)-4/b*a*c^3*d*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)+c^4*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a))","B"
81,1,1074,95,0.025000," ","int((d*x+c)^3*cos(b*x+a)^2*sin(b*x+a)^2,x)","\frac{\frac{d^{3} \left(\left(b x +a \right)^{3} \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{3 \left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{16}+\frac{3 \left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{8}-\frac{21 \left(b x +a \right)^{2}}{128}-\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{128}-\frac{3 \left(b x +a \right)^{4}}{32}-\left(b x +a \right)^{3} \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{3 \left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{16}+\frac{3 \left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{8}+\frac{3 \left(\sin^{4}\left(b x +a \right)\right)}{128}\right)}{b^{3}}-\frac{3 a \,d^{3} \left(\left(b x +a \right)^{2} \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{8}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{16}+\frac{7 b x}{64}+\frac{7 a}{64}-\frac{\left(b x +a \right)^{3}}{12}-\left(b x +a \right)^{2} \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{8}-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{32}\right)}{b^{3}}+\frac{3 c \,d^{2} \left(\left(b x +a \right)^{2} \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{8}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{16}+\frac{7 b x}{64}+\frac{7 a}{64}-\frac{\left(b x +a \right)^{3}}{12}-\left(b x +a \right)^{2} \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{8}-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{32}\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(\left(b x +a \right) \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{16}+\frac{\left(\sin^{2}\left(b x +a \right)\right)}{16}-\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{16}\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(\left(b x +a \right) \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{16}+\frac{\left(\sin^{2}\left(b x +a \right)\right)}{16}-\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{16}\right)}{b^{2}}+\frac{3 c^{2} d \left(\left(b x +a \right) \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{16}+\frac{\left(\sin^{2}\left(b x +a \right)\right)}{16}-\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{16}\right)}{b}-\frac{a^{3} d^{3} \left(-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{4}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{8}+\frac{b x}{8}+\frac{a}{8}\right)}{b^{3}}+\frac{3 a^{2} c \,d^{2} \left(-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{4}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{8}+\frac{b x}{8}+\frac{a}{8}\right)}{b^{2}}-\frac{3 a \,c^{2} d \left(-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{4}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{8}+\frac{b x}{8}+\frac{a}{8}\right)}{b}+c^{3} \left(-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{4}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{8}+\frac{b x}{8}+\frac{a}{8}\right)}{b}"," ",0,"1/b*(1/b^3*d^3*((b*x+a)^3*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-3/16*(b*x+a)^2*cos(b*x+a)^2+3/8*(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-21/128*(b*x+a)^2-3/128*sin(b*x+a)^2-3/32*(b*x+a)^4-(b*x+a)^3*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-3/16*(b*x+a)^2*sin(b*x+a)^4+3/8*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+3/128*sin(b*x+a)^4)-3/b^3*a*d^3*((b*x+a)^2*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/8*(b*x+a)*cos(b*x+a)^2+1/16*cos(b*x+a)*sin(b*x+a)+7/64*b*x+7/64*a-1/12*(b*x+a)^3-(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/8*(b*x+a)*sin(b*x+a)^4-1/32*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a))+3/b^2*c*d^2*((b*x+a)^2*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/8*(b*x+a)*cos(b*x+a)^2+1/16*cos(b*x+a)*sin(b*x+a)+7/64*b*x+7/64*a-1/12*(b*x+a)^3-(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/8*(b*x+a)*sin(b*x+a)^4-1/32*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a))+3/b^3*a^2*d^3*((b*x+a)*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/16*(b*x+a)^2+1/16*sin(b*x+a)^2-(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/16*sin(b*x+a)^4)-6/b^2*a*c*d^2*((b*x+a)*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/16*(b*x+a)^2+1/16*sin(b*x+a)^2-(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/16*sin(b*x+a)^4)+3/b*c^2*d*((b*x+a)*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/16*(b*x+a)^2+1/16*sin(b*x+a)^2-(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/16*sin(b*x+a)^4)-1/b^3*a^3*d^3*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)+3/b^2*a^2*c*d^2*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)-3/b*a*c^2*d*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)+c^3*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a))","B"
82,1,519,71,0.021000," ","int((d*x+c)^2*cos(b*x+a)^2*sin(b*x+a)^2,x)","\frac{\frac{d^{2} \left(\left(b x +a \right)^{2} \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{8}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{16}+\frac{7 b x}{64}+\frac{7 a}{64}-\frac{\left(b x +a \right)^{3}}{12}-\left(b x +a \right)^{2} \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{8}-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{32}\right)}{b^{2}}-\frac{2 a \,d^{2} \left(\left(b x +a \right) \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{16}+\frac{\left(\sin^{2}\left(b x +a \right)\right)}{16}-\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{16}\right)}{b^{2}}+\frac{2 c d \left(\left(b x +a \right) \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{16}+\frac{\left(\sin^{2}\left(b x +a \right)\right)}{16}-\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{16}\right)}{b}+\frac{a^{2} d^{2} \left(-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{4}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{8}+\frac{b x}{8}+\frac{a}{8}\right)}{b^{2}}-\frac{2 a c d \left(-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{4}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{8}+\frac{b x}{8}+\frac{a}{8}\right)}{b}+c^{2} \left(-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{4}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{8}+\frac{b x}{8}+\frac{a}{8}\right)}{b}"," ",0,"1/b*(1/b^2*d^2*((b*x+a)^2*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/8*(b*x+a)*cos(b*x+a)^2+1/16*cos(b*x+a)*sin(b*x+a)+7/64*b*x+7/64*a-1/12*(b*x+a)^3-(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/8*(b*x+a)*sin(b*x+a)^4-1/32*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a))-2/b^2*a*d^2*((b*x+a)*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/16*(b*x+a)^2+1/16*sin(b*x+a)^2-(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/16*sin(b*x+a)^4)+2/b*c*d*((b*x+a)*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/16*(b*x+a)^2+1/16*sin(b*x+a)^2-(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/16*sin(b*x+a)^4)+1/b^2*a^2*d^2*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)-2/b*a*c*d*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)+c^2*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a))","B"
83,1,194,47,0.023000," ","int((d*x+c)*cos(b*x+a)^2*sin(b*x+a)^2,x)","\frac{\frac{d \left(\left(b x +a \right) \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{16}+\frac{\left(\sin^{2}\left(b x +a \right)\right)}{16}-\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{16}\right)}{b}-\frac{d a \left(-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{4}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{8}+\frac{b x}{8}+\frac{a}{8}\right)}{b}+c \left(-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{4}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{8}+\frac{b x}{8}+\frac{a}{8}\right)}{b}"," ",0,"1/b*(1/b*d*((b*x+a)*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/16*(b*x+a)^2+1/16*sin(b*x+a)^2-(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/16*sin(b*x+a)^4)-1/b*d*a*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)+c*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a))","B"
84,1,105,72,0.026000," ","int(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c),x)","-\frac{\Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{8 d}-\frac{\Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{8 d}+\frac{\ln \left(\left(b x +a \right) d -d a +c b \right)}{8 d}"," ",0,"-1/8*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d-1/8*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d+1/8*ln((b*x+a)*d-d*a+c*b)/d","A"
85,1,156,96,0.026000," ","int(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c)^2,x)","\frac{-\frac{b^{2} \left(-\frac{4 \cos \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{4 \left(\frac{4 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}-\frac{4 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}\right)}{d}\right)}{32}-\frac{b^{2}}{8 \left(\left(b x +a \right) d -d a +c b \right) d}}{b}"," ",0,"1/b*(-1/32*b^2*(-4*cos(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)/d-4*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d-4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d)/d)-1/8*b^2/((b*x+a)*d-d*a+c*b)/d)","A"
86,1,193,121,0.026000," ","int(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c)^3,x)","\frac{-\frac{b^{3} \left(-\frac{2 \cos \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{2 \left(-\frac{4 \sin \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{16 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}+\frac{16 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}}{d}\right)}{d}\right)}{32}-\frac{b^{3}}{16 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}}{b}"," ",0,"1/b*(-1/32*b^3*(-2*cos(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)^2/d-2*(-4*sin(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)/d+4*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d+4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d)/d)/d)-1/16*b^3/((b*x+a)*d-d*a+c*b)^2/d)","A"
87,1,230,146,0.027000," ","int(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c)^4,x)","\frac{-\frac{b^{4} \left(-\frac{4 \cos \left(4 b x +4 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}-\frac{4 \left(-\frac{2 \sin \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{8 \cos \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{8 \left(\frac{4 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}-\frac{4 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}\right)}{d}}{d}\right)}{3 d}\right)}{32}-\frac{b^{4}}{24 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}}{b}"," ",0,"1/b*(-1/32*b^4*(-4/3*cos(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)^3/d-4/3*(-2*sin(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)^2/d+2*(-4*cos(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)/d-4*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d-4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d)/d)/d)/d)-1/24*b^4/((b*x+a)*d-d*a+c*b)^3/d)","A"
88,0,0,377,0.211000," ","int((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \left(\cos^{2}\left(b x +a \right)\right) \left(\sin^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a)^3,x)","F"
89,1,1812,304,0.115000," ","int((d*x+c)^4*cos(b*x+a)^2*sin(b*x+a)^3,x)","\text{Expression too large to display}"," ",0,"1/b*(1/b^4*d^4*(-1/3*(b*x+a)^4*(2+sin(b*x+a)^2)*cos(b*x+a)+8/15*(b*x+a)^3*sin(b*x+a)+8/5*(b*x+a)^2*cos(b*x+a)-3424/1125*cos(b*x+a)-3424/1125*(b*x+a)*sin(b*x+a)+4/45*(b*x+a)^3*sin(b*x+a)^3+4/45*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+88/3375*(b*x+a)*sin(b*x+a)^3+88/10125*(2+sin(b*x+a)^2)*cos(b*x+a)+1/5*(b*x+a)^4*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-4/25*(b*x+a)^3*sin(b*x+a)^5-12/125*(b*x+a)^2*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)+24/625*(b*x+a)*sin(b*x+a)^5+24/3125*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))-4/b^4*a*d^4*(-1/3*(b*x+a)^3*(2+sin(b*x+a)^2)*cos(b*x+a)+2/5*(b*x+a)^2*sin(b*x+a)-856/1125*sin(b*x+a)+4/5*(b*x+a)*cos(b*x+a)+1/15*(b*x+a)^2*sin(b*x+a)^3+2/45*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+22/3375*sin(b*x+a)^3+1/5*(b*x+a)^3*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-3/25*(b*x+a)^2*sin(b*x+a)^5-6/125*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)+6/625*sin(b*x+a)^5)+4/b^3*c*d^3*(-1/3*(b*x+a)^3*(2+sin(b*x+a)^2)*cos(b*x+a)+2/5*(b*x+a)^2*sin(b*x+a)-856/1125*sin(b*x+a)+4/5*(b*x+a)*cos(b*x+a)+1/15*(b*x+a)^2*sin(b*x+a)^3+2/45*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+22/3375*sin(b*x+a)^3+1/5*(b*x+a)^3*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-3/25*(b*x+a)^2*sin(b*x+a)^5-6/125*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)+6/625*sin(b*x+a)^5)+6/b^4*a^2*d^4*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/15*cos(b*x+a)+4/15*(b*x+a)*sin(b*x+a)+2/45*(b*x+a)*sin(b*x+a)^3+2/135*(2+sin(b*x+a)^2)*cos(b*x+a)+1/5*(b*x+a)^2*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-2/25*(b*x+a)*sin(b*x+a)^5-2/125*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))-12/b^3*a*c*d^3*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/15*cos(b*x+a)+4/15*(b*x+a)*sin(b*x+a)+2/45*(b*x+a)*sin(b*x+a)^3+2/135*(2+sin(b*x+a)^2)*cos(b*x+a)+1/5*(b*x+a)^2*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-2/25*(b*x+a)*sin(b*x+a)^5-2/125*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))+6/b^2*c^2*d^2*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/15*cos(b*x+a)+4/15*(b*x+a)*sin(b*x+a)+2/45*(b*x+a)*sin(b*x+a)^3+2/135*(2+sin(b*x+a)^2)*cos(b*x+a)+1/5*(b*x+a)^2*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-2/25*(b*x+a)*sin(b*x+a)^5-2/125*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))-4/b^4*a^3*d^4*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/45*sin(b*x+a)^3+2/15*sin(b*x+a)+1/5*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-1/25*sin(b*x+a)^5)+12/b^3*a^2*c*d^3*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/45*sin(b*x+a)^3+2/15*sin(b*x+a)+1/5*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-1/25*sin(b*x+a)^5)-12/b^2*a*c^2*d^2*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/45*sin(b*x+a)^3+2/15*sin(b*x+a)+1/5*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-1/25*sin(b*x+a)^5)+4/b*c^3*d*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/45*sin(b*x+a)^3+2/15*sin(b*x+a)+1/5*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-1/25*sin(b*x+a)^5)+1/b^4*a^4*d^4*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3)-4/b^3*a^3*c*d^3*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3)+6/b^2*a^2*c^2*d^2*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3)-4/b*a*c^3*d*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3)+c^4*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3))","B"
90,1,992,235,0.023000," ","int((d*x+c)^3*cos(b*x+a)^2*sin(b*x+a)^3,x)","\frac{\frac{d^{3} \left(-\frac{\left(b x +a \right)^{3} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right)^{2} \sin \left(b x +a \right)}{5}-\frac{856 \sin \left(b x +a \right)}{1125}+\frac{4 \left(b x +a \right) \cos \left(b x +a \right)}{5}+\frac{\left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{15}+\frac{2 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{45}+\frac{22 \left(\sin^{3}\left(b x +a \right)\right)}{3375}+\frac{\left(b x +a \right)^{3} \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}-\frac{3 \left(b x +a \right)^{2} \left(\sin^{5}\left(b x +a \right)\right)}{25}-\frac{6 \left(b x +a \right) \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{125}+\frac{6 \left(\sin^{5}\left(b x +a \right)\right)}{625}\right)}{b^{3}}-\frac{3 a \,d^{3} \left(-\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{4 \cos \left(b x +a \right)}{15}+\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{15}+\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{45}+\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{135}+\frac{\left(b x +a \right)^{2} \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}-\frac{2 \left(b x +a \right) \left(\sin^{5}\left(b x +a \right)\right)}{25}-\frac{2 \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{125}\right)}{b^{3}}+\frac{3 c \,d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{4 \cos \left(b x +a \right)}{15}+\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{15}+\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{45}+\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{135}+\frac{\left(b x +a \right)^{2} \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}-\frac{2 \left(b x +a \right) \left(\sin^{5}\left(b x +a \right)\right)}{25}-\frac{2 \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{125}\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{45}+\frac{2 \sin \left(b x +a \right)}{15}+\frac{\left(b x +a \right) \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}-\frac{\left(\sin^{5}\left(b x +a \right)\right)}{25}\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{45}+\frac{2 \sin \left(b x +a \right)}{15}+\frac{\left(b x +a \right) \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}-\frac{\left(\sin^{5}\left(b x +a \right)\right)}{25}\right)}{b^{2}}+\frac{3 c^{2} d \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{45}+\frac{2 \sin \left(b x +a \right)}{15}+\frac{\left(b x +a \right) \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}-\frac{\left(\sin^{5}\left(b x +a \right)\right)}{25}\right)}{b}-\frac{a^{3} d^{3} \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{3}\left(b x +a \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{15}\right)}{b^{3}}+\frac{3 a^{2} c \,d^{2} \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{3}\left(b x +a \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{15}\right)}{b^{2}}-\frac{3 a \,c^{2} d \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{3}\left(b x +a \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{15}\right)}{b}+c^{3} \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{3}\left(b x +a \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{15}\right)}{b}"," ",0,"1/b*(1/b^3*d^3*(-1/3*(b*x+a)^3*(2+sin(b*x+a)^2)*cos(b*x+a)+2/5*(b*x+a)^2*sin(b*x+a)-856/1125*sin(b*x+a)+4/5*(b*x+a)*cos(b*x+a)+1/15*(b*x+a)^2*sin(b*x+a)^3+2/45*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+22/3375*sin(b*x+a)^3+1/5*(b*x+a)^3*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-3/25*(b*x+a)^2*sin(b*x+a)^5-6/125*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)+6/625*sin(b*x+a)^5)-3/b^3*a*d^3*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/15*cos(b*x+a)+4/15*(b*x+a)*sin(b*x+a)+2/45*(b*x+a)*sin(b*x+a)^3+2/135*(2+sin(b*x+a)^2)*cos(b*x+a)+1/5*(b*x+a)^2*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-2/25*(b*x+a)*sin(b*x+a)^5-2/125*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))+3/b^2*c*d^2*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/15*cos(b*x+a)+4/15*(b*x+a)*sin(b*x+a)+2/45*(b*x+a)*sin(b*x+a)^3+2/135*(2+sin(b*x+a)^2)*cos(b*x+a)+1/5*(b*x+a)^2*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-2/25*(b*x+a)*sin(b*x+a)^5-2/125*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))+3/b^3*a^2*d^3*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/45*sin(b*x+a)^3+2/15*sin(b*x+a)+1/5*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-1/25*sin(b*x+a)^5)-6/b^2*a*c*d^2*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/45*sin(b*x+a)^3+2/15*sin(b*x+a)+1/5*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-1/25*sin(b*x+a)^5)+3/b*c^2*d*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/45*sin(b*x+a)^3+2/15*sin(b*x+a)+1/5*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-1/25*sin(b*x+a)^5)-1/b^3*a^3*d^3*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3)+3/b^2*a^2*c*d^2*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3)-3/b*a*c^2*d*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3)+c^3*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3))","B"
91,1,466,166,0.023000," ","int((d*x+c)^2*cos(b*x+a)^2*sin(b*x+a)^3,x)","\frac{\frac{d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{4 \cos \left(b x +a \right)}{15}+\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{15}+\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{45}+\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{135}+\frac{\left(b x +a \right)^{2} \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}-\frac{2 \left(b x +a \right) \left(\sin^{5}\left(b x +a \right)\right)}{25}-\frac{2 \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{125}\right)}{b^{2}}-\frac{2 a \,d^{2} \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{45}+\frac{2 \sin \left(b x +a \right)}{15}+\frac{\left(b x +a \right) \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}-\frac{\left(\sin^{5}\left(b x +a \right)\right)}{25}\right)}{b^{2}}+\frac{2 c d \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{45}+\frac{2 \sin \left(b x +a \right)}{15}+\frac{\left(b x +a \right) \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}-\frac{\left(\sin^{5}\left(b x +a \right)\right)}{25}\right)}{b}+\frac{a^{2} d^{2} \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{3}\left(b x +a \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{15}\right)}{b^{2}}-\frac{2 a c d \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{3}\left(b x +a \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{15}\right)}{b}+c^{2} \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{3}\left(b x +a \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{15}\right)}{b}"," ",0,"1/b*(1/b^2*d^2*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/15*cos(b*x+a)+4/15*(b*x+a)*sin(b*x+a)+2/45*(b*x+a)*sin(b*x+a)^3+2/135*(2+sin(b*x+a)^2)*cos(b*x+a)+1/5*(b*x+a)^2*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-2/25*(b*x+a)*sin(b*x+a)^5-2/125*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))-2/b^2*a*d^2*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/45*sin(b*x+a)^3+2/15*sin(b*x+a)+1/5*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-1/25*sin(b*x+a)^5)+2/b*c*d*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/45*sin(b*x+a)^3+2/15*sin(b*x+a)+1/5*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-1/25*sin(b*x+a)^5)+1/b^2*a^2*d^2*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3)-2/b*a*c*d*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3)+c^2*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3))","B"
92,1,163,97,0.023000," ","int((d*x+c)*cos(b*x+a)^2*sin(b*x+a)^3,x)","\frac{\frac{d \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{45}+\frac{2 \sin \left(b x +a \right)}{15}+\frac{\left(b x +a \right) \left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}-\frac{\left(\sin^{5}\left(b x +a \right)\right)}{25}\right)}{b}-\frac{d a \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{3}\left(b x +a \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{15}\right)}{b}+c \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{3}\left(b x +a \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{15}\right)}{b}"," ",0,"1/b*(1/b*d*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/45*sin(b*x+a)^3+2/15*sin(b*x+a)+1/5*(b*x+a)*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)-1/25*sin(b*x+a)^5)-1/b*d*a*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3)+c*(-1/5*sin(b*x+a)^2*cos(b*x+a)^3-2/15*cos(b*x+a)^3))","A"
93,1,253,173,0.024000," ","int(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c),x)","\frac{-\frac{b \left(\frac{5 \Si \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \cos \left(\frac{-5 d a +5 c b}{d}\right)}{d}-\frac{5 \Ci \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \sin \left(\frac{-5 d a +5 c b}{d}\right)}{d}\right)}{80}+\frac{b \left(\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}\right)}{8}+\frac{b \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}-\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{48}}{b}"," ",0,"1/b*(-1/80*b*(5*Si(5*b*x+5*a+5*(-a*d+b*c)/d)*cos(5*(-a*d+b*c)/d)/d-5*Ci(5*b*x+5*a+5*(-a*d+b*c)/d)*sin(5*(-a*d+b*c)/d)/d)+1/8*b*(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d)+1/48*b*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d-3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d))","A"
94,1,365,239,0.027000," ","int(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c)^2,x)","\frac{-\frac{b^{2} \left(-\frac{5 \sin \left(5 b x +5 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{25 \Si \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \sin \left(\frac{-5 d a +5 c b}{d}\right)}{d}+\frac{25 \Ci \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \cos \left(\frac{-5 d a +5 c b}{d}\right)}{d}}{d}\right)}{80}+\frac{b^{2} \left(-\frac{\sin \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}+\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}}{d}\right)}{8}+\frac{b^{2} \left(-\frac{3 \sin \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{9 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}+\frac{9 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}}{d}\right)}{48}}{b}"," ",0,"1/b*(-1/80*b^2*(-5*sin(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)/d+5*(5*Si(5*b*x+5*a+5*(-a*d+b*c)/d)*sin(5*(-a*d+b*c)/d)/d+5*Ci(5*b*x+5*a+5*(-a*d+b*c)/d)*cos(5*(-a*d+b*c)/d)/d)/d)+1/8*b^2*(-sin(b*x+a)/((b*x+a)*d-d*a+c*b)/d+(Si(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)/d)+1/48*b^2*(-3*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d+3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d+3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d)/d))","A"
95,1,475,314,0.027000," ","int(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c)^3,x)","\frac{-\frac{b^{3} \left(-\frac{5 \sin \left(5 b x +5 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{25 \cos \left(5 b x +5 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right) d}-\frac{25 \left(\frac{5 \Si \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \cos \left(\frac{-5 d a +5 c b}{d}\right)}{d}-\frac{5 \Ci \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \sin \left(\frac{-5 d a +5 c b}{d}\right)}{d}\right)}{2 d}}{d}\right)}{80}+\frac{b^{3} \left(-\frac{\sin \left(b x +a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{\cos \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}}{d}}{2 d}\right)}{8}+\frac{b^{3} \left(-\frac{3 \sin \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{9 \cos \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right) d}-\frac{9 \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}-\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{2 d}}{d}\right)}{48}}{b}"," ",0,"1/b*(-1/80*b^3*(-5/2*sin(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)^2/d+5/2*(-5*cos(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)/d-5*(5*Si(5*b*x+5*a+5*(-a*d+b*c)/d)*cos(5*(-a*d+b*c)/d)/d-5*Ci(5*b*x+5*a+5*(-a*d+b*c)/d)*sin(5*(-a*d+b*c)/d)/d)/d)/d)+1/8*b^3*(-1/2*sin(b*x+a)/((b*x+a)*d-d*a+c*b)^2/d+1/2*(-cos(b*x+a)/((b*x+a)*d-d*a+c*b)/d-(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d)/d)/d)+1/48*b^3*(-3/2*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^2/d+3/2*(-3*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d-3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d-3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d)/d)/d))","A"
96,1,580,383,0.027000," ","int(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c)^4,x)","\frac{-\frac{b^{4} \left(-\frac{5 \sin \left(5 b x +5 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{25 \cos \left(5 b x +5 a \right)}{6 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{25 \left(-\frac{5 \sin \left(5 b x +5 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{25 \Si \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \sin \left(\frac{-5 d a +5 c b}{d}\right)}{d}+\frac{25 \Ci \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \cos \left(\frac{-5 d a +5 c b}{d}\right)}{d}}{d}\right)}{6 d}}{d}\right)}{80}+\frac{b^{4} \left(-\frac{\sin \left(b x +a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{\cos \left(b x +a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{-\frac{\sin \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}+\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}}{d}}{2 d}}{3 d}\right)}{8}+\frac{b^{4} \left(-\frac{\sin \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{3 \cos \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{3 \left(-\frac{3 \sin \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{9 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}+\frac{9 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}}{d}\right)}{2 d}}{d}\right)}{48}}{b}"," ",0,"1/b*(-1/80*b^4*(-5/3*sin(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)^3/d+5/3*(-5/2*cos(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)^2/d-5/2*(-5*sin(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)/d+5*(5*Si(5*b*x+5*a+5*(-a*d+b*c)/d)*sin(5*(-a*d+b*c)/d)/d+5*Ci(5*b*x+5*a+5*(-a*d+b*c)/d)*cos(5*(-a*d+b*c)/d)/d)/d)/d)/d)+1/8*b^4*(-1/3*sin(b*x+a)/((b*x+a)*d-d*a+c*b)^3/d+1/3*(-1/2*cos(b*x+a)/((b*x+a)*d-d*a+c*b)^2/d-1/2*(-sin(b*x+a)/((b*x+a)*d-d*a+c*b)/d+(Si(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)/d)/d)/d)+1/48*b^4*(-sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^3/d+(-3/2*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^2/d-3/2*(-3*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d+3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d+3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d)/d)/d)/d))","A"
97,0,0,133,0.241000," ","int((d*x+c)^m*cos(b*x+a)*cot(b*x+a),x)","\int \left(d x +c \right)^{m} \cos \left(b x +a \right) \cot \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)*cot(b*x+a),x)","F"
98,1,1295,311,0.227000," ","int((d*x+c)^4*cos(b*x+a)*cot(b*x+a),x)","-\frac{d^{4} a^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{12 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 c^{2} d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{12 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{4}}{b}-\frac{d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{4}}{b}+\frac{\left(d^{4} x^{4} b^{4}+4 b^{4} c \,d^{3} x^{3}-4 i b^{3} d^{4} x^{3}+6 b^{4} c^{2} d^{2} x^{2}-12 i b^{3} c \,d^{3} x^{2}+4 b^{4} c^{3} d x -12 i b^{3} c^{2} d^{2} x +b^{4} c^{4}-4 i b^{3} c^{3} d -12 b^{2} d^{4} x^{2}-24 b^{2} c \,d^{3} x +24 i b \,d^{4} x -12 c^{2} d^{2} b^{2}+24 i b c \,d^{3}+24 d^{4}\right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{5}}+\frac{\left(d^{4} x^{4} b^{4}+4 b^{4} c \,d^{3} x^{3}+4 i b^{3} d^{4} x^{3}+6 b^{4} c^{2} d^{2} x^{2}+12 i b^{3} c \,d^{3} x^{2}+4 b^{4} c^{3} d x +12 i b^{3} c^{2} d^{2} x +b^{4} c^{4}+4 i b^{3} c^{3} d -12 b^{2} d^{4} x^{2}-24 b^{2} c \,d^{3} x -24 i b \,d^{4} x -12 c^{2} d^{2} b^{2}-24 i b c \,d^{3}+24 d^{4}\right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{5}}-\frac{2 c^{4} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{24 d^{4} \polylog \left(5, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 d^{4} \polylog \left(5, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{4 c^{3} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}+\frac{6 c^{2} d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{b^{3}}+\frac{8 c \,d^{3} a^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 c^{2} d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{8 c^{3} d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{3}}{b^{4}}-\frac{4 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}-\frac{24 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{4 i c^{3} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 i c^{3} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{24 c \,d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 c \,d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{24 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 i c \,d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{4 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{24 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{4 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{4 c^{3} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{6 c^{2} d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{6 c^{2} d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{12 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{12 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c^{2} d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c \,d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{5}}-\frac{2 d^{4} a^{4} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}"," ",0,"-12/b^3*c^2*d^2*polylog(3,-exp(I*(b*x+a)))+12/b^3*c^2*d^2*polylog(3,exp(I*(b*x+a)))-1/b^5*d^4*a^4*ln(1-exp(I*(b*x+a)))+12/b^3*d^4*polylog(3,exp(I*(b*x+a)))*x^2-12/b^3*d^4*polylog(3,-exp(I*(b*x+a)))*x^2+24*d^4*polylog(5,-exp(I*(b*x+a)))/b^5-24*d^4*polylog(5,exp(I*(b*x+a)))/b^5+1/2*(d^4*x^4*b^4+4*b^4*c*d^3*x^3+6*b^4*c^2*d^2*x^2+4*b^4*c^3*d*x-4*I*b^3*d^4*x^3+b^4*c^4-12*b^2*d^4*x^2-12*I*b^3*c*d^3*x^2-24*b^2*c*d^3*x-12*I*b^3*c^2*d^2*x-12*c^2*d^2*b^2-4*I*b^3*c^3*d+24*I*b*d^4*x+24*d^4+24*I*b*c*d^3)/b^5*exp(-I*(b*x+a))+1/2*(d^4*x^4*b^4+4*b^4*c*d^3*x^3+6*b^4*c^2*d^2*x^2+4*b^4*c^3*d*x+4*I*b^3*d^4*x^3+b^4*c^4-12*b^2*d^4*x^2+12*I*b^3*c*d^3*x^2-24*b^2*c*d^3*x+12*I*b^3*c^2*d^2*x-12*c^2*d^2*b^2+4*I*b^3*c^3*d-24*I*b*d^4*x+24*d^4-24*I*b*c*d^3)/b^5*exp(I*(b*x+a))-2/b*c^4*arctanh(exp(I*(b*x+a)))-4/b^2*c^3*d*ln(exp(I*(b*x+a))+1)*a-24*I/b^4*d^4*polylog(4,-exp(I*(b*x+a)))*x-24*I/b^4*c*d^3*polylog(4,-exp(I*(b*x+a)))+4*I/b^2*c^3*d*polylog(2,-exp(I*(b*x+a)))+4*I/b^2*d^4*polylog(2,-exp(I*(b*x+a)))*x^3+8/b^4*c*d^3*a^3*arctanh(exp(I*(b*x+a)))-12/b^3*c^2*d^2*a^2*arctanh(exp(I*(b*x+a)))+8/b^2*c^3*d*a*arctanh(exp(I*(b*x+a)))+6/b^3*c^2*d^2*ln(exp(I*(b*x+a))+1)*a^2+1/b^5*d^4*a^4*ln(exp(I*(b*x+a))+1)-2/b^5*d^4*a^4*arctanh(exp(I*(b*x+a)))-4/b*c^3*d*ln(exp(I*(b*x+a))+1)*x+4/b*c^3*d*ln(1-exp(I*(b*x+a)))*x+4/b^2*c^3*d*ln(1-exp(I*(b*x+a)))*a-6/b*c^2*d^2*ln(exp(I*(b*x+a))+1)*x^2-24/b^3*c*d^3*polylog(3,-exp(I*(b*x+a)))*x-6/b^3*c^2*d^2*a^2*ln(1-exp(I*(b*x+a)))+6/b*c^2*d^2*ln(1-exp(I*(b*x+a)))*x^2+24/b^3*c*d^3*polylog(3,exp(I*(b*x+a)))*x+24*I/b^4*c*d^3*polylog(4,exp(I*(b*x+a)))-4*I/b^2*d^4*polylog(2,exp(I*(b*x+a)))*x^3+24*I/b^4*d^4*polylog(4,exp(I*(b*x+a)))*x-4*I/b^2*c^3*d*polylog(2,exp(I*(b*x+a)))+1/b*d^4*ln(1-exp(I*(b*x+a)))*x^4-1/b*d^4*ln(exp(I*(b*x+a))+1)*x^4-12*I/b^2*c^2*d^2*polylog(2,exp(I*(b*x+a)))*x-12*I/b^2*c*d^3*polylog(2,exp(I*(b*x+a)))*x^2-4/b*c*d^3*ln(exp(I*(b*x+a))+1)*x^3+4/b*c*d^3*ln(1-exp(I*(b*x+a)))*x^3+4/b^4*c*d^3*ln(1-exp(I*(b*x+a)))*a^3-4/b^4*c*d^3*ln(exp(I*(b*x+a))+1)*a^3+12*I/b^2*c*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+12*I/b^2*c^2*d^2*polylog(2,-exp(I*(b*x+a)))*x","B"
99,1,847,236,0.151000," ","int((d*x+c)^3*cos(b*x+a)*cot(b*x+a),x)","-\frac{6 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}-\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{6 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{\left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}+3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x +6 i b^{2} c \,d^{2} x +b^{3} c^{3}+3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b -6 i d^{3}\right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{4}}+\frac{\left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}-3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x -6 i b^{2} c \,d^{2} x +b^{3} c^{3}-3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b +6 i d^{3}\right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{4}}-\frac{2 c^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}+\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{6 c \,d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c^{2} d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{3}}{b^{4}}+\frac{2 d^{3} a^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"-6*I/b^2*c*d^2*polylog(2,exp(I*(b*x+a)))*x+6*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4-6/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+6/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))+6/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x-6/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x-6*I*d^3*polylog(4,-exp(I*(b*x+a)))/b^4+6*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x+1/2*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3+3*I*b^2*d^3*x^2-6*b*d^3*x+6*I*b^2*c*d^2*x-6*c*d^2*b+3*I*b^2*c^2*d-6*I*d^3)/b^4*exp(I*(b*x+a))+1/2*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3-3*I*b^2*d^3*x^2-6*b*d^3*x-6*I*b^2*c*d^2*x-6*c*d^2*b-3*I*b^2*c^2*d+6*I*d^3)/b^4*exp(-I*(b*x+a))-2/b*c^3*arctanh(exp(I*(b*x+a)))+2/b^4*d^3*a^3*arctanh(exp(I*(b*x+a)))-3/b^2*c^2*d*ln(exp(I*(b*x+a))+1)*a+3/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))+1)-1/b^4*d^3*ln(exp(I*(b*x+a))+1)*a^3-6/b^3*c*d^2*a^2*arctanh(exp(I*(b*x+a)))+6/b^2*c^2*d*a*arctanh(exp(I*(b*x+a)))+3*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+3*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-3*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))-3*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2-3/b*c^2*d*ln(exp(I*(b*x+a))+1)*x+3/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+3/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-3/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+3/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2-3/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2+1/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+1/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3-1/b*d^3*ln(exp(I*(b*x+a))+1)*x^3","B"
100,1,479,159,0.128000," ","int((d*x+c)^2*cos(b*x+a)*cot(b*x+a),x)","\frac{\left(d^{2} x^{2} b^{2}+2 b^{2} c d x +2 i b \,d^{2} x +b^{2} c^{2}+2 i b c d -2 d^{2}\right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{3}}+\frac{\left(d^{2} x^{2} b^{2}+2 b^{2} c d x -2 i b \,d^{2} x +b^{2} c^{2}-2 i b c d -2 d^{2}\right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{3}}-\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{2 d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 c^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{b^{3}}+\frac{2 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{4 c d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}"," ",0,"1/2*(d^2*x^2*b^2+2*b^2*c*d*x+b^2*c^2+2*I*b*d^2*x-2*d^2+2*I*b*c*d)/b^3*exp(I*(b*x+a))+1/2*(d^2*x^2*b^2+2*b^2*c*d*x+b^2*c^2-2*I*b*d^2*x-2*d^2-2*I*b*c*d)/b^3*exp(-I*(b*x+a))-2/b*c*d*ln(exp(I*(b*x+a))+1)*x-2/b^2*c*d*ln(exp(I*(b*x+a))+1)*a+2/b*c*d*ln(1-exp(I*(b*x+a)))*x+2/b^2*c*d*ln(1-exp(I*(b*x+a)))*a-2/b^3*d^2*a^2*arctanh(exp(I*(b*x+a)))-2*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+2*d^2*polylog(3,exp(I*(b*x+a)))/b^3-2/b*c^2*arctanh(exp(I*(b*x+a)))-1/b*d^2*ln(exp(I*(b*x+a))+1)*x^2+1/b^3*d^2*ln(exp(I*(b*x+a))+1)*a^2+2*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x+1/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-1/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2-2*I/b^2*d^2*polylog(2,exp(I*(b*x+a)))*x+4/b^2*c*d*a*arctanh(exp(I*(b*x+a)))-2*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))+2*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))","B"
101,1,199,86,0.076000," ","int((d*x+c)*cos(b*x+a)*cot(b*x+a),x)","\frac{d \cos \left(b x +a \right) x}{b}-\frac{d \sin \left(b x +a \right)}{b^{2}}+\frac{c \cos \left(b x +a \right)}{b}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{i d \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{i d \dilog \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}-\frac{d a \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b^{2}}+\frac{c \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b}"," ",0,"1/b*d*cos(b*x+a)*x-d*sin(b*x+a)/b^2+1/b*c*cos(b*x+a)+1/b*d*ln(1-exp(I*(b*x+a)))*x-1/b*d*ln(exp(I*(b*x+a))+1)*x+I/b^2*d*dilog(exp(I*(b*x+a))+1)-I/b^2*d*dilog(1-exp(I*(b*x+a)))+1/b^2*d*ln(1-exp(I*(b*x+a)))*a-1/b^2*d*ln(exp(I*(b*x+a))+1)*a-1/b^2*d*a*ln(csc(b*x+a)-cot(b*x+a))+1/b*c*ln(csc(b*x+a)-cot(b*x+a))","B"
102,0,0,69,0.237000," ","int(cos(b*x+a)*cot(b*x+a)/(d*x+c),x)","\int \frac{\cos \left(b x +a \right) \cot \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(cos(b*x+a)*cot(b*x+a)/(d*x+c),x)","F"
103,0,0,87,0.471000," ","int(cos(b*x+a)*cot(b*x+a)/(d*x+c)^2,x)","\int \frac{\cos \left(b x +a \right) \cot \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(cos(b*x+a)*cot(b*x+a)/(d*x+c)^2,x)","F"
104,0,0,18,0.089000," ","int((d*x+c)^m*cot(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \left(\cot^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cot(b*x+a)^2,x)","F"
105,1,913,142,0.130000," ","int((d*x+c)^4*cot(b*x+a)^2,x)","\frac{24 d^{3} c \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 d^{3} c \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{24 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{24 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{24 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{4 d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{4 d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{5}}+\frac{4 d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b^{2}}-\frac{24 i d^{3} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{24 i d^{3} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-c \,d^{3} x^{4}-\frac{d^{4} x^{5}}{5}-c^{4} x -2 c^{2} d^{2} x^{3}-2 c^{3} d \,x^{2}+\frac{8 d^{4} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{4 d^{4} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{5}}+\frac{4 d \,c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{4 d \,c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{8 d \,c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 i d^{4} a^{4}}{b^{5}}-\frac{2 i d^{4} x^{4}}{b}-\frac{2 i \left(d^{4} x^{4}+4 c \,d^{3} x^{3}+6 c^{2} d^{2} x^{2}+4 c^{3} d x +c^{4}\right)}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}-\frac{24 i d^{2} c^{2} a x}{b^{2}}+\frac{24 i d^{3} c \,a^{2} x}{b^{3}}+\frac{16 i d^{3} c \,a^{3}}{b^{4}}-\frac{8 i d^{4} a^{3} x}{b^{4}}-\frac{8 i d^{3} c \,x^{3}}{b}-\frac{12 i d^{2} c^{2} x^{2}}{b}-\frac{12 i d^{2} c^{2} a^{2}}{b^{3}}+\frac{24 d^{2} c^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{24 d^{3} c \,a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 d^{2} c^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{12 d^{3} c \,a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}-\frac{12 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{12 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{12 i d^{2} c^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{12 i d^{2} c^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{2} c^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{12 d^{2} c^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{12 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}+\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}+\frac{12 d^{3} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}"," ",0,"24/b^4*d^3*c*polylog(3,-exp(I*(b*x+a)))+24/b^4*d^3*c*polylog(3,exp(I*(b*x+a)))+24/b^4*d^4*polylog(3,-exp(I*(b*x+a)))*x+24/b^4*d^4*polylog(3,exp(I*(b*x+a)))*x-24*I/b^3*d^3*c*polylog(2,exp(I*(b*x+a)))*x-c*d^3*x^4+24*I*d^4*polylog(4,exp(I*(b*x+a)))/b^5-1/5*d^4*x^5-c^4*x-2*c^2*d^2*x^3-2*c^3*d*x^2+8/b^5*d^4*a^3*ln(exp(I*(b*x+a)))-4/b^5*d^4*a^3*ln(exp(I*(b*x+a))-1)+4/b^2*d*c^3*ln(exp(I*(b*x+a))-1)+4/b^2*d*c^3*ln(exp(I*(b*x+a))+1)-8/b^2*d*c^3*ln(exp(I*(b*x+a)))+24*I/b^5*d^4*polylog(4,-exp(I*(b*x+a)))-6*I/b^5*d^4*a^4-2*I/b*d^4*x^4-24*I/b^2*d^2*c^2*a*x+24*I/b^3*d^3*c*a^2*x-24*I/b^3*d^3*c*polylog(2,-exp(I*(b*x+a)))*x-12*I/b^3*d^2*c^2*polylog(2,-exp(I*(b*x+a)))+16*I/b^4*d^3*c*a^3-8*I/b^4*d^4*a^3*x-8*I/b*d^3*c*x^3-12*I/b*d^2*c^2*x^2-12*I/b^3*d^2*c^2*a^2-12*I/b^3*d^4*polylog(2,-exp(I*(b*x+a)))*x^2+24/b^3*d^2*c^2*a*ln(exp(I*(b*x+a)))-24/b^4*d^3*c*a^2*ln(exp(I*(b*x+a)))-12/b^3*d^2*c^2*a*ln(exp(I*(b*x+a))-1)+12/b^4*d^3*c*a^2*ln(exp(I*(b*x+a))-1)-2*I*(d^4*x^4+4*c*d^3*x^3+6*c^2*d^2*x^2+4*c^3*d*x+c^4)/b/(exp(2*I*(b*x+a))-1)+12/b^2*d^2*c^2*ln(1-exp(I*(b*x+a)))*x+12/b^3*d^2*c^2*ln(1-exp(I*(b*x+a)))*a+12/b^2*d^2*c^2*ln(exp(I*(b*x+a))+1)*x+12/b^2*d^3*c*ln(1-exp(I*(b*x+a)))*x^2-12/b^4*d^3*c*ln(1-exp(I*(b*x+a)))*a^2+12/b^2*d^3*c*ln(exp(I*(b*x+a))+1)*x^2+4/b^2*d^4*ln(1-exp(I*(b*x+a)))*x^3+4/b^5*d^4*ln(1-exp(I*(b*x+a)))*a^3+4/b^2*d^4*ln(exp(I*(b*x+a))+1)*x^3-12*I/b^3*d^4*polylog(2,exp(I*(b*x+a)))*x^2-12*I/b^3*d^2*c^2*polylog(2,exp(I*(b*x+a)))","B"
106,1,573,115,0.108000," ","int((d*x+c)^3*cot(b*x+a)^2,x)","\frac{3 d^{3} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}-\frac{6 d^{3} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d \,c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{3 d \,c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{6 d \,c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i d^{3} x^{3}}{b}+\frac{4 i d^{3} a^{3}}{b^{4}}-\frac{2 i \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}-\frac{12 i d^{2} c a x}{b^{2}}-\frac{3 c^{2} d \,x^{2}}{2}-c \,d^{2} x^{3}-\frac{d^{3} x^{4}}{4}-c^{3} x +\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}+\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 i d^{2} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{2} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{2} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 d^{2} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}+\frac{12 d^{2} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 d^{2} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{6 i d^{3} a^{2} x}{b^{3}}-\frac{6 i d^{2} c \,x^{2}}{b}-\frac{6 i d^{2} c \,a^{2}}{b^{3}}"," ",0,"3/b^4*d^3*a^2*ln(exp(I*(b*x+a))-1)-6/b^4*d^3*a^2*ln(exp(I*(b*x+a)))+3/b^2*d*c^2*ln(exp(I*(b*x+a))-1)+3/b^2*d*c^2*ln(exp(I*(b*x+a))+1)-6/b^2*d*c^2*ln(exp(I*(b*x+a)))-2*I/b*d^3*x^3+4*I/b^4*d^3*a^3-12*I/b^2*d^2*c*a*x+6*d^3*polylog(3,-exp(I*(b*x+a)))/b^4+6*d^3*polylog(3,exp(I*(b*x+a)))/b^4-3/2*c^2*d*x^2-c*d^2*x^3-1/4*d^3*x^4-c^3*x+3/b^2*d^3*ln(exp(I*(b*x+a))+1)*x^2+3/b^2*d^3*ln(1-exp(I*(b*x+a)))*x^2-3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^2-2*I*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/b/(exp(2*I*(b*x+a))-1)-6*I/b^3*d^3*polylog(2,exp(I*(b*x+a)))*x+6/b^2*d^2*c*ln(exp(I*(b*x+a))+1)*x-6*I/b^3*d^2*c*polylog(2,exp(I*(b*x+a)))+12/b^3*d^2*c*a*ln(exp(I*(b*x+a)))-6/b^3*d^2*c*a*ln(exp(I*(b*x+a))-1)-6*I/b^3*d^2*c*polylog(2,-exp(I*(b*x+a)))+6*I/b^3*d^3*a^2*x-6*I/b*d^2*c*x^2-6*I/b^3*d^2*c*a^2-6*I/b^3*d^3*polylog(2,-exp(I*(b*x+a)))*x+6/b^2*d^2*c*ln(1-exp(I*(b*x+a)))*x+6/b^3*d^2*c*ln(1-exp(I*(b*x+a)))*a","B"
107,1,297,89,0.093000," ","int((d*x+c)^2*cot(b*x+a)^2,x)","-\frac{d^{2} x^{3}}{3}-c d \,x^{2}-c^{2} x -\frac{4 i d^{2} a x}{b^{2}}+\frac{2 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{2 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{4 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i d^{2} a^{2}}{b^{3}}+\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}-\frac{2 i \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 i d^{2} x^{2}}{b}-\frac{2 d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{4 d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"-1/3*d^2*x^3-c*d*x^2-c^2*x-4*I/b^2*d^2*a*x+2/b^2*d*c*ln(exp(I*(b*x+a))-1)+2/b^2*d*c*ln(exp(I*(b*x+a))+1)-4/b^2*d*c*ln(exp(I*(b*x+a)))-2*I/b^3*d^2*polylog(2,-exp(I*(b*x+a)))-2*I/b^3*d^2*a^2-2*I*d^2*polylog(2,exp(I*(b*x+a)))/b^3+2/b^2*d^2*ln(exp(I*(b*x+a))+1)*x-2*I*(d^2*x^2+2*c*d*x+c^2)/b/(exp(2*I*(b*x+a))-1)+2/b^2*d^2*ln(1-exp(I*(b*x+a)))*x+2/b^3*d^2*ln(1-exp(I*(b*x+a)))*a-2*I/b*d^2*x^2-2/b^3*d^2*a*ln(exp(I*(b*x+a))-1)+4/b^3*d^2*a*ln(exp(I*(b*x+a)))","B"
108,1,49,39,0.053000," ","int((d*x+c)*cot(b*x+a)^2,x)","-\frac{d \,x^{2}}{2}-c x -\frac{d \cot \left(b x +a \right) x}{b}+\frac{d \ln \left(\sin \left(b x +a \right)\right)}{b^{2}}-\frac{c \cot \left(b x +a \right)}{b}"," ",0,"-1/2*d*x^2-c*x-1/b*d*cot(b*x+a)*x+d*ln(sin(b*x+a))/b^2-1/b*c*cot(b*x+a)","A"
109,0,0,18,0.223000," ","int(cot(b*x+a)^2/(d*x+c),x)","\int \frac{\cot^{2}\left(b x +a \right)}{d x +c}\, dx"," ",0,"int(cot(b*x+a)^2/(d*x+c),x)","F"
110,0,0,18,0.372000," ","int(cot(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\cot^{2}\left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(cot(b*x+a)^2/(d*x+c)^2,x)","F"
111,0,0,37,0.104000," ","int((d*x+c)^m*cot(b*x+a)^2*csc(b*x+a),x)","\int \left(d x +c \right)^{m} \left(\cot^{2}\left(b x +a \right)\right) \csc \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*cot(b*x+a)^2*csc(b*x+a),x)","F"
112,1,1673,380,0.187000," ","int((d*x+c)^4*cot(b*x+a)^2*csc(b*x+a),x)","\frac{d^{4} a^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{5}}+\frac{6 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 c^{2} d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{6 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{4}}{2 b}+\frac{d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{4}}{2 b}-\frac{12 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{4}}+\frac{c^{4} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{12 d^{4} \polylog \left(5, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{12 d^{4} \polylog \left(5, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{12 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{12 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{6 d^{4} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{6 d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{6 d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{3}}+\frac{d^{4} x^{4} b \,{\mathrm e}^{3 i \left(b x +a \right)}+4 c \,d^{3} x^{3} b \,{\mathrm e}^{3 i \left(b x +a \right)}+6 c^{2} d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+d^{4} x^{4} b \,{\mathrm e}^{i \left(b x +a \right)}+4 c^{3} d x b \,{\mathrm e}^{3 i \left(b x +a \right)}+4 c \,d^{3} x^{3} b \,{\mathrm e}^{i \left(b x +a \right)}-4 i d^{4} x^{3} {\mathrm e}^{3 i \left(b x +a \right)}+c^{4} b \,{\mathrm e}^{3 i \left(b x +a \right)}+6 c^{2} d^{2} x^{2} b \,{\mathrm e}^{i \left(b x +a \right)}-12 i c^{2} d^{2} x \,{\mathrm e}^{3 i \left(b x +a \right)}+4 c^{3} d x b \,{\mathrm e}^{i \left(b x +a \right)}+4 i d^{4} x^{3} {\mathrm e}^{i \left(b x +a \right)}+4 i c^{3} d \,{\mathrm e}^{i \left(b x +a \right)}+c^{4} b \,{\mathrm e}^{i \left(b x +a \right)}-12 i c \,d^{3} x^{2} {\mathrm e}^{3 i \left(b x +a \right)}+12 i c \,d^{3} x^{2} {\mathrm e}^{i \left(b x +a \right)}-4 i c^{3} d \,{\mathrm e}^{3 i \left(b x +a \right)}+12 i c^{2} d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{2 c^{3} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}-\frac{3 c^{2} d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{b^{3}}-\frac{4 c \,d^{3} a^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 c^{2} d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{4 c^{3} d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{3}}{b^{4}}+\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}+\frac{12 i d^{3} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 i d^{3} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{12 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{12 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{2 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}-\frac{2 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}-\frac{2 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{12 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{2 i c^{3} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 i c^{3} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{12 c \,d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{12 c \,d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{12 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 i c \,d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{2 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{12 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{2 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{2 c^{3} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{2 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{2 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{3 c^{2} d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{3 c^{2} d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 c^{2} d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{6 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{6 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i c^{2} d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i c \,d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{24 c \,d^{3} a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 c^{2} d^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{12 d^{4} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{6 d^{4} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{5}}-\frac{d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{2 b^{5}}+\frac{d^{4} a^{4} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{12 d^{3} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}"," ",0,"6/b^3*c^2*d^2*polylog(3,-exp(I*(b*x+a)))-6/b^3*c^2*d^2*polylog(3,exp(I*(b*x+a)))+1/2/b^5*d^4*a^4*ln(1-exp(I*(b*x+a)))-6/b^3*d^4*polylog(3,exp(I*(b*x+a)))*x^2+6/b^3*d^4*polylog(3,-exp(I*(b*x+a)))*x^2-12*d^4*polylog(3,-exp(I*(b*x+a)))/b^5+12*d^4*polylog(3,exp(I*(b*x+a)))/b^5-12*d^4*polylog(5,-exp(I*(b*x+a)))/b^5+12*d^4*polylog(5,exp(I*(b*x+a)))/b^5+1/b*c^4*arctanh(exp(I*(b*x+a)))-6/b^5*d^4*a^2*ln(1-exp(I*(b*x+a)))+6/b^3*d^4*ln(1-exp(I*(b*x+a)))*x^2-6/b^3*d^4*ln(exp(I*(b*x+a))+1)*x^2+2/b^2*c^3*d*ln(exp(I*(b*x+a))+1)*a-4/b^4*c*d^3*a^3*arctanh(exp(I*(b*x+a)))+6/b^3*c^2*d^2*a^2*arctanh(exp(I*(b*x+a)))-4/b^2*c^3*d*a*arctanh(exp(I*(b*x+a)))-3/b^3*c^2*d^2*ln(exp(I*(b*x+a))+1)*a^2+1/b^2/(exp(2*I*(b*x+a))-1)^2*(d^4*x^4*b*exp(3*I*(b*x+a))+4*c*d^3*x^3*b*exp(3*I*(b*x+a))+6*c^2*d^2*x^2*b*exp(3*I*(b*x+a))+d^4*x^4*b*exp(I*(b*x+a))+4*c^3*d*x*b*exp(3*I*(b*x+a))+4*c*d^3*x^3*b*exp(I*(b*x+a))-4*I*d^4*x^3*exp(3*I*(b*x+a))+c^4*b*exp(3*I*(b*x+a))+6*c^2*d^2*x^2*b*exp(I*(b*x+a))-12*I*c^2*d^2*x*exp(3*I*(b*x+a))+4*c^3*d*x*b*exp(I*(b*x+a))+4*I*d^4*x^3*exp(I*(b*x+a))+4*I*c^3*d*exp(I*(b*x+a))+c^4*b*exp(I*(b*x+a))-12*I*c*d^3*x^2*exp(3*I*(b*x+a))+12*I*c*d^3*x^2*exp(I*(b*x+a))-4*I*c^3*d*exp(3*I*(b*x+a))+12*I*c^2*d^2*x*exp(I*(b*x+a)))+24/b^4*c*d^3*a*arctanh(exp(I*(b*x+a)))-1/2/b^5*d^4*a^4*ln(exp(I*(b*x+a))+1)+1/b^5*d^4*a^4*arctanh(exp(I*(b*x+a)))+2/b*c^3*d*ln(exp(I*(b*x+a))+1)*x-2/b*c^3*d*ln(1-exp(I*(b*x+a)))*x-2/b^2*c^3*d*ln(1-exp(I*(b*x+a)))*a+3/b*c^2*d^2*ln(exp(I*(b*x+a))+1)*x^2+12/b^3*c*d^3*polylog(3,-exp(I*(b*x+a)))*x+3/b^3*c^2*d^2*a^2*ln(1-exp(I*(b*x+a)))-3/b*c^2*d^2*ln(1-exp(I*(b*x+a)))*x^2-12/b^3*c*d^3*polylog(3,exp(I*(b*x+a)))*x-1/2/b*d^4*ln(1-exp(I*(b*x+a)))*x^4+1/2/b*d^4*ln(exp(I*(b*x+a))+1)*x^4+2/b*c*d^3*ln(exp(I*(b*x+a))+1)*x^3-2/b*c*d^3*ln(1-exp(I*(b*x+a)))*x^3-2/b^4*c*d^3*ln(1-exp(I*(b*x+a)))*a^3+2/b^4*c*d^3*ln(exp(I*(b*x+a))+1)*a^3-12/b^3*d^3*c*ln(exp(I*(b*x+a))+1)*x+12/b^3*d^3*c*ln(1-exp(I*(b*x+a)))*x+12/b^4*d^3*c*ln(1-exp(I*(b*x+a)))*a-12/b^4*c*d^3*ln(exp(I*(b*x+a))+1)*a-2*I/b^2*d^4*polylog(2,-exp(I*(b*x+a)))*x^3+12*I/b^4*d^4*polylog(4,-exp(I*(b*x+a)))*x+2*I/b^2*d^4*polylog(2,exp(I*(b*x+a)))*x^3-12*I/b^4*d^4*polylog(4,exp(I*(b*x+a)))*x+12*I/b^4*d^4*polylog(2,-exp(I*(b*x+a)))*x+12*I/b^4*c*d^3*polylog(4,-exp(I*(b*x+a)))-12*I/b^4*c*d^3*polylog(4,exp(I*(b*x+a)))-2*I/b^2*c^3*d*polylog(2,-exp(I*(b*x+a)))+2*I/b^2*c^3*d*polylog(2,exp(I*(b*x+a)))+12*I/b^4*c*d^3*polylog(2,-exp(I*(b*x+a)))+6/b^5*d^4*a^2*ln(exp(I*(b*x+a))+1)-12/b^3*c^2*d^2*arctanh(exp(I*(b*x+a)))-12/b^5*d^4*a^2*arctanh(exp(I*(b*x+a)))-12*I/b^4*d^3*c*polylog(2,exp(I*(b*x+a)))-12*I/b^4*d^4*polylog(2,exp(I*(b*x+a)))*x-6*I/b^2*c*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+6*I/b^2*c*d^3*polylog(2,exp(I*(b*x+a)))*x^2-6*I/b^2*polylog(2,-exp(I*(b*x+a)))*c^2*d^2*x+6*I/b^2*polylog(2,exp(I*(b*x+a)))*c^2*d^2*x","B"
113,1,1056,274,0.144000," ","int((d*x+c)^3*cot(b*x+a)^2*csc(b*x+a),x)","\frac{3 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{3 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{2 b}-\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{2 b^{4}}+\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{2 b}-\frac{3 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{c^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{d^{3} x^{3} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 c \,d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 c^{2} d x b \,{\mathrm e}^{3 i \left(b x +a \right)}+d^{3} x^{3} b \,{\mathrm e}^{i \left(b x +a \right)}+c^{3} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 c \,d^{2} x^{2} b \,{\mathrm e}^{i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{3 i \left(b x +a \right)}+3 c^{2} d x b \,{\mathrm e}^{i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{3 i \left(b x +a \right)}+c^{3} b \,{\mathrm e}^{i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{3 i \left(b x +a \right)}+3 i d^{3} x^{2} {\mathrm e}^{i \left(b x +a \right)}+6 i c \,d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}+3 i c^{2} d \,{\mathrm e}^{i \left(b x +a \right)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{2 b^{2}}-\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{2 b^{3}}+\frac{3 c \,d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 c^{2} d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}+\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{2 b}-\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}-\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}+\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}+\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{2 b}-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{4}}+\frac{6 d^{3} a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 c \,d^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{3}}{2 b^{4}}-\frac{d^{3} a^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"3*I*d^3*polylog(2,-exp(I*(b*x+a)))/b^4+3*I*d^3*polylog(4,-exp(I*(b*x+a)))/b^4+3/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))-3/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))-3/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x+3/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x-3*I*d^3*polylog(2,exp(I*(b*x+a)))/b^4-3*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4+1/b^2/(exp(2*I*(b*x+a))-1)^2*(d^3*x^3*b*exp(3*I*(b*x+a))+3*c*d^2*x^2*b*exp(3*I*(b*x+a))+3*c^2*d*x*b*exp(3*I*(b*x+a))+d^3*x^3*b*exp(I*(b*x+a))+c^3*b*exp(3*I*(b*x+a))+3*c*d^2*x^2*b*exp(I*(b*x+a))-3*I*d^3*x^2*exp(3*I*(b*x+a))+3*c^2*d*x*b*exp(I*(b*x+a))-6*I*c*d^2*x*exp(3*I*(b*x+a))+c^3*b*exp(I*(b*x+a))-3*I*c^2*d*exp(3*I*(b*x+a))+3*I*d^3*x^2*exp(I*(b*x+a))+6*I*c*d^2*x*exp(I*(b*x+a))+3*I*c^2*d*exp(I*(b*x+a)))+1/b*c^3*arctanh(exp(I*(b*x+a)))-3/b^3*d^3*ln(exp(I*(b*x+a))+1)*x+3/b^3*d^3*ln(1-exp(I*(b*x+a)))*x+3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a-1/b^4*d^3*a^3*arctanh(exp(I*(b*x+a)))+3/2/b^2*c^2*d*ln(exp(I*(b*x+a))+1)*a-3/2/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))+1)+1/2/b^4*d^3*ln(exp(I*(b*x+a))+1)*a^3+3/2*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2+3/b^3*c*d^2*a^2*arctanh(exp(I*(b*x+a)))-3/b^2*c^2*d*a*arctanh(exp(I*(b*x+a)))-3/2*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2-3/2*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))+3/2*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))+3/2/b*c^2*d*ln(exp(I*(b*x+a))+1)*x-3/2/b*c^2*d*ln(1-exp(I*(b*x+a)))*x-3/2/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a+3/2/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))-3/2/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2+3/2/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2-1/2/b*d^3*ln(1-exp(I*(b*x+a)))*x^3-1/2/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3+1/2/b*d^3*ln(exp(I*(b*x+a))+1)*x^3-3/b^4*d^3*ln(exp(I*(b*x+a))+1)*a+6/b^4*d^3*a*arctanh(exp(I*(b*x+a)))-6/b^3*c*d^2*arctanh(exp(I*(b*x+a)))-3*I/b^2*polylog(2,-exp(I*(b*x+a)))*c*d^2*x+3*I/b^2*polylog(2,exp(I*(b*x+a)))*c*d^2*x","B"
114,1,546,165,0.120000," ","int((d*x+c)^2*cot(b*x+a)^2*csc(b*x+a),x)","\frac{d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+2 c d x b \,{\mathrm e}^{3 i \left(b x +a \right)}+c^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+d^{2} x^{2} b \,{\mathrm e}^{i \left(b x +a \right)}+2 c d x b \,{\mathrm e}^{i \left(b x +a \right)}-2 i d^{2} x \,{\mathrm e}^{3 i \left(b x +a \right)}+c^{2} b \,{\mathrm e}^{i \left(b x +a \right)}-2 i d c \,{\mathrm e}^{3 i \left(b x +a \right)}+2 i d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}+2 i d c \,{\mathrm e}^{i \left(b x +a \right)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}-\frac{c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 d^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{c^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{2 b}-\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}+\frac{i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 c d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{2 b^{3}}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{2 b^{3}}"," ",0,"1/b^2/(exp(2*I*(b*x+a))-1)^2*(d^2*x^2*b*exp(3*I*(b*x+a))+2*c*d*x*b*exp(3*I*(b*x+a))+c^2*b*exp(3*I*(b*x+a))+d^2*x^2*b*exp(I*(b*x+a))+2*c*d*x*b*exp(I*(b*x+a))-2*I*d^2*x*exp(3*I*(b*x+a))+c^2*b*exp(I*(b*x+a))-2*I*d*c*exp(3*I*(b*x+a))+2*I*d^2*x*exp(I*(b*x+a))+2*I*d*c*exp(I*(b*x+a)))+1/b*c*d*ln(exp(I*(b*x+a))+1)*x+1/b^2*c*d*ln(exp(I*(b*x+a))+1)*a-1/b*c*d*ln(1-exp(I*(b*x+a)))*x-1/b^2*c*d*ln(1-exp(I*(b*x+a)))*a+d^2*polylog(3,-exp(I*(b*x+a)))/b^3-d^2*polylog(3,exp(I*(b*x+a)))/b^3-2/b^3*d^2*arctanh(exp(I*(b*x+a)))+1/b*c^2*arctanh(exp(I*(b*x+a)))+1/b^3*d^2*a^2*arctanh(exp(I*(b*x+a)))+1/2/b*d^2*ln(exp(I*(b*x+a))+1)*x^2-I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))-1/2/b*d^2*ln(1-exp(I*(b*x+a)))*x^2+I/b^2*polylog(2,exp(I*(b*x+a)))*d^2*x-2/b^2*c*d*a*arctanh(exp(I*(b*x+a)))-I/b^2*polylog(2,-exp(I*(b*x+a)))*d^2*x+I/b^2*c*d*polylog(2,exp(I*(b*x+a)))-1/2/b^3*d^2*ln(exp(I*(b*x+a))+1)*a^2+1/2/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2","B"
115,1,246,92,0.099000," ","int((d*x+c)*cot(b*x+a)^2*csc(b*x+a),x)","\frac{b d x \,{\mathrm e}^{3 i \left(b x +a \right)}+c b \,{\mathrm e}^{3 i \left(b x +a \right)}+b d x \,{\mathrm e}^{i \left(b x +a \right)}+c b \,{\mathrm e}^{i \left(b x +a \right)}-i d \,{\mathrm e}^{3 i \left(b x +a \right)}+i d \,{\mathrm e}^{i \left(b x +a \right)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{c \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{2 b}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{2 b^{2}}-\frac{i d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}-\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}+\frac{i d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"1/b^2/(exp(2*I*(b*x+a))-1)^2*(b*d*x*exp(3*I*(b*x+a))+c*b*exp(3*I*(b*x+a))+b*d*x*exp(I*(b*x+a))+c*b*exp(I*(b*x+a))-I*d*exp(3*I*(b*x+a))+I*d*exp(I*(b*x+a)))+1/b*c*arctanh(exp(I*(b*x+a)))+1/2/b*d*ln(exp(I*(b*x+a))+1)*x+1/2/b^2*d*ln(exp(I*(b*x+a))+1)*a-1/2*I*d*polylog(2,-exp(I*(b*x+a)))/b^2-1/2/b*d*ln(1-exp(I*(b*x+a)))*x-1/2/b^2*d*ln(1-exp(I*(b*x+a)))*a+1/2*I*d*polylog(2,exp(I*(b*x+a)))/b^2-1/b^2*d*a*arctanh(exp(I*(b*x+a)))","B"
116,0,0,37,2.760000," ","int(cot(b*x+a)^2*csc(b*x+a)/(d*x+c),x)","\int \frac{\left(\cot^{2}\left(b x +a \right)\right) \csc \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(cot(b*x+a)^2*csc(b*x+a)/(d*x+c),x)","F"
117,0,0,37,4.191000," ","int(cot(b*x+a)^2*csc(b*x+a)/(d*x+c)^2,x)","\int \frac{\left(\cot^{2}\left(b x +a \right)\right) \csc \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(cot(b*x+a)^2*csc(b*x+a)/(d*x+c)^2,x)","F"
118,1,476,310,0.043000," ","int((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{4 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{12 b}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(5/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+5/8/b*d*(1/2/b*d*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/2/b*d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/24/b*d*(d*x+c)^(5/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+5/24/b*d*(1/6/b*d*(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/2/b*d*(-1/6/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
119,1,384,265,0.038000," ","int((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{4 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{4 b}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/8/b*d*(1/2/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/24/b*d*(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/8/b*d*(1/6/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
120,1,296,224,0.034000," ","int((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a),x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{72 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/16/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/24/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/144/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
121,1,296,224,0.000000," ","int((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a),x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{72 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/16/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/24/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/144/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
122,1,384,265,0.000000," ","int((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{4 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{4 b}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/8/b*d*(1/2/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/24/b*d*(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/8/b*d*(1/6/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
123,1,476,310,0.000000," ","int((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{4 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{12 b}}{d}"," ",0,"2/d*(-1/8/b*d*(d*x+c)^(5/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+5/8/b*d*(1/2/b*d*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/2/b*d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/24/b*d*(d*x+c)^(5/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+5/24/b*d*(1/6/b*d*(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/2/b*d*(-1/6/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
124,1,251,176,0.049000," ","int((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^2,x)","\frac{\frac{\left(d x +c \right)^{\frac{7}{2}}}{28}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{5 d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{8 b}\right)}{32 b}}{d}"," ",0,"2/d*(1/56*(d*x+c)^(7/2)-1/64/b*d*(d*x+c)^(5/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+5/64/b*d*(-1/8/b*d*(d*x+c)^(3/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+3/8/b*d*(1/8/b*d*(d*x+c)^(1/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
125,1,206,152,0.049000," ","int((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^2,x)","\frac{\frac{\left(d x +c \right)^{\frac{5}{2}}}{20}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{32 b}}{d}"," ",0,"2/d*(1/40*(d*x+c)^(5/2)-1/64/b*d*(d*x+c)^(3/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+3/64/b*d*(-1/8/b*d*(d*x+c)^(1/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
126,1,159,130,0.046000," ","int((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^2,x)","\frac{\frac{\left(d x +c \right)^{\frac{3}{2}}}{12}-\frac{d \sqrt{d x +c}\, \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{128 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(1/24*(d*x+c)^(3/2)-1/64/b*d*(d*x+c)^(1/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+1/256/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
127,1,159,130,0.000000," ","int((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^2,x)","\frac{\frac{\left(d x +c \right)^{\frac{3}{2}}}{12}-\frac{d \sqrt{d x +c}\, \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{128 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(1/24*(d*x+c)^(3/2)-1/64/b*d*(d*x+c)^(1/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+1/256/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
128,1,206,152,0.000000," ","int((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^2,x)","\frac{\frac{\left(d x +c \right)^{\frac{5}{2}}}{20}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{32 b}}{d}"," ",0,"2/d*(1/40*(d*x+c)^(5/2)-1/64/b*d*(d*x+c)^(3/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+3/64/b*d*(-1/8/b*d*(d*x+c)^(1/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
129,1,251,176,0.000000," ","int((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^2,x)","\frac{\frac{\left(d x +c \right)^{\frac{7}{2}}}{28}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{5 d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{8 b}\right)}{32 b}}{d}"," ",0,"2/d*(1/56*(d*x+c)^(7/2)-1/64/b*d*(d*x+c)^(5/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+5/64/b*d*(-1/8/b*d*(d*x+c)^(3/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+3/8/b*d*(1/8/b*d*(d*x+c)^(1/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
130,1,719,471,0.047000," ","int((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^3,x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{48 b}+\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}-\frac{d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{100 b \sqrt{\frac{b}{d}}}\right)}{10 b}\right)}{16 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(5/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+5/16/b*d*(1/2/b*d*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/2/b*d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/96/b*d*(d*x+c)^(5/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+5/96/b*d*(1/6/b*d*(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/2/b*d*(-1/6/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))+1/160/b*d*(d*x+c)^(5/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-1/32/b*d*(1/10/b*d*(d*x+c)^(3/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-3/10/b*d*(-1/10/b*d*(d*x+c)^(1/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+1/100/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
131,1,580,402,0.045000," ","int((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^3,x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{16 b}+\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}-\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{100 b \sqrt{\frac{b}{d}}}\right)}{80 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/16/b*d*(1/2/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/96/b*d*(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/32/b*d*(1/6/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))+1/160/b*d*(d*x+c)^(3/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-3/160/b*d*(1/10/b*d*(d*x+c)^(1/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-1/100/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
132,1,447,339,0.045000," ","int((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^3,x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{16 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{288 b \sqrt{\frac{b}{d}}}+\frac{d \sqrt{d x +c}\, \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{800 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/96/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/576/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))+1/160/b*d*(d*x+c)^(1/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-1/1600/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
133,1,447,339,0.000000," ","int((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^3,x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{16 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{288 b \sqrt{\frac{b}{d}}}+\frac{d \sqrt{d x +c}\, \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{800 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/96/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/576/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))+1/160/b*d*(d*x+c)^(1/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-1/1600/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
134,1,580,402,0.000000," ","int((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^3,x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{16 b}+\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}-\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{100 b \sqrt{\frac{b}{d}}}\right)}{80 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/16/b*d*(1/2/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/96/b*d*(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/32/b*d*(1/6/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))+1/160/b*d*(d*x+c)^(3/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-3/160/b*d*(1/10/b*d*(d*x+c)^(1/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-1/100/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
135,1,719,471,0.000000," ","int((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^3,x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{48 b}+\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}-\frac{d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{100 b \sqrt{\frac{b}{d}}}\right)}{10 b}\right)}{16 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(5/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+5/16/b*d*(1/2/b*d*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/2/b*d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/96/b*d*(d*x+c)^(5/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+5/96/b*d*(1/6/b*d*(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/2/b*d*(-1/6/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))+1/160/b*d*(d*x+c)^(5/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-1/32/b*d*(1/10/b*d*(d*x+c)^(3/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-3/10/b*d*(-1/10/b*d*(d*x+c)^(1/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+1/100/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
136,0,0,265,0.176000," ","int((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a),x)","\int \left(d x +c \right)^{m} \left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a),x)","F"
137,1,1150,236,0.089000," ","int((d*x+c)^4*cos(b*x+a)^3*sin(b*x+a),x)","\frac{\frac{d^{4} \left(-\frac{\left(b x +a \right)^{4} \left(\cos^{4}\left(b x +a \right)\right)}{4}+\left(b x +a \right)^{3} \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)+\frac{3 \left(b x +a \right)^{2} \left(\cos^{4}\left(b x +a \right)\right)}{16}-\frac{3 \left(b x +a \right) \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{8}+\frac{45 \left(b x +a \right)^{2}}{128}-\frac{3 \left(\cos^{4}\left(b x +a \right)\right)}{128}-\frac{9 \left(\cos^{2}\left(b x +a \right)\right)}{128}+\frac{9 \left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{16}-\frac{9 \left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{8}+\frac{9 \left(\sin^{2}\left(b x +a \right)\right)}{32}-\frac{9 \left(b x +a \right)^{4}}{32}\right)}{b^{4}}-\frac{4 a \,d^{4} \left(-\frac{\left(b x +a \right)^{3} \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{3 \left(b x +a \right)^{2} \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{4}+\frac{3 \left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{128}-\frac{45 b x}{256}-\frac{45 a}{256}+\frac{9 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{32}-\frac{9 \cos \left(b x +a \right) \sin \left(b x +a \right)}{64}-\frac{3 \left(b x +a \right)^{3}}{16}\right)}{b^{4}}+\frac{4 c \,d^{3} \left(-\frac{\left(b x +a \right)^{3} \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{3 \left(b x +a \right)^{2} \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{4}+\frac{3 \left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{128}-\frac{45 b x}{256}-\frac{45 a}{256}+\frac{9 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{32}-\frac{9 \cos \left(b x +a \right) \sin \left(b x +a \right)}{64}-\frac{3 \left(b x +a \right)^{3}}{16}\right)}{b^{3}}+\frac{6 a^{2} d^{4} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(b x +a \right) \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}-\frac{3 \left(b x +a \right)^{2}}{32}+\frac{\left(\cos^{4}\left(b x +a \right)\right)}{32}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{32}\right)}{b^{4}}-\frac{12 a c \,d^{3} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(b x +a \right) \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}-\frac{3 \left(b x +a \right)^{2}}{32}+\frac{\left(\cos^{4}\left(b x +a \right)\right)}{32}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{32}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(b x +a \right) \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}-\frac{3 \left(b x +a \right)^{2}}{32}+\frac{\left(\cos^{4}\left(b x +a \right)\right)}{32}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{32}\right)}{b^{2}}-\frac{4 a^{3} d^{4} \left(-\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{16}+\frac{3 b x}{32}+\frac{3 a}{32}\right)}{b^{4}}+\frac{12 a^{2} c \,d^{3} \left(-\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{16}+\frac{3 b x}{32}+\frac{3 a}{32}\right)}{b^{3}}-\frac{12 a \,c^{2} d^{2} \left(-\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{16}+\frac{3 b x}{32}+\frac{3 a}{32}\right)}{b^{2}}+\frac{4 c^{3} d \left(-\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{16}+\frac{3 b x}{32}+\frac{3 a}{32}\right)}{b}-\frac{a^{4} d^{4} \left(\cos^{4}\left(b x +a \right)\right)}{4 b^{4}}+\frac{a^{3} c \,d^{3} \left(\cos^{4}\left(b x +a \right)\right)}{b^{3}}-\frac{3 a^{2} c^{2} d^{2} \left(\cos^{4}\left(b x +a \right)\right)}{2 b^{2}}+\frac{a \,c^{3} d \left(\cos^{4}\left(b x +a \right)\right)}{b}-\frac{c^{4} \left(\cos^{4}\left(b x +a \right)\right)}{4}}{b}"," ",0,"1/b*(1/b^4*d^4*(-1/4*(b*x+a)^4*cos(b*x+a)^4+(b*x+a)^3*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)+3/16*(b*x+a)^2*cos(b*x+a)^4-3/8*(b*x+a)*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)+45/128*(b*x+a)^2-3/128*cos(b*x+a)^4-9/128*cos(b*x+a)^2+9/16*(b*x+a)^2*cos(b*x+a)^2-9/8*(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+9/32*sin(b*x+a)^2-9/32*(b*x+a)^4)-4/b^4*a*d^4*(-1/4*(b*x+a)^3*cos(b*x+a)^4+3/4*(b*x+a)^2*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)+3/32*(b*x+a)*cos(b*x+a)^4-3/128*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)-45/256*b*x-45/256*a+9/32*(b*x+a)*cos(b*x+a)^2-9/64*cos(b*x+a)*sin(b*x+a)-3/16*(b*x+a)^3)+4/b^3*c*d^3*(-1/4*(b*x+a)^3*cos(b*x+a)^4+3/4*(b*x+a)^2*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)+3/32*(b*x+a)*cos(b*x+a)^4-3/128*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)-45/256*b*x-45/256*a+9/32*(b*x+a)*cos(b*x+a)^2-9/64*cos(b*x+a)*sin(b*x+a)-3/16*(b*x+a)^3)+6/b^4*a^2*d^4*(-1/4*(b*x+a)^2*cos(b*x+a)^4+1/2*(b*x+a)*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)-3/32*(b*x+a)^2+1/32*cos(b*x+a)^4+3/32*cos(b*x+a)^2)-12/b^3*a*c*d^3*(-1/4*(b*x+a)^2*cos(b*x+a)^4+1/2*(b*x+a)*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)-3/32*(b*x+a)^2+1/32*cos(b*x+a)^4+3/32*cos(b*x+a)^2)+6/b^2*c^2*d^2*(-1/4*(b*x+a)^2*cos(b*x+a)^4+1/2*(b*x+a)*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)-3/32*(b*x+a)^2+1/32*cos(b*x+a)^4+3/32*cos(b*x+a)^2)-4/b^4*a^3*d^4*(-1/4*(b*x+a)*cos(b*x+a)^4+1/16*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/32*b*x+3/32*a)+12/b^3*a^2*c*d^3*(-1/4*(b*x+a)*cos(b*x+a)^4+1/16*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/32*b*x+3/32*a)-12/b^2*a*c^2*d^2*(-1/4*(b*x+a)*cos(b*x+a)^4+1/16*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/32*b*x+3/32*a)+4/b*c^3*d*(-1/4*(b*x+a)*cos(b*x+a)^4+1/16*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/32*b*x+3/32*a)-1/4/b^4*a^4*d^4*cos(b*x+a)^4+1/b^3*a^3*c*d^3*cos(b*x+a)^4-3/2/b^2*a^2*c^2*d^2*cos(b*x+a)^4+1/b*a*c^3*d*cos(b*x+a)^4-1/4*c^4*cos(b*x+a)^4)","B"
138,1,594,178,0.020000," ","int((d*x+c)^3*cos(b*x+a)^3*sin(b*x+a),x)","\frac{\frac{d^{3} \left(-\frac{\left(b x +a \right)^{3} \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{3 \left(b x +a \right)^{2} \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{4}+\frac{3 \left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{32}-\frac{3 \left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{128}-\frac{45 b x}{256}-\frac{45 a}{256}+\frac{9 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{32}-\frac{9 \cos \left(b x +a \right) \sin \left(b x +a \right)}{64}-\frac{3 \left(b x +a \right)^{3}}{16}\right)}{b^{3}}-\frac{3 a \,d^{3} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(b x +a \right) \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}-\frac{3 \left(b x +a \right)^{2}}{32}+\frac{\left(\cos^{4}\left(b x +a \right)\right)}{32}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{32}\right)}{b^{3}}+\frac{3 c \,d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(b x +a \right) \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}-\frac{3 \left(b x +a \right)^{2}}{32}+\frac{\left(\cos^{4}\left(b x +a \right)\right)}{32}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{32}\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(-\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{16}+\frac{3 b x}{32}+\frac{3 a}{32}\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(-\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{16}+\frac{3 b x}{32}+\frac{3 a}{32}\right)}{b^{2}}+\frac{3 c^{2} d \left(-\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{16}+\frac{3 b x}{32}+\frac{3 a}{32}\right)}{b}+\frac{a^{3} d^{3} \left(\cos^{4}\left(b x +a \right)\right)}{4 b^{3}}-\frac{3 a^{2} c \,d^{2} \left(\cos^{4}\left(b x +a \right)\right)}{4 b^{2}}+\frac{3 a \,c^{2} d \left(\cos^{4}\left(b x +a \right)\right)}{4 b}-\frac{c^{3} \left(\cos^{4}\left(b x +a \right)\right)}{4}}{b}"," ",0,"1/b*(1/b^3*d^3*(-1/4*(b*x+a)^3*cos(b*x+a)^4+3/4*(b*x+a)^2*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)+3/32*(b*x+a)*cos(b*x+a)^4-3/128*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)-45/256*b*x-45/256*a+9/32*(b*x+a)*cos(b*x+a)^2-9/64*cos(b*x+a)*sin(b*x+a)-3/16*(b*x+a)^3)-3/b^3*a*d^3*(-1/4*(b*x+a)^2*cos(b*x+a)^4+1/2*(b*x+a)*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)-3/32*(b*x+a)^2+1/32*cos(b*x+a)^4+3/32*cos(b*x+a)^2)+3/b^2*c*d^2*(-1/4*(b*x+a)^2*cos(b*x+a)^4+1/2*(b*x+a)*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)-3/32*(b*x+a)^2+1/32*cos(b*x+a)^4+3/32*cos(b*x+a)^2)+3/b^3*a^2*d^3*(-1/4*(b*x+a)*cos(b*x+a)^4+1/16*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/32*b*x+3/32*a)-6/b^2*a*c*d^2*(-1/4*(b*x+a)*cos(b*x+a)^4+1/16*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/32*b*x+3/32*a)+3/b*c^2*d*(-1/4*(b*x+a)*cos(b*x+a)^4+1/16*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/32*b*x+3/32*a)+1/4/b^3*a^3*d^3*cos(b*x+a)^4-3/4/b^2*a^2*c*d^2*cos(b*x+a)^4+3/4/b*a*c^2*d*cos(b*x+a)^4-1/4*c^3*cos(b*x+a)^4)","B"
139,1,260,120,0.018000," ","int((d*x+c)^2*cos(b*x+a)^3*sin(b*x+a),x)","\frac{\frac{d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(b x +a \right) \left(\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}-\frac{3 \left(b x +a \right)^{2}}{32}+\frac{\left(\cos^{4}\left(b x +a \right)\right)}{32}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{32}\right)}{b^{2}}-\frac{2 a \,d^{2} \left(-\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{16}+\frac{3 b x}{32}+\frac{3 a}{32}\right)}{b^{2}}+\frac{2 c d \left(-\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{16}+\frac{3 b x}{32}+\frac{3 a}{32}\right)}{b}-\frac{d^{2} a^{2} \left(\cos^{4}\left(b x +a \right)\right)}{4 b^{2}}+\frac{c d a \left(\cos^{4}\left(b x +a \right)\right)}{2 b}-\frac{c^{2} \left(\cos^{4}\left(b x +a \right)\right)}{4}}{b}"," ",0,"1/b*(1/b^2*d^2*(-1/4*(b*x+a)^2*cos(b*x+a)^4+1/2*(b*x+a)*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)-3/32*(b*x+a)^2+1/32*cos(b*x+a)^4+3/32*cos(b*x+a)^2)-2/b^2*a*d^2*(-1/4*(b*x+a)*cos(b*x+a)^4+1/16*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/32*b*x+3/32*a)+2/b*c*d*(-1/4*(b*x+a)*cos(b*x+a)^4+1/16*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/32*b*x+3/32*a)-1/4*d^2/b^2*a^2*cos(b*x+a)^4+1/2*c*d/b*a*cos(b*x+a)^4-1/4*c^2*cos(b*x+a)^4)","B"
140,1,85,64,0.020000," ","int((d*x+c)*cos(b*x+a)^3*sin(b*x+a),x)","\frac{\frac{d \left(-\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{16}+\frac{3 b x}{32}+\frac{3 a}{32}\right)}{b}+\frac{d a \left(\cos^{4}\left(b x +a \right)\right)}{4 b}-\frac{c \left(\cos^{4}\left(b x +a \right)\right)}{4}}{b}"," ",0,"1/b*(1/b*d*(-1/4*(b*x+a)*cos(b*x+a)^4+1/16*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/32*b*x+3/32*a)+1/4/b*d*a*cos(b*x+a)^4-1/4*c*cos(b*x+a)^4)","A"
141,1,178,121,0.022000," ","int(cos(b*x+a)^3*sin(b*x+a)/(d*x+c),x)","\frac{\frac{b \left(\frac{4 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}-\frac{4 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}\right)}{32}+\frac{b \left(\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}-\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}\right)}{8}}{b}"," ",0,"1/b*(1/32*b*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d-4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d)+1/8*b*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d))","A"
142,1,256,167,0.022000," ","int(cos(b*x+a)^3*sin(b*x+a)/(d*x+c)^2,x)","\frac{\frac{b^{2} \left(-\frac{4 \sin \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{16 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}+\frac{16 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}}{d}\right)}{32}+\frac{b^{2} \left(-\frac{2 \sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{4 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{4 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}}{d}\right)}{8}}{b}"," ",0,"1/b*(1/32*b^2*(-4*sin(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)/d+4*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d+4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d)/d)+1/8*b^2*(-2*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d+2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d)/d))","A"
143,1,329,219,0.022000," ","int(cos(b*x+a)^3*sin(b*x+a)/(d*x+c)^3,x)","\frac{\frac{b^{3} \left(-\frac{2 \sin \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{8 \cos \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{8 \left(\frac{4 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}-\frac{4 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}\right)}{d}}{d}\right)}{32}+\frac{b^{3} \left(-\frac{\sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{2 \cos \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{2 \left(\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}-\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}\right)}{d}}{d}\right)}{8}}{b}"," ",0,"1/b*(1/32*b^3*(-2*sin(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)^2/d+2*(-4*cos(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)/d-4*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d-4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d)/d)/d)+1/8*b^3*(-sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d+(-2*cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d-2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d)/d)/d))","A"
144,1,404,267,0.020000," ","int(cos(b*x+a)^3*sin(b*x+a)/(d*x+c)^4,x)","\frac{\frac{b^{4} \left(-\frac{4 \sin \left(4 b x +4 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{8 \cos \left(4 b x +4 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{8 \left(-\frac{4 \sin \left(4 b x +4 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{16 \Si \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \sin \left(\frac{-4 d a +4 c b}{d}\right)}{d}+\frac{16 \Ci \left(4 b x +4 a +\frac{-4 d a +4 c b}{d}\right) \cos \left(\frac{-4 d a +4 c b}{d}\right)}{d}}{d}\right)}{3 d}}{d}\right)}{32}+\frac{b^{4} \left(-\frac{2 \sin \left(2 b x +2 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{2 \cos \left(2 b x +2 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{2 \left(-\frac{2 \sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{4 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{4 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}}{d}\right)}{3 d}}{d}\right)}{8}}{b}"," ",0,"1/b*(1/32*b^4*(-4/3*sin(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)^3/d+4/3*(-2*cos(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)^2/d-2*(-4*sin(4*b*x+4*a)/((b*x+a)*d-d*a+c*b)/d+4*(4*Si(4*b*x+4*a+4*(-a*d+b*c)/d)*sin(4*(-a*d+b*c)/d)/d+4*Ci(4*b*x+4*a+4*(-a*d+b*c)/d)*cos(4*(-a*d+b*c)/d)/d)/d)/d)/d)+1/8*b^4*(-2/3*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^3/d+2/3*(-cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d-(-2*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d+2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d)/d)/d)/d))","A"
145,0,0,383,0.316000," ","int((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \left(\cos^{3}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a)^2,x)","F"
146,1,1842,304,0.073000," ","int((d*x+c)^4*cos(b*x+a)^3*sin(b*x+a)^2,x)","\text{Expression too large to display}"," ",0,"1/b*(1/b^4*d^4*(1/3*(b*x+a)^4*(2+cos(b*x+a)^2)*sin(b*x+a)+8/15*(b*x+a)^3*cos(b*x+a)-8/5*(b*x+a)^2*sin(b*x+a)+3424/1125*sin(b*x+a)-3424/1125*(b*x+a)*cos(b*x+a)+4/45*(b*x+a)^3*cos(b*x+a)^3-4/45*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)+88/3375*(b*x+a)*cos(b*x+a)^3-88/10125*(2+cos(b*x+a)^2)*sin(b*x+a)-1/5*(b*x+a)^4*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-4/25*(b*x+a)^3*cos(b*x+a)^5+12/125*(b*x+a)^2*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)+24/625*(b*x+a)*cos(b*x+a)^5-24/3125*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))-4/b^4*a*d^4*(1/3*(b*x+a)^3*(2+cos(b*x+a)^2)*sin(b*x+a)+2/5*(b*x+a)^2*cos(b*x+a)-856/1125*cos(b*x+a)-4/5*(b*x+a)*sin(b*x+a)+1/15*(b*x+a)^2*cos(b*x+a)^3-2/45*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+22/3375*cos(b*x+a)^3-1/5*(b*x+a)^3*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-3/25*(b*x+a)^2*cos(b*x+a)^5+6/125*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)+6/625*cos(b*x+a)^5)+4/b^3*c*d^3*(1/3*(b*x+a)^3*(2+cos(b*x+a)^2)*sin(b*x+a)+2/5*(b*x+a)^2*cos(b*x+a)-856/1125*cos(b*x+a)-4/5*(b*x+a)*sin(b*x+a)+1/15*(b*x+a)^2*cos(b*x+a)^3-2/45*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+22/3375*cos(b*x+a)^3-1/5*(b*x+a)^3*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-3/25*(b*x+a)^2*cos(b*x+a)^5+6/125*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)+6/625*cos(b*x+a)^5)+6/b^4*a^2*d^4*(1/3*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)-4/15*sin(b*x+a)+4/15*(b*x+a)*cos(b*x+a)+2/45*(b*x+a)*cos(b*x+a)^3-2/135*(2+cos(b*x+a)^2)*sin(b*x+a)-1/5*(b*x+a)^2*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-2/25*(b*x+a)*cos(b*x+a)^5+2/125*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))-12/b^3*a*c*d^3*(1/3*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)-4/15*sin(b*x+a)+4/15*(b*x+a)*cos(b*x+a)+2/45*(b*x+a)*cos(b*x+a)^3-2/135*(2+cos(b*x+a)^2)*sin(b*x+a)-1/5*(b*x+a)^2*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-2/25*(b*x+a)*cos(b*x+a)^5+2/125*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))+6/b^2*c^2*d^2*(1/3*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)-4/15*sin(b*x+a)+4/15*(b*x+a)*cos(b*x+a)+2/45*(b*x+a)*cos(b*x+a)^3-2/135*(2+cos(b*x+a)^2)*sin(b*x+a)-1/5*(b*x+a)^2*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-2/25*(b*x+a)*cos(b*x+a)^5+2/125*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))-4/b^4*a^3*d^4*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/45*cos(b*x+a)^3+2/15*cos(b*x+a)-1/5*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-1/25*cos(b*x+a)^5)+12/b^3*a^2*c*d^3*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/45*cos(b*x+a)^3+2/15*cos(b*x+a)-1/5*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-1/25*cos(b*x+a)^5)-12/b^2*a*c^2*d^2*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/45*cos(b*x+a)^3+2/15*cos(b*x+a)-1/5*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-1/25*cos(b*x+a)^5)+4/b*c^3*d*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/45*cos(b*x+a)^3+2/15*cos(b*x+a)-1/5*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-1/25*cos(b*x+a)^5)+1/b^4*a^4*d^4*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))-4/b^3*a^3*c*d^3*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))+6/b^2*a^2*c^2*d^2*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))-4/b*a*c^3*d*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))+c^4*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a)))","B"
147,1,1016,235,0.022000," ","int((d*x+c)^3*cos(b*x+a)^3*sin(b*x+a)^2,x)","\frac{\frac{d^{3} \left(\frac{\left(b x +a \right)^{3} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right)^{2} \cos \left(b x +a \right)}{5}-\frac{856 \cos \left(b x +a \right)}{1125}-\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{5}+\frac{\left(b x +a \right)^{2} \left(\cos^{3}\left(b x +a \right)\right)}{15}-\frac{2 \left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{45}+\frac{22 \left(\cos^{3}\left(b x +a \right)\right)}{3375}-\frac{\left(b x +a \right)^{3} \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5}-\frac{3 \left(b x +a \right)^{2} \left(\cos^{5}\left(b x +a \right)\right)}{25}+\frac{6 \left(b x +a \right) \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{125}+\frac{6 \left(\cos^{5}\left(b x +a \right)\right)}{625}\right)}{b^{3}}-\frac{3 a \,d^{3} \left(\frac{\left(b x +a \right)^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}-\frac{4 \sin \left(b x +a \right)}{15}+\frac{4 \left(b x +a \right) \cos \left(b x +a \right)}{15}+\frac{2 \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{45}-\frac{2 \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{135}-\frac{\left(b x +a \right)^{2} \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5}-\frac{2 \left(b x +a \right) \left(\cos^{5}\left(b x +a \right)\right)}{25}+\frac{2 \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{125}\right)}{b^{3}}+\frac{3 c \,d^{2} \left(\frac{\left(b x +a \right)^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}-\frac{4 \sin \left(b x +a \right)}{15}+\frac{4 \left(b x +a \right) \cos \left(b x +a \right)}{15}+\frac{2 \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{45}-\frac{2 \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{135}-\frac{\left(b x +a \right)^{2} \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5}-\frac{2 \left(b x +a \right) \left(\cos^{5}\left(b x +a \right)\right)}{25}+\frac{2 \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{125}\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(\frac{\left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}+\frac{\left(\cos^{3}\left(b x +a \right)\right)}{45}+\frac{2 \cos \left(b x +a \right)}{15}-\frac{\left(b x +a \right) \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5}-\frac{\left(\cos^{5}\left(b x +a \right)\right)}{25}\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(\frac{\left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}+\frac{\left(\cos^{3}\left(b x +a \right)\right)}{45}+\frac{2 \cos \left(b x +a \right)}{15}-\frac{\left(b x +a \right) \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5}-\frac{\left(\cos^{5}\left(b x +a \right)\right)}{25}\right)}{b^{2}}+\frac{3 c^{2} d \left(\frac{\left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}+\frac{\left(\cos^{3}\left(b x +a \right)\right)}{45}+\frac{2 \cos \left(b x +a \right)}{15}-\frac{\left(b x +a \right) \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5}-\frac{\left(\cos^{5}\left(b x +a \right)\right)}{25}\right)}{b}-\frac{a^{3} d^{3} \left(-\frac{\left(\cos^{4}\left(b x +a \right)\right) \sin \left(b x +a \right)}{5}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}\right)}{b^{3}}+\frac{3 a^{2} c \,d^{2} \left(-\frac{\left(\cos^{4}\left(b x +a \right)\right) \sin \left(b x +a \right)}{5}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}\right)}{b^{2}}-\frac{3 a \,c^{2} d \left(-\frac{\left(\cos^{4}\left(b x +a \right)\right) \sin \left(b x +a \right)}{5}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}\right)}{b}+c^{3} \left(-\frac{\left(\cos^{4}\left(b x +a \right)\right) \sin \left(b x +a \right)}{5}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}\right)}{b}"," ",0,"1/b*(1/b^3*d^3*(1/3*(b*x+a)^3*(2+cos(b*x+a)^2)*sin(b*x+a)+2/5*(b*x+a)^2*cos(b*x+a)-856/1125*cos(b*x+a)-4/5*(b*x+a)*sin(b*x+a)+1/15*(b*x+a)^2*cos(b*x+a)^3-2/45*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+22/3375*cos(b*x+a)^3-1/5*(b*x+a)^3*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-3/25*(b*x+a)^2*cos(b*x+a)^5+6/125*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)+6/625*cos(b*x+a)^5)-3/b^3*a*d^3*(1/3*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)-4/15*sin(b*x+a)+4/15*(b*x+a)*cos(b*x+a)+2/45*(b*x+a)*cos(b*x+a)^3-2/135*(2+cos(b*x+a)^2)*sin(b*x+a)-1/5*(b*x+a)^2*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-2/25*(b*x+a)*cos(b*x+a)^5+2/125*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))+3/b^2*c*d^2*(1/3*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)-4/15*sin(b*x+a)+4/15*(b*x+a)*cos(b*x+a)+2/45*(b*x+a)*cos(b*x+a)^3-2/135*(2+cos(b*x+a)^2)*sin(b*x+a)-1/5*(b*x+a)^2*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-2/25*(b*x+a)*cos(b*x+a)^5+2/125*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))+3/b^3*a^2*d^3*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/45*cos(b*x+a)^3+2/15*cos(b*x+a)-1/5*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-1/25*cos(b*x+a)^5)-6/b^2*a*c*d^2*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/45*cos(b*x+a)^3+2/15*cos(b*x+a)-1/5*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-1/25*cos(b*x+a)^5)+3/b*c^2*d*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/45*cos(b*x+a)^3+2/15*cos(b*x+a)-1/5*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-1/25*cos(b*x+a)^5)-1/b^3*a^3*d^3*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))+3/b^2*a^2*c*d^2*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))-3/b*a*c^2*d*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))+c^3*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a)))","B"
148,1,484,166,0.020000," ","int((d*x+c)^2*cos(b*x+a)^3*sin(b*x+a)^2,x)","\frac{\frac{d^{2} \left(\frac{\left(b x +a \right)^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}-\frac{4 \sin \left(b x +a \right)}{15}+\frac{4 \left(b x +a \right) \cos \left(b x +a \right)}{15}+\frac{2 \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{45}-\frac{2 \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{135}-\frac{\left(b x +a \right)^{2} \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5}-\frac{2 \left(b x +a \right) \left(\cos^{5}\left(b x +a \right)\right)}{25}+\frac{2 \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{125}\right)}{b^{2}}-\frac{2 a \,d^{2} \left(\frac{\left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}+\frac{\left(\cos^{3}\left(b x +a \right)\right)}{45}+\frac{2 \cos \left(b x +a \right)}{15}-\frac{\left(b x +a \right) \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5}-\frac{\left(\cos^{5}\left(b x +a \right)\right)}{25}\right)}{b^{2}}+\frac{2 c d \left(\frac{\left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}+\frac{\left(\cos^{3}\left(b x +a \right)\right)}{45}+\frac{2 \cos \left(b x +a \right)}{15}-\frac{\left(b x +a \right) \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5}-\frac{\left(\cos^{5}\left(b x +a \right)\right)}{25}\right)}{b}+\frac{d^{2} a^{2} \left(-\frac{\left(\cos^{4}\left(b x +a \right)\right) \sin \left(b x +a \right)}{5}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}\right)}{b^{2}}-\frac{2 c d a \left(-\frac{\left(\cos^{4}\left(b x +a \right)\right) \sin \left(b x +a \right)}{5}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}\right)}{b}+c^{2} \left(-\frac{\left(\cos^{4}\left(b x +a \right)\right) \sin \left(b x +a \right)}{5}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}\right)}{b}"," ",0,"1/b*(1/b^2*d^2*(1/3*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)-4/15*sin(b*x+a)+4/15*(b*x+a)*cos(b*x+a)+2/45*(b*x+a)*cos(b*x+a)^3-2/135*(2+cos(b*x+a)^2)*sin(b*x+a)-1/5*(b*x+a)^2*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-2/25*(b*x+a)*cos(b*x+a)^5+2/125*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))-2/b^2*a*d^2*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/45*cos(b*x+a)^3+2/15*cos(b*x+a)-1/5*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-1/25*cos(b*x+a)^5)+2/b*c*d*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/45*cos(b*x+a)^3+2/15*cos(b*x+a)-1/5*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-1/25*cos(b*x+a)^5)+d^2/b^2*a^2*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))-2*c*d/b*a*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))+c^2*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a)))","B"
149,1,175,97,0.022000," ","int((d*x+c)*cos(b*x+a)^3*sin(b*x+a)^2,x)","\frac{\frac{d \left(\frac{\left(b x +a \right) \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}+\frac{\left(\cos^{3}\left(b x +a \right)\right)}{45}+\frac{2 \cos \left(b x +a \right)}{15}-\frac{\left(b x +a \right) \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5}-\frac{\left(\cos^{5}\left(b x +a \right)\right)}{25}\right)}{b}-\frac{d a \left(-\frac{\left(\cos^{4}\left(b x +a \right)\right) \sin \left(b x +a \right)}{5}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}\right)}{b}+c \left(-\frac{\left(\cos^{4}\left(b x +a \right)\right) \sin \left(b x +a \right)}{5}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}\right)}{b}"," ",0,"1/b*(1/b*d*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/45*cos(b*x+a)^3+2/15*cos(b*x+a)-1/5*(b*x+a)*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)-1/25*cos(b*x+a)^5)-1/b*d*a*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))+c*(-1/5*cos(b*x+a)^4*sin(b*x+a)+1/15*(2+cos(b*x+a)^2)*sin(b*x+a)))","A"
150,1,252,173,0.021000," ","int(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c),x)","\frac{\frac{b \left(\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}+\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}\right)}{8}-\frac{b \left(\frac{5 \Si \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \sin \left(\frac{-5 d a +5 c b}{d}\right)}{d}+\frac{5 \Ci \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \cos \left(\frac{-5 d a +5 c b}{d}\right)}{d}\right)}{80}-\frac{b \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}+\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{48}}{b}"," ",0,"1/b*(1/8*b*(Si(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)-1/80*b*(5*Si(5*b*x+5*a+5*(-a*d+b*c)/d)*sin(5*(-a*d+b*c)/d)/d+5*Ci(5*b*x+5*a+5*(-a*d+b*c)/d)*cos(5*(-a*d+b*c)/d)/d)-1/48*b*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d+3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d))","A"
151,1,367,239,0.023000," ","int(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c)^2,x)","\frac{\frac{b^{2} \left(-\frac{\cos \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}}{d}\right)}{8}-\frac{b^{2} \left(-\frac{5 \cos \left(5 b x +5 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{5 \left(\frac{5 \Si \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \cos \left(\frac{-5 d a +5 c b}{d}\right)}{d}-\frac{5 \Ci \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \sin \left(\frac{-5 d a +5 c b}{d}\right)}{d}\right)}{d}\right)}{80}-\frac{b^{2} \left(-\frac{3 \cos \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{3 \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}-\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{d}\right)}{48}}{b}"," ",0,"1/b*(1/8*b^2*(-cos(b*x+a)/((b*x+a)*d-d*a+c*b)/d-(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d)/d)-1/80*b^2*(-5*cos(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)/d-5*(5*Si(5*b*x+5*a+5*(-a*d+b*c)/d)*cos(5*(-a*d+b*c)/d)/d-5*Ci(5*b*x+5*a+5*(-a*d+b*c)/d)*sin(5*(-a*d+b*c)/d)/d)/d)-1/48*b^2*(-3*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d-3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d-3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d)/d))","A"
152,1,473,314,0.023000," ","int(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c)^3,x)","\frac{\frac{b^{3} \left(-\frac{\cos \left(b x +a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{-\frac{\sin \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}+\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}}{d}}{2 d}\right)}{8}-\frac{b^{3} \left(-\frac{5 \cos \left(5 b x +5 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{5 \left(-\frac{5 \sin \left(5 b x +5 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{25 \Si \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \sin \left(\frac{-5 d a +5 c b}{d}\right)}{d}+\frac{25 \Ci \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \cos \left(\frac{-5 d a +5 c b}{d}\right)}{d}}{d}\right)}{2 d}\right)}{80}-\frac{b^{3} \left(-\frac{3 \cos \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{3 \left(-\frac{3 \sin \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{9 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}+\frac{9 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}}{d}\right)}{2 d}\right)}{48}}{b}"," ",0,"1/b*(1/8*b^3*(-1/2*cos(b*x+a)/((b*x+a)*d-d*a+c*b)^2/d-1/2*(-sin(b*x+a)/((b*x+a)*d-d*a+c*b)/d+(Si(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)/d)/d)-1/80*b^3*(-5/2*cos(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)^2/d-5/2*(-5*sin(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)/d+5*(5*Si(5*b*x+5*a+5*(-a*d+b*c)/d)*sin(5*(-a*d+b*c)/d)/d+5*Ci(5*b*x+5*a+5*(-a*d+b*c)/d)*cos(5*(-a*d+b*c)/d)/d)/d)/d)-1/48*b^3*(-3/2*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^2/d-3/2*(-3*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d+3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d+3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d)/d)/d))","A"
153,1,583,383,0.023000," ","int(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c)^4,x)","\frac{\frac{b^{4} \left(-\frac{\cos \left(b x +a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}-\frac{-\frac{\sin \left(b x +a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{\cos \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}}{d}}{2 d}}{3 d}\right)}{8}-\frac{b^{4} \left(-\frac{5 \cos \left(5 b x +5 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}-\frac{5 \left(-\frac{5 \sin \left(5 b x +5 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{25 \cos \left(5 b x +5 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right) d}-\frac{25 \left(\frac{5 \Si \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \cos \left(\frac{-5 d a +5 c b}{d}\right)}{d}-\frac{5 \Ci \left(5 b x +5 a +\frac{-5 d a +5 c b}{d}\right) \sin \left(\frac{-5 d a +5 c b}{d}\right)}{d}\right)}{2 d}}{d}\right)}{3 d}\right)}{80}-\frac{b^{4} \left(-\frac{\cos \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{3} d}-\frac{-\frac{3 \sin \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{9 \cos \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right) d}-\frac{9 \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}-\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{2 d}}{d}}{d}\right)}{48}}{b}"," ",0,"1/b*(1/8*b^4*(-1/3*cos(b*x+a)/((b*x+a)*d-d*a+c*b)^3/d-1/3*(-1/2*sin(b*x+a)/((b*x+a)*d-d*a+c*b)^2/d+1/2*(-cos(b*x+a)/((b*x+a)*d-d*a+c*b)/d-(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d)/d)/d)/d)-1/80*b^4*(-5/3*cos(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)^3/d-5/3*(-5/2*sin(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)^2/d+5/2*(-5*cos(5*b*x+5*a)/((b*x+a)*d-d*a+c*b)/d-5*(5*Si(5*b*x+5*a+5*(-a*d+b*c)/d)*cos(5*(-a*d+b*c)/d)/d-5*Ci(5*b*x+5*a+5*(-a*d+b*c)/d)*sin(5*(-a*d+b*c)/d)/d)/d)/d)/d)-1/48*b^4*(-cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^3/d-(-3/2*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^2/d+3/2*(-3*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d-3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d-3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d)/d)/d)/d))","A"
154,0,0,273,0.252000," ","int((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \left(\cos^{3}\left(b x +a \right)\right) \left(\sin^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a)^3,x)","F"
155,1,2061,213,0.132000," ","int((d*x+c)^4*cos(b*x+a)^3*sin(b*x+a)^3,x)","\text{Expression too large to display}"," ",0,"1/b*(1/b^4*d^4*(1/4*(b*x+a)^4*sin(b*x+a)^4-(b*x+a)^3*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/12*(b*x+a)^2*sin(b*x+a)^4+1/6*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+1/9*(b*x+a)^2+1/216*sin(b*x+a)^4+5/36*sin(b*x+a)^2+1/4*(b*x+a)^2*cos(b*x+a)^2-1/2*(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+1/8*(b*x+a)^4-1/6*(b*x+a)^4*sin(b*x+a)^6+2/3*(b*x+a)^3*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)+1/18*(b*x+a)^2*sin(b*x+a)^6-1/9*(b*x+a)*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)-1/324*sin(b*x+a)^6)-4/b^4*a*d^4*(1/4*(b*x+a)^3*sin(b*x+a)^4-3/4*(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/24*(b*x+a)*sin(b*x+a)^4-1/96*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/18*b*x-1/18*a+1/8*(b*x+a)*cos(b*x+a)^2-1/16*cos(b*x+a)*sin(b*x+a)+1/12*(b*x+a)^3-1/6*(b*x+a)^3*sin(b*x+a)^6+1/2*(b*x+a)^2*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)+1/36*(b*x+a)*sin(b*x+a)^6+1/216*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))+4/b^3*c*d^3*(1/4*(b*x+a)^3*sin(b*x+a)^4-3/4*(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/24*(b*x+a)*sin(b*x+a)^4-1/96*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/18*b*x-1/18*a+1/8*(b*x+a)*cos(b*x+a)^2-1/16*cos(b*x+a)*sin(b*x+a)+1/12*(b*x+a)^3-1/6*(b*x+a)^3*sin(b*x+a)^6+1/2*(b*x+a)^2*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)+1/36*(b*x+a)*sin(b*x+a)^6+1/216*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))+6/b^4*a^2*d^4*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+1/24*(b*x+a)^2-1/72*sin(b*x+a)^4-1/24*sin(b*x+a)^2-1/6*(b*x+a)^2*sin(b*x+a)^6+1/3*(b*x+a)*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)+1/108*sin(b*x+a)^6)-12/b^3*a*c*d^3*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+1/24*(b*x+a)^2-1/72*sin(b*x+a)^4-1/24*sin(b*x+a)^2-1/6*(b*x+a)^2*sin(b*x+a)^6+1/3*(b*x+a)*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)+1/108*sin(b*x+a)^6)+6/b^2*c^2*d^2*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+1/24*(b*x+a)^2-1/72*sin(b*x+a)^4-1/24*sin(b*x+a)^2-1/6*(b*x+a)^2*sin(b*x+a)^6+1/3*(b*x+a)*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)+1/108*sin(b*x+a)^6)-4/b^4*a^3*d^4*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/24*b*x-1/24*a-1/6*(b*x+a)*sin(b*x+a)^6-1/36*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))+12/b^3*a^2*c*d^3*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/24*b*x-1/24*a-1/6*(b*x+a)*sin(b*x+a)^6-1/36*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))-12/b^2*a*c^2*d^2*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/24*b*x-1/24*a-1/6*(b*x+a)*sin(b*x+a)^6-1/36*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))+4/b*c^3*d*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/24*b*x-1/24*a-1/6*(b*x+a)*sin(b*x+a)^6-1/36*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))+1/b^4*a^4*d^4*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4)-4/b^3*a^3*c*d^3*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4)+6/b^2*a^2*c^2*d^2*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4)-4/b*a*c^3*d*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4)+c^4*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4))","B"
156,1,1100,165,0.023000," ","int((d*x+c)^3*cos(b*x+a)^3*sin(b*x+a)^3,x)","\frac{\frac{d^{3} \left(\frac{\left(b x +a \right)^{3} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{3 \left(b x +a \right)^{2} \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{4}-\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{24}-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{96}-\frac{b x}{18}-\frac{a}{18}+\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{8}-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{16}+\frac{\left(b x +a \right)^{3}}{12}-\frac{\left(b x +a \right)^{3} \left(\sin^{6}\left(b x +a \right)\right)}{6}+\frac{\left(b x +a \right)^{2} \left(-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{6}+\frac{5 b x}{16}+\frac{5 a}{16}\right)}{2}+\frac{\left(b x +a \right) \left(\sin^{6}\left(b x +a \right)\right)}{36}+\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{216}\right)}{b^{3}}-\frac{3 a \,d^{3} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}+\frac{\left(b x +a \right)^{2}}{24}-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{72}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{24}-\frac{\left(b x +a \right)^{2} \left(\sin^{6}\left(b x +a \right)\right)}{6}+\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{6}+\frac{5 b x}{16}+\frac{5 a}{16}\right)}{3}+\frac{\left(\sin^{6}\left(b x +a \right)\right)}{108}\right)}{b^{3}}+\frac{3 c \,d^{2} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}+\frac{\left(b x +a \right)^{2}}{24}-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{72}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{24}-\frac{\left(b x +a \right)^{2} \left(\sin^{6}\left(b x +a \right)\right)}{6}+\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{6}+\frac{5 b x}{16}+\frac{5 a}{16}\right)}{3}+\frac{\left(\sin^{6}\left(b x +a \right)\right)}{108}\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{b x}{24}-\frac{a}{24}-\frac{\left(b x +a \right) \left(\sin^{6}\left(b x +a \right)\right)}{6}-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{36}\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{b x}{24}-\frac{a}{24}-\frac{\left(b x +a \right) \left(\sin^{6}\left(b x +a \right)\right)}{6}-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{36}\right)}{b^{2}}+\frac{3 c^{2} d \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{b x}{24}-\frac{a}{24}-\frac{\left(b x +a \right) \left(\sin^{6}\left(b x +a \right)\right)}{6}-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{36}\right)}{b}-\frac{a^{3} d^{3} \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{4}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{12}\right)}{b^{3}}+\frac{3 a^{2} c \,d^{2} \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{4}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{12}\right)}{b^{2}}-\frac{3 a \,c^{2} d \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{4}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{12}\right)}{b}+c^{3} \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{4}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{12}\right)}{b}"," ",0,"1/b*(1/b^3*d^3*(1/4*(b*x+a)^3*sin(b*x+a)^4-3/4*(b*x+a)^2*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)-1/24*(b*x+a)*sin(b*x+a)^4-1/96*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/18*b*x-1/18*a+1/8*(b*x+a)*cos(b*x+a)^2-1/16*cos(b*x+a)*sin(b*x+a)+1/12*(b*x+a)^3-1/6*(b*x+a)^3*sin(b*x+a)^6+1/2*(b*x+a)^2*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)+1/36*(b*x+a)*sin(b*x+a)^6+1/216*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))-3/b^3*a*d^3*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+1/24*(b*x+a)^2-1/72*sin(b*x+a)^4-1/24*sin(b*x+a)^2-1/6*(b*x+a)^2*sin(b*x+a)^6+1/3*(b*x+a)*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)+1/108*sin(b*x+a)^6)+3/b^2*c*d^2*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+1/24*(b*x+a)^2-1/72*sin(b*x+a)^4-1/24*sin(b*x+a)^2-1/6*(b*x+a)^2*sin(b*x+a)^6+1/3*(b*x+a)*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)+1/108*sin(b*x+a)^6)+3/b^3*a^2*d^3*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/24*b*x-1/24*a-1/6*(b*x+a)*sin(b*x+a)^6-1/36*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))-6/b^2*a*c*d^2*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/24*b*x-1/24*a-1/6*(b*x+a)*sin(b*x+a)^6-1/36*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))+3/b*c^2*d*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/24*b*x-1/24*a-1/6*(b*x+a)*sin(b*x+a)^6-1/36*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))-1/b^3*a^3*d^3*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4)+3/b^2*a^2*c*d^2*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4)-3/b*a*c^2*d*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4)+c^3*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4))","B"
157,1,498,117,0.020000," ","int((d*x+c)^2*cos(b*x+a)^3*sin(b*x+a)^3,x)","\frac{\frac{d^{2} \left(\frac{\left(b x +a \right)^{2} \left(\sin^{4}\left(b x +a \right)\right)}{4}-\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}\right)}{2}+\frac{\left(b x +a \right)^{2}}{24}-\frac{\left(\sin^{4}\left(b x +a \right)\right)}{72}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{24}-\frac{\left(b x +a \right)^{2} \left(\sin^{6}\left(b x +a \right)\right)}{6}+\frac{\left(b x +a \right) \left(-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{6}+\frac{5 b x}{16}+\frac{5 a}{16}\right)}{3}+\frac{\left(\sin^{6}\left(b x +a \right)\right)}{108}\right)}{b^{2}}-\frac{2 a \,d^{2} \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{b x}{24}-\frac{a}{24}-\frac{\left(b x +a \right) \left(\sin^{6}\left(b x +a \right)\right)}{6}-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{36}\right)}{b^{2}}+\frac{2 c d \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{b x}{24}-\frac{a}{24}-\frac{\left(b x +a \right) \left(\sin^{6}\left(b x +a \right)\right)}{6}-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{36}\right)}{b}+\frac{d^{2} a^{2} \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{4}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{12}\right)}{b^{2}}-\frac{2 c d a \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{4}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{12}\right)}{b}+c^{2} \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{4}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{12}\right)}{b}"," ",0,"1/b*(1/b^2*d^2*(1/4*(b*x+a)^2*sin(b*x+a)^4-1/2*(b*x+a)*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)+1/24*(b*x+a)^2-1/72*sin(b*x+a)^4-1/24*sin(b*x+a)^2-1/6*(b*x+a)^2*sin(b*x+a)^6+1/3*(b*x+a)*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)+1/108*sin(b*x+a)^6)-2/b^2*a*d^2*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/24*b*x-1/24*a-1/6*(b*x+a)*sin(b*x+a)^6-1/36*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))+2/b*c*d*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/24*b*x-1/24*a-1/6*(b*x+a)*sin(b*x+a)^6-1/36*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))+d^2/b^2*a^2*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4)-2*c*d/b*a*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4)+c^2*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4))","B"
158,1,176,69,0.020000," ","int((d*x+c)*cos(b*x+a)^3*sin(b*x+a)^3,x)","\frac{\frac{d \left(\frac{\left(b x +a \right) \left(\sin^{4}\left(b x +a \right)\right)}{4}+\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{16}-\frac{b x}{24}-\frac{a}{24}-\frac{\left(b x +a \right) \left(\sin^{6}\left(b x +a \right)\right)}{6}-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{36}\right)}{b}-\frac{d a \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{4}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{12}\right)}{b}+c \left(-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{4}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{12}\right)}{b}"," ",0,"1/b*(1/b*d*(1/4*(b*x+a)*sin(b*x+a)^4+1/16*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-1/24*b*x-1/24*a-1/6*(b*x+a)*sin(b*x+a)^6-1/36*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a))-1/b*d*a*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4)+c*(-1/6*sin(b*x+a)^2*cos(b*x+a)^4-1/12*cos(b*x+a)^4))","B"
159,1,178,121,0.023000," ","int(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c),x)","\frac{-\frac{b \left(\frac{6 \Si \left(6 b x +6 a +\frac{-6 d a +6 c b}{d}\right) \cos \left(\frac{-6 d a +6 c b}{d}\right)}{d}-\frac{6 \Ci \left(6 b x +6 a +\frac{-6 d a +6 c b}{d}\right) \sin \left(\frac{-6 d a +6 c b}{d}\right)}{d}\right)}{192}+\frac{3 b \left(\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}-\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}\right)}{64}}{b}"," ",0,"1/b*(-1/192*b*(6*Si(6*b*x+6*a+6*(-a*d+b*c)/d)*cos(6*(-a*d+b*c)/d)/d-6*Ci(6*b*x+6*a+6*(-a*d+b*c)/d)*sin(6*(-a*d+b*c)/d)/d)+3/64*b*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d))","A"
160,1,256,167,0.025000," ","int(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c)^2,x)","\frac{-\frac{b^{2} \left(-\frac{6 \sin \left(6 b x +6 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{36 \Si \left(6 b x +6 a +\frac{-6 d a +6 c b}{d}\right) \sin \left(\frac{-6 d a +6 c b}{d}\right)}{d}+\frac{36 \Ci \left(6 b x +6 a +\frac{-6 d a +6 c b}{d}\right) \cos \left(\frac{-6 d a +6 c b}{d}\right)}{d}}{d}\right)}{192}+\frac{3 b^{2} \left(-\frac{2 \sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{4 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{4 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}}{d}\right)}{64}}{b}"," ",0,"1/b*(-1/192*b^2*(-6*sin(6*b*x+6*a)/((b*x+a)*d-d*a+c*b)/d+6*(6*Si(6*b*x+6*a+6*(-a*d+b*c)/d)*sin(6*(-a*d+b*c)/d)/d+6*Ci(6*b*x+6*a+6*(-a*d+b*c)/d)*cos(6*(-a*d+b*c)/d)/d)/d)+3/64*b^2*(-2*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d+2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d)/d))","A"
161,1,329,219,0.025000," ","int(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c)^3,x)","\frac{-\frac{b^{3} \left(-\frac{3 \sin \left(6 b x +6 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{18 \cos \left(6 b x +6 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{18 \left(\frac{6 \Si \left(6 b x +6 a +\frac{-6 d a +6 c b}{d}\right) \cos \left(\frac{-6 d a +6 c b}{d}\right)}{d}-\frac{6 \Ci \left(6 b x +6 a +\frac{-6 d a +6 c b}{d}\right) \sin \left(\frac{-6 d a +6 c b}{d}\right)}{d}\right)}{d}}{d}\right)}{192}+\frac{3 b^{3} \left(-\frac{\sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{2 \cos \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{2 \left(\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}-\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}\right)}{d}}{d}\right)}{64}}{b}"," ",0,"1/b*(-1/192*b^3*(-3*sin(6*b*x+6*a)/((b*x+a)*d-d*a+c*b)^2/d+3*(-6*cos(6*b*x+6*a)/((b*x+a)*d-d*a+c*b)/d-6*(6*Si(6*b*x+6*a+6*(-a*d+b*c)/d)*cos(6*(-a*d+b*c)/d)/d-6*Ci(6*b*x+6*a+6*(-a*d+b*c)/d)*sin(6*(-a*d+b*c)/d)/d)/d)/d)+3/64*b^3*(-sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d+(-2*cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d-2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d)/d)/d))","A"
162,1,404,267,0.024000," ","int(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c)^4,x)","\frac{\frac{3 b^{4} \left(-\frac{2 \sin \left(2 b x +2 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{2 \cos \left(2 b x +2 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{2 \left(-\frac{2 \sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{4 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{4 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}}{d}\right)}{3 d}}{d}\right)}{64}-\frac{b^{4} \left(-\frac{2 \sin \left(6 b x +6 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{3} d}+\frac{-\frac{6 \cos \left(6 b x +6 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{6 \left(-\frac{6 \sin \left(6 b x +6 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{36 \Si \left(6 b x +6 a +\frac{-6 d a +6 c b}{d}\right) \sin \left(\frac{-6 d a +6 c b}{d}\right)}{d}+\frac{36 \Ci \left(6 b x +6 a +\frac{-6 d a +6 c b}{d}\right) \cos \left(\frac{-6 d a +6 c b}{d}\right)}{d}}{d}\right)}{d}}{d}\right)}{192}}{b}"," ",0,"1/b*(3/64*b^4*(-2/3*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^3/d+2/3*(-cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d-(-2*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d+2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d)/d)/d)/d)-1/192*b^4*(-2*sin(6*b*x+6*a)/((b*x+a)*d-d*a+c*b)^3/d+2*(-3*cos(6*b*x+6*a)/((b*x+a)*d-d*a+c*b)^2/d-3*(-6*sin(6*b*x+6*a)/((b*x+a)*d-d*a+c*b)/d+6*(6*Si(6*b*x+6*a+6*(-a*d+b*c)/d)*sin(6*(-a*d+b*c)/d)/d+6*Ci(6*b*x+6*a+6*(-a*d+b*c)/d)*cos(6*(-a*d+b*c)/d)/d)/d)/d)/d))","A"
163,0,0,145,0.125000," ","int((d*x+c)^m*cos(b*x+a)^2*cot(b*x+a),x)","\int \left(d x +c \right)^{m} \left(\cos^{2}\left(b x +a \right)\right) \cot \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)^2*cot(b*x+a),x)","F"
164,1,1326,276,0.536000," ","int((d*x+c)^4*cos(b*x+a)^2*cot(b*x+a),x)","-\frac{d^{4} a^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{12 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 c^{2} d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{12 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{4}}{b}+\frac{d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{4}}{b}+\frac{\left(2 d^{4} x^{4} b^{4}+8 b^{4} c \,d^{3} x^{3}+12 b^{4} c^{2} d^{2} x^{2}+8 b^{4} c^{3} d x +2 b^{4} c^{4}-6 b^{2} d^{4} x^{2}-12 b^{2} c \,d^{3} x -6 c^{2} d^{2} b^{2}+3 d^{4}\right) \cos \left(2 b x +2 a \right)}{8 b^{5}}+i c^{4} x -\frac{2 c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{i d^{4} x^{5}}{5}+\frac{d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{5}}-\frac{2 d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{8 i d^{4} a^{5}}{5 b^{5}}-i c \,d^{3} x^{4}-2 i c^{2} d^{2} x^{3}-2 i c^{3} d \,x^{2}-\frac{24 d^{4} \polylog \left(5, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 d^{4} \polylog \left(5, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{4 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{24 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{4 i c^{3} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 i c^{3} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{24 c \,d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 c \,d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 i c \,d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{4 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{24 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{4 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{4 c^{3} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{6 c^{2} d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{6 c^{2} d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{12 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{12 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c^{2} d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c \,d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{2 i d^{4} a^{4} x}{b^{4}}-\frac{4 i c^{3} d \,a^{2}}{b^{2}}+\frac{8 i c^{2} d^{2} a^{3}}{b^{3}}-\frac{6 i c \,d^{3} a^{4}}{b^{4}}+\frac{8 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{8 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{12 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{4 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{8 i c \,d^{3} a^{3} x}{b^{3}}+\frac{12 i c^{2} d^{2} a^{2} x}{b^{2}}-\frac{8 i c^{3} d a x}{b}-\frac{d \left(2 b^{2} d^{3} x^{3}+6 b^{2} c \,d^{2} x^{2}+6 b^{2} c^{2} d x +2 b^{2} c^{3}-3 d^{3} x -3 c \,d^{2}\right) \sin \left(2 b x +2 a \right)}{4 b^{4}}"," ",0,"1/b^5*d^4*a^4*ln(exp(I*(b*x+a))-1)-2/b^5*d^4*a^4*ln(exp(I*(b*x+a)))+12/b^3*c^2*d^2*polylog(3,-exp(I*(b*x+a)))+12/b^3*c^2*d^2*polylog(3,exp(I*(b*x+a)))-1/b^5*d^4*a^4*ln(1-exp(I*(b*x+a)))+12/b^3*d^4*polylog(3,exp(I*(b*x+a)))*x^2+12/b^3*d^4*polylog(3,-exp(I*(b*x+a)))*x^2+8/5*I/b^5*d^4*a^5-I*c*d^3*x^4-2*I*c^2*d^2*x^3-2*I*c^3*d*x^2-24*d^4*polylog(5,-exp(I*(b*x+a)))/b^5-24*d^4*polylog(5,exp(I*(b*x+a)))/b^5+1/8*(2*b^4*d^4*x^4+8*b^4*c*d^3*x^3+12*b^4*c^2*d^2*x^2+8*b^4*c^3*d*x+2*b^4*c^4-6*b^2*d^4*x^2-12*b^2*c*d^3*x-6*b^2*c^2*d^2+3*d^4)/b^5*cos(2*b*x+2*a)+I*c^4*x-2/b*c^4*ln(exp(I*(b*x+a)))+1/b*c^4*ln(exp(I*(b*x+a))+1)+1/b*c^4*ln(exp(I*(b*x+a))-1)-1/5*I*d^4*x^5+4/b*c^3*d*ln(exp(I*(b*x+a))+1)*x+4/b*c^3*d*ln(1-exp(I*(b*x+a)))*x+4/b^2*c^3*d*ln(1-exp(I*(b*x+a)))*a+6/b*c^2*d^2*ln(exp(I*(b*x+a))+1)*x^2+24/b^3*c*d^3*polylog(3,-exp(I*(b*x+a)))*x-6/b^3*c^2*d^2*a^2*ln(1-exp(I*(b*x+a)))+6/b*c^2*d^2*ln(1-exp(I*(b*x+a)))*x^2+24/b^3*c*d^3*polylog(3,exp(I*(b*x+a)))*x+24*I/b^4*c*d^3*polylog(4,-exp(I*(b*x+a)))+24*I/b^4*c*d^3*polylog(4,exp(I*(b*x+a)))+2*I/b^4*d^4*a^4*x-4*I/b^2*c^3*d*a^2+8*I/b^3*c^2*d^2*a^3-6*I/b^4*c*d^3*a^4-4*I/b^2*d^4*polylog(2,exp(I*(b*x+a)))*x^3+24*I/b^4*d^4*polylog(4,exp(I*(b*x+a)))*x-4*I/b^2*d^4*polylog(2,-exp(I*(b*x+a)))*x^3+24*I/b^4*d^4*polylog(4,-exp(I*(b*x+a)))*x-4*I/b^2*c^3*d*polylog(2,-exp(I*(b*x+a)))-4*I/b^2*c^3*d*polylog(2,exp(I*(b*x+a)))+8/b^2*c^3*d*a*ln(exp(I*(b*x+a)))-4/b^4*c*d^3*a^3*ln(exp(I*(b*x+a))-1)+8/b^4*c*d^3*a^3*ln(exp(I*(b*x+a)))+6/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a))-1)-12/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a)))-4/b^2*c^3*d*a*ln(exp(I*(b*x+a))-1)+1/b*d^4*ln(1-exp(I*(b*x+a)))*x^4+1/b*d^4*ln(exp(I*(b*x+a))+1)*x^4-8*I/b^3*c*d^3*a^3*x+12*I/b^2*c^2*d^2*a^2*x-8*I/b*c^3*d*a*x-12*I/b^2*c*d^3*polylog(2,-exp(I*(b*x+a)))*x^2-12*I/b^2*c^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-12*I/b^2*c^2*d^2*polylog(2,exp(I*(b*x+a)))*x-12*I/b^2*c*d^3*polylog(2,exp(I*(b*x+a)))*x^2+4/b*c*d^3*ln(exp(I*(b*x+a))+1)*x^3+4/b*c*d^3*ln(1-exp(I*(b*x+a)))*x^3+4/b^4*c*d^3*ln(1-exp(I*(b*x+a)))*a^3-1/4/b^4*d*(2*b^2*d^3*x^3+6*b^2*c*d^2*x^2+6*b^2*c^2*d*x+2*b^2*c^3-3*d^3*x-3*c*d^2)*sin(2*b*x+2*a)","B"
165,1,899,215,0.463000," ","int((d*x+c)^3*cos(b*x+a)^2*cot(b*x+a),x)","\frac{6 i c \,d^{2} a^{2} x}{b^{2}}-\frac{6 i c^{2} d a x}{b}-\frac{6 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{6 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{\left(2 b^{2} d^{3} x^{3}+6 b^{2} c \,d^{2} x^{2}+6 b^{2} c^{2} d x +2 b^{2} c^{3}-3 d^{3} x -3 c \,d^{2}\right) \cos \left(2 b x +2 a \right)}{8 b^{3}}-\frac{d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{2 d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i a^{4} d^{3}}{2 b^{4}}-i c \,d^{2} x^{3}-\frac{3 i c^{2} d \,x^{2}}{2}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{6 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+i c^{3} x -\frac{i d^{3} x^{4}}{4}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{2 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{6 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i c^{2} d \,a^{2}}{b^{2}}-\frac{2 i a^{3} d^{3} x}{b^{3}}+\frac{4 i c \,d^{2} a^{3}}{b^{3}}-\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{3 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{6 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 d \left(2 d^{2} x^{2} b^{2}+4 b^{2} c d x +2 b^{2} c^{2}-d^{2}\right) \sin \left(2 b x +2 a \right)}{16 b^{4}}"," ",0,"6*I/b^2*c*d^2*a^2*x-6*I/b^2*c*d^2*polylog(2,exp(I*(b*x+a)))*x-6*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x-6*I/b*c^2*d*a*x+6*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4+I*c^3*x+1/8/b^3*(2*b^2*d^3*x^3+6*b^2*c*d^2*x^2+6*b^2*c^2*d*x+2*b^2*c^3-3*d^3*x-3*c*d^2)*cos(2*b*x+2*a)-1/b^4*d^3*a^3*ln(exp(I*(b*x+a))-1)+2/b^4*d^3*a^3*ln(exp(I*(b*x+a)))+6/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+6/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))+6/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x+6/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x-3/2*I/b^4*a^4*d^3+6*I/b^4*d^3*polylog(4,-exp(I*(b*x+a)))-I*c*d^2*x^3-3/2*I*c^2*d*x^2-1/4*I*d^3*x^4+1/b*c^3*ln(exp(I*(b*x+a))-1)+1/b*c^3*ln(exp(I*(b*x+a))+1)-2/b*c^3*ln(exp(I*(b*x+a)))+3/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))-1)-6/b^3*c*d^2*a^2*ln(exp(I*(b*x+a)))-3*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))-3*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-3*I/b^2*c^2*d*a^2-2*I/b^3*a^3*d^3*x+4*I/b^3*c*d^2*a^3-3*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2-3*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+3/b*c^2*d*ln(exp(I*(b*x+a))+1)*x+3/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+3/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-3/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+3/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2+3/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2-3/b^2*c^2*d*a*ln(exp(I*(b*x+a))-1)+6/b^2*c^2*d*a*ln(exp(I*(b*x+a)))+1/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+1/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3+1/b*d^3*ln(exp(I*(b*x+a))+1)*x^3-3/16*d*(2*b^2*d^2*x^2+4*b^2*c*d*x+2*b^2*c^2-d^2)/b^4*sin(2*b*x+2*a)","B"
166,1,535,159,0.493000," ","int((d*x+c)^2*cos(b*x+a)^2*cot(b*x+a),x)","\frac{d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{2 d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{4 i d^{2} a^{3}}{3 b^{3}}-i c d \,x^{2}-\frac{4 i c d a x}{b}+i c^{2} x -\frac{2 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{i d^{2} x^{3}}{3}+\frac{2 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{d \left(d x +c \right) \sin \left(2 b x +2 a \right)}{4 b^{2}}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{4 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{2 i d^{2} a^{2} x}{b^{2}}-\frac{2 i c d \,a^{2}}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{\left(2 d^{2} x^{2} b^{2}+4 b^{2} c d x +2 b^{2} c^{2}-d^{2}\right) \cos \left(2 b x +2 a \right)}{8 b^{3}}"," ",0,"1/b^3*d^2*a^2*ln(exp(I*(b*x+a))-1)-2/b^3*d^2*a^2*ln(exp(I*(b*x+a)))+1/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-1/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2+1/b*d^2*ln(exp(I*(b*x+a))+1)*x^2+4/3*I/b^3*d^2*a^3-I*c*d*x^2-4*I/b*c*d*a*x+2*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+2*d^2*polylog(3,exp(I*(b*x+a)))/b^3+I*c^2*x-2/b*c^2*ln(exp(I*(b*x+a)))+1/b*c^2*ln(exp(I*(b*x+a))-1)+1/b*c^2*ln(exp(I*(b*x+a))+1)-1/3*I*d^2*x^3-1/4*d*(d*x+c)*sin(2*b*x+2*a)/b^2+2/b*c*d*ln(1-exp(I*(b*x+a)))*x+2/b^2*c*d*ln(1-exp(I*(b*x+a)))*a+2/b*c*d*ln(exp(I*(b*x+a))+1)*x+4/b^2*c*d*a*ln(exp(I*(b*x+a)))-2/b^2*c*d*a*ln(exp(I*(b*x+a))-1)+2*I/b^2*d^2*a^2*x-2*I/b^2*c*d*a^2-2*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-2*I/b^2*d^2*polylog(2,exp(I*(b*x+a)))*x-2*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))-2*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))+1/8*(2*b^2*d^2*x^2+4*b^2*c*d*x+2*b^2*c^2-d^2)/b^3*cos(2*b*x+2*a)","B"
167,1,249,98,0.411000," ","int((d*x+c)*cos(b*x+a)^2*cot(b*x+a),x)","i c x -\frac{i d \,x^{2}}{2}+\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{2 c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{i d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{i d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{i d \,a^{2}}{b^{2}}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{2 i d a x}{b}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{2 d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{\left(d x +c \right) \cos \left(2 b x +2 a \right)}{4 b}-\frac{d \sin \left(2 b x +2 a \right)}{8 b^{2}}"," ",0,"I*c*x-2*I/b*d*a*x+1/b*c*ln(exp(I*(b*x+a))-1)+1/b*c*ln(exp(I*(b*x+a))+1)-2/b*c*ln(exp(I*(b*x+a)))-1/2*I*d*x^2-I/b^2*d*a^2-I*d*polylog(2,exp(I*(b*x+a)))/b^2+1/b*d*ln(exp(I*(b*x+a))+1)*x-I*d*polylog(2,-exp(I*(b*x+a)))/b^2+1/b*d*ln(1-exp(I*(b*x+a)))*x+1/b^2*d*ln(1-exp(I*(b*x+a)))*a-1/b^2*d*a*ln(exp(I*(b*x+a))-1)+2/b^2*d*a*ln(exp(I*(b*x+a)))+1/4*(d*x+c)*cos(2*b*x+2*a)/b-1/8*d*sin(2*b*x+2*a)/b^2","B"
168,0,0,77,0.302000," ","int(cos(b*x+a)^2*cot(b*x+a)/(d*x+c),x)","\int \frac{\left(\cos^{2}\left(b x +a \right)\right) \cot \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(cos(b*x+a)^2*cot(b*x+a)/(d*x+c),x)","F"
169,0,0,99,0.461000," ","int(cos(b*x+a)^2*cot(b*x+a)/(d*x+c)^2,x)","\int \frac{\left(\cos^{2}\left(b x +a \right)\right) \cot \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(cos(b*x+a)^2*cot(b*x+a)/(d*x+c)^2,x)","F"
170,0,0,141,0.096000," ","int((d*x+c)^m*cos(b*x+a)*cot(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \cos \left(b x +a \right) \left(\cot^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)*cot(b*x+a)^2,x)","F"
171,1,1056,281,0.161000," ","int((d*x+c)^4*cos(b*x+a)*cot(b*x+a)^2,x)","\frac{8 d^{4} a^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 d^{3} c \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 d^{3} c \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{8 d \,c^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{24 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{24 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{24 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{24 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{4 d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{4 d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{5}}-\frac{4 d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b^{2}}-\frac{4 d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{3}}{b^{5}}+\frac{24 i d^{3} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{24 i d^{3} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{i \left(d^{4} x^{4} b^{4}+4 b^{4} c \,d^{3} x^{3}+4 i b^{3} d^{4} x^{3}+6 b^{4} c^{2} d^{2} x^{2}+12 i b^{3} c \,d^{3} x^{2}+4 b^{4} c^{3} d x +12 i b^{3} c^{2} d^{2} x +b^{4} c^{4}+4 i b^{3} c^{3} d -12 b^{2} d^{4} x^{2}-24 b^{2} c \,d^{3} x -24 i b \,d^{4} x -12 c^{2} d^{2} b^{2}-24 i b c \,d^{3}+24 d^{4}\right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{5}}-\frac{i \left(d^{4} x^{4} b^{4}+4 b^{4} c \,d^{3} x^{3}-4 i b^{3} d^{4} x^{3}+6 b^{4} c^{2} d^{2} x^{2}-12 i b^{3} c \,d^{3} x^{2}+4 b^{4} c^{3} d x -12 i b^{3} c^{2} d^{2} x +b^{4} c^{4}-4 i b^{3} c^{3} d -12 b^{2} d^{4} x^{2}-24 b^{2} c \,d^{3} x +24 i b \,d^{4} x -12 c^{2} d^{2} b^{2}+24 i b c \,d^{3}+24 d^{4}\right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{5}}-\frac{2 i \left(d^{4} x^{4}+4 c \,d^{3} x^{3}+6 c^{2} d^{2} x^{2}+4 c^{3} d x +c^{4}\right) {\mathrm e}^{i \left(b x +a \right)}}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}-\frac{24 d^{3} c \,a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 d^{2} c^{2} a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{12 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{12 i d^{2} c^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{12 i d^{2} c^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{2} c^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{12 d^{2} c^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{12 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}-\frac{12 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{3}}+\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}-\frac{12 d^{3} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}+\frac{12 d^{3} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{b^{4}}"," ",0,"8/b^5*d^4*a^3*arctanh(exp(I*(b*x+a)))-24/b^4*d^3*c*polylog(3,-exp(I*(b*x+a)))+24/b^4*d^3*c*polylog(3,exp(I*(b*x+a)))-8/b^2*d*c^3*arctanh(exp(I*(b*x+a)))-24/b^4*d^4*polylog(3,-exp(I*(b*x+a)))*x+24/b^4*d^4*polylog(3,exp(I*(b*x+a)))*x-24*I*d^4*polylog(4,-exp(I*(b*x+a)))/b^5+24*I/b^3*d^3*c*polylog(2,-exp(I*(b*x+a)))*x-24*I/b^3*d^3*c*polylog(2,exp(I*(b*x+a)))*x+24*I*d^4*polylog(4,exp(I*(b*x+a)))/b^5+1/2*I*(d^4*x^4*b^4+4*b^4*c*d^3*x^3+6*b^4*c^2*d^2*x^2+4*b^4*c^3*d*x+4*I*b^3*d^4*x^3+b^4*c^4-12*b^2*d^4*x^2+12*I*b^3*c*d^3*x^2-24*b^2*c*d^3*x+12*I*b^3*c^2*d^2*x-12*c^2*d^2*b^2+4*I*b^3*c^3*d-24*I*b*d^4*x+24*d^4-24*I*b*c*d^3)/b^5*exp(I*(b*x+a))-2*I*(d^4*x^4+4*c*d^3*x^3+6*c^2*d^2*x^2+4*c^3*d*x+c^4)*exp(I*(b*x+a))/b/(exp(2*I*(b*x+a))-1)-1/2*I*(d^4*x^4*b^4+4*b^4*c*d^3*x^3+6*b^4*c^2*d^2*x^2+4*b^4*c^3*d*x-4*I*b^3*d^4*x^3+b^4*c^4-12*b^2*d^4*x^2-12*I*b^3*c*d^3*x^2-24*b^2*c*d^3*x-12*I*b^3*c^2*d^2*x-12*c^2*d^2*b^2-4*I*b^3*c^3*d+24*I*b*d^4*x+24*d^4+24*I*b*c*d^3)/b^5*exp(-I*(b*x+a))+12/b^2*d^2*c^2*ln(1-exp(I*(b*x+a)))*x+12/b^3*d^2*c^2*ln(1-exp(I*(b*x+a)))*a-12/b^2*d^2*c^2*ln(exp(I*(b*x+a))+1)*x-12/b^3*d^2*c^2*ln(exp(I*(b*x+a))+1)*a+12/b^2*d^3*c*ln(1-exp(I*(b*x+a)))*x^2-12/b^4*d^3*c*ln(1-exp(I*(b*x+a)))*a^2-12/b^2*d^3*c*ln(exp(I*(b*x+a))+1)*x^2+12/b^4*d^3*c*ln(exp(I*(b*x+a))+1)*a^2+4/b^2*d^4*ln(1-exp(I*(b*x+a)))*x^3+4/b^5*d^4*ln(1-exp(I*(b*x+a)))*a^3-4/b^2*d^4*ln(exp(I*(b*x+a))+1)*x^3-4/b^5*d^4*ln(exp(I*(b*x+a))+1)*a^3-24/b^4*d^3*c*a^2*arctanh(exp(I*(b*x+a)))+24/b^3*d^2*c^2*a*arctanh(exp(I*(b*x+a)))+12*I/b^3*d^4*polylog(2,-exp(I*(b*x+a)))*x^2-12*I/b^3*d^4*polylog(2,exp(I*(b*x+a)))*x^2+12*I/b^3*d^2*c^2*polylog(2,-exp(I*(b*x+a)))-12*I/b^3*d^2*c^2*polylog(2,exp(I*(b*x+a)))","B"
172,1,649,204,0.129000," ","int((d*x+c)^3*cos(b*x+a)*cot(b*x+a)^2,x)","\frac{i \left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}+3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x +6 i b^{2} c \,d^{2} x +b^{3} c^{3}+3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b -6 i d^{3}\right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{4}}-\frac{i \left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}-3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x -6 i b^{2} c \,d^{2} x +b^{3} c^{3}-3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b +6 i d^{3}\right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{4}}-\frac{2 i \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right) {\mathrm e}^{i \left(b x +a \right)}}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}+\frac{6 d^{2} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 d^{2} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}-\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{3}}-\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 d \,c^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 d^{3} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{12 d^{2} c a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}+\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{b^{4}}-\frac{6 i d^{2} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}+\frac{6 i d^{2} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"1/2*I*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3+3*I*b^2*d^3*x^2-6*b*d^3*x+6*I*b^2*c*d^2*x-6*c*d^2*b+3*I*b^2*c^2*d-6*I*d^3)/b^4*exp(I*(b*x+a))-1/2*I*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3-3*I*b^2*d^3*x^2-6*b*d^3*x-6*I*b^2*c*d^2*x-6*c*d^2*b-3*I*b^2*c^2*d+6*I*d^3)/b^4*exp(-I*(b*x+a))+6*I/b^3*d^3*polylog(2,-exp(I*(b*x+a)))*x+6/b^2*d^2*c*ln(1-exp(I*(b*x+a)))*x+6/b^3*d^2*c*ln(1-exp(I*(b*x+a)))*a-6/b^2*d^2*c*ln(exp(I*(b*x+a))+1)*x-6/b^3*d^2*c*ln(exp(I*(b*x+a))+1)*a-6*d^3*polylog(3,-exp(I*(b*x+a)))/b^4+6*d^3*polylog(3,exp(I*(b*x+a)))/b^4-6/b^2*d*c^2*arctanh(exp(I*(b*x+a)))-6/b^4*d^3*a^2*arctanh(exp(I*(b*x+a)))+12/b^3*d^2*c*a*arctanh(exp(I*(b*x+a)))-6*I/b^3*d^3*polylog(2,exp(I*(b*x+a)))*x-6*I/b^3*d^2*c*polylog(2,exp(I*(b*x+a)))-3/b^2*d^3*ln(exp(I*(b*x+a))+1)*x^2+3/b^4*d^3*ln(exp(I*(b*x+a))+1)*a^2+6*I/b^3*d^2*c*polylog(2,-exp(I*(b*x+a)))+3/b^2*d^3*ln(1-exp(I*(b*x+a)))*x^2-3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^2-2*I*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)*exp(I*(b*x+a))/b/(exp(2*I*(b*x+a))-1)","B"
173,1,332,131,0.131000," ","int((d*x+c)^2*cos(b*x+a)*cot(b*x+a)^2,x)","\frac{i \left(d^{2} x^{2} b^{2}+2 b^{2} c d x +2 i b \,d^{2} x +b^{2} c^{2}+2 i b c d -2 d^{2}\right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{3}}-\frac{i \left(d^{2} x^{2} b^{2}+2 b^{2} c d x -2 i b \,d^{2} x +b^{2} c^{2}-2 i b c d -2 d^{2}\right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{3}}-\frac{2 i {\mathrm e}^{i \left(b x +a \right)} \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}-\frac{4 d c \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}-\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{3}}+\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{4 d^{2} a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"1/2*I*(d^2*x^2*b^2+2*b^2*c*d*x+b^2*c^2+2*I*b*d^2*x-2*d^2+2*I*b*c*d)/b^3*exp(I*(b*x+a))-1/2*I*(d^2*x^2*b^2+2*b^2*c*d*x+b^2*c^2-2*I*b*d^2*x-2*d^2-2*I*b*c*d)/b^3*exp(-I*(b*x+a))-2*I*exp(I*(b*x+a))*(d^2*x^2+2*c*d*x+c^2)/b/(exp(2*I*(b*x+a))-1)-4/b^2*d*c*arctanh(exp(I*(b*x+a)))-2/b^2*d^2*ln(exp(I*(b*x+a))+1)*x-2/b^3*d^2*ln(exp(I*(b*x+a))+1)*a+2*I*d^2*polylog(2,-exp(I*(b*x+a)))/b^3+2/b^2*d^2*ln(1-exp(I*(b*x+a)))*x+2/b^3*d^2*ln(1-exp(I*(b*x+a)))*a-2*I*d^2*polylog(2,exp(I*(b*x+a)))/b^3+4/b^3*d^2*a*arctanh(exp(I*(b*x+a)))","B"
174,1,124,58,0.141000," ","int((d*x+c)*cos(b*x+a)*cot(b*x+a)^2,x)","\frac{i \left(b d x +c b +i d \right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{2}}-\frac{i \left(b d x +c b -i d \right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{2}}-\frac{2 i {\mathrm e}^{i \left(b x +a \right)} \left(d x +c \right)}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}"," ",0,"1/2*I*(b*d*x+c*b+I*d)/b^2*exp(I*(b*x+a))-1/2*I*(b*d*x+c*b-I*d)/b^2*exp(-I*(b*x+a))-2*I*exp(I*(b*x+a))*(d*x+c)/b/(exp(2*I*(b*x+a))-1)-d/b^2*ln(exp(I*(b*x+a))+1)+d/b^2*ln(exp(I*(b*x+a))-1)","C"
175,0,0,74,0.273000," ","int(cos(b*x+a)*cot(b*x+a)^2/(d*x+c),x)","\int \frac{\cos \left(b x +a \right) \left(\cot^{2}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(cos(b*x+a)*cot(b*x+a)^2/(d*x+c),x)","F"
176,0,0,92,0.435000," ","int(cos(b*x+a)*cot(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\cos \left(b x +a \right) \left(\cot^{2}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(cos(b*x+a)*cot(b*x+a)^2/(d*x+c)^2,x)","F"
177,0,0,18,0.115000," ","int((d*x+c)^m*cot(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \left(\cot^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cot(b*x+a)^3,x)","F"
178,1,1868,273,0.204000," ","int((d*x+c)^4*cot(b*x+a)^3,x)","\frac{d^{4} a^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{12 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{12 c^{2} d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{12 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{12 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{4}}{b}-\frac{d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{4}}{b}-\frac{24 i d^{3} c a x}{b^{3}}-i c^{4} x +\frac{2 c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{i d^{4} x^{5}}{5}-\frac{d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{5}}+\frac{2 d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{8 i d^{4} a^{5}}{5 b^{5}}+i c \,d^{3} x^{4}+2 i c^{2} d^{2} x^{3}+2 i c^{3} d \,x^{2}+\frac{24 d^{4} \polylog \left(5, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{24 d^{4} \polylog \left(5, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{12 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{12 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{6 d^{4} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{5}}-\frac{12 d^{4} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{6 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{6 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{12 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 d^{4} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{6 d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{6 d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{3}}-\frac{4 i d^{4} x^{3}}{b^{2}}+\frac{8 i d^{4} a^{3}}{b^{5}}+\frac{2 b \,d^{4} x^{4} {\mathrm e}^{2 i \left(b x +a \right)}+8 b c \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}+12 b \,c^{2} d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+8 b \,c^{3} d x \,{\mathrm e}^{2 i \left(b x +a \right)}-4 i d^{4} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}+2 b \,c^{4} {\mathrm e}^{2 i \left(b x +a \right)}-12 i c \,d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-12 i c^{2} d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+4 i d^{4} x^{3}-4 i c^{3} d \,{\mathrm e}^{2 i \left(b x +a \right)}+12 i c \,d^{3} x^{2}+12 i c^{2} d^{2} x +4 i c^{3} d}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{12 d^{3} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}+\frac{24 d^{3} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 d^{3} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{12 i d^{4} a^{2} x}{b^{4}}-\frac{12 i d^{3} c \,x^{2}}{b^{2}}-\frac{12 i d^{3} c \,a^{2}}{b^{4}}-\frac{12 i d^{3} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 i d^{3} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{12 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{4 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}-\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}-\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}-\frac{24 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{4 i c^{3} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{4 i c^{3} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{24 c \,d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{24 c \,d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{24 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{24 i c \,d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{4 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{24 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{4 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{4 c^{3} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{6 c^{2} d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{6 c^{2} d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 c^{2} d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{12 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{12 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{12 i c^{2} d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{12 i c \,d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{12 d^{3} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}-\frac{2 i d^{4} a^{4} x}{b^{4}}+\frac{4 i c^{3} d \,a^{2}}{b^{2}}-\frac{8 i c^{2} d^{2} a^{3}}{b^{3}}+\frac{6 i c \,d^{3} a^{4}}{b^{4}}-\frac{8 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{4 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}-\frac{8 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{12 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{4 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{8 i c \,d^{3} a^{3} x}{b^{3}}-\frac{12 i c^{2} d^{2} a^{2} x}{b^{2}}+\frac{8 i c^{3} d a x}{b}"," ",0,"-1/b^5*d^4*a^4*ln(exp(I*(b*x+a))-1)+2/b^5*d^4*a^4*ln(exp(I*(b*x+a)))-12/b^3*c^2*d^2*polylog(3,-exp(I*(b*x+a)))-12/b^3*c^2*d^2*polylog(3,exp(I*(b*x+a)))+1/b^5*d^4*a^4*ln(1-exp(I*(b*x+a)))-12/b^3*d^4*polylog(3,exp(I*(b*x+a)))*x^2-12/b^3*d^4*polylog(3,-exp(I*(b*x+a)))*x^2+1/5*I*d^4*x^5+I*c*d^3*x^4-24*I/b^3*d^3*c*a*x+12*d^4*polylog(3,-exp(I*(b*x+a)))/b^5+12*d^4*polylog(3,exp(I*(b*x+a)))/b^5+24*d^4*polylog(5,-exp(I*(b*x+a)))/b^5+24*d^4*polylog(5,exp(I*(b*x+a)))/b^5+8*I/b*a*c^3*d*x-12*I/b^2*a^2*c^2*d^2*x+8*I/b^3*c*d^3*a^3*x+12*I/b^2*polylog(2,exp(I*(b*x+a)))*c^2*d^2*x+12*I/b^2*c*d^3*polylog(2,exp(I*(b*x+a)))*x^2+6*I/b^4*c*d^3*a^4-24*I/b^4*c*d^3*polylog(4,exp(I*(b*x+a)))+4*I/b^2*c^3*d*polylog(2,exp(I*(b*x+a)))-8*I/b^3*a^3*c^2*d^2+4*I/b^2*d^4*polylog(2,exp(I*(b*x+a)))*x^3-24*I/b^4*d^4*polylog(4,exp(I*(b*x+a)))*x-2*I/b^4*d^4*a^4*x+4*I/b^2*a^2*c^3*d-I*c^4*x+2/b*c^4*ln(exp(I*(b*x+a)))-1/b*c^4*ln(exp(I*(b*x+a))+1)-1/b*c^4*ln(exp(I*(b*x+a))-1)+6/b^5*d^4*a^2*ln(exp(I*(b*x+a))-1)-12/b^5*d^4*a^2*ln(exp(I*(b*x+a)))+6/b^3*d^2*c^2*ln(exp(I*(b*x+a))-1)+6/b^3*d^2*c^2*ln(exp(I*(b*x+a))+1)-12/b^3*d^2*c^2*ln(exp(I*(b*x+a)))-6/b^5*d^4*a^2*ln(1-exp(I*(b*x+a)))+6/b^3*d^4*ln(1-exp(I*(b*x+a)))*x^2+6/b^3*d^4*ln(exp(I*(b*x+a))+1)*x^2-4*I/b^2*d^4*x^3+8*I/b^5*d^4*a^3-24*I/b^4*d^4*polylog(4,-exp(I*(b*x+a)))*x-24*I/b^4*c*d^3*polylog(4,-exp(I*(b*x+a)))+4*I/b^2*c^3*d*polylog(2,-exp(I*(b*x+a)))+4*I/b^2*d^4*polylog(2,-exp(I*(b*x+a)))*x^3+2*(b*d^4*x^4*exp(2*I*(b*x+a))+4*b*c*d^3*x^3*exp(2*I*(b*x+a))+6*b*c^2*d^2*x^2*exp(2*I*(b*x+a))+4*b*c^3*d*x*exp(2*I*(b*x+a))-2*I*d^4*x^3*exp(2*I*(b*x+a))+b*c^4*exp(2*I*(b*x+a))-6*I*c*d^3*x^2*exp(2*I*(b*x+a))-6*I*c^2*d^2*x*exp(2*I*(b*x+a))+2*I*d^4*x^3-2*I*c^3*d*exp(2*I*(b*x+a))+6*I*c*d^3*x^2+6*I*c^2*d^2*x+2*I*c^3*d)/b^2/(exp(2*I*(b*x+a))-1)^2-4/b*c^3*d*ln(exp(I*(b*x+a))+1)*x-4/b*c^3*d*ln(1-exp(I*(b*x+a)))*x-4/b^2*c^3*d*ln(1-exp(I*(b*x+a)))*a-6/b*c^2*d^2*ln(exp(I*(b*x+a))+1)*x^2-24/b^3*c*d^3*polylog(3,-exp(I*(b*x+a)))*x+6/b^3*c^2*d^2*a^2*ln(1-exp(I*(b*x+a)))-6/b*c^2*d^2*ln(1-exp(I*(b*x+a)))*x^2-24/b^3*c*d^3*polylog(3,exp(I*(b*x+a)))*x-8/b^2*c^3*d*a*ln(exp(I*(b*x+a)))+4/b^4*c*d^3*a^3*ln(exp(I*(b*x+a))-1)-8/b^4*c*d^3*a^3*ln(exp(I*(b*x+a)))-6/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a))-1)+12/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a)))+4/b^2*c^3*d*a*ln(exp(I*(b*x+a))-1)-1/b*d^4*ln(1-exp(I*(b*x+a)))*x^4-1/b*d^4*ln(exp(I*(b*x+a))+1)*x^4-4/b*c*d^3*ln(exp(I*(b*x+a))+1)*x^3-4/b*c*d^3*ln(1-exp(I*(b*x+a)))*x^3-4/b^4*c*d^3*ln(1-exp(I*(b*x+a)))*a^3+2*I*c^2*d^2*x^3+2*I*c^3*d*x^2+12/b^3*d^3*c*ln(exp(I*(b*x+a))+1)*x+12/b^3*d^3*c*ln(1-exp(I*(b*x+a)))*x+12/b^4*d^3*c*ln(1-exp(I*(b*x+a)))*a+24/b^4*d^3*c*a*ln(exp(I*(b*x+a)))+12*I/b^2*c*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+12*I/b^2*c^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-8/5*I/b^5*d^4*a^5-12/b^4*d^3*c*a*ln(exp(I*(b*x+a))-1)-12*I/b^4*d^3*c*polylog(2,-exp(I*(b*x+a)))-12*I/b^4*d^3*c*polylog(2,exp(I*(b*x+a)))+12*I/b^4*d^4*a^2*x-12*I/b^2*d^3*c*x^2-12*I/b^4*d^3*c*a^2-12*I/b^4*d^4*polylog(2,-exp(I*(b*x+a)))*x-12*I/b^4*d^4*polylog(2,exp(I*(b*x+a)))*x","B"
179,1,1194,221,0.139000," ","int((d*x+c)^3*cot(b*x+a)^3,x)","-\frac{6 i c \,d^{2} a^{2} x}{b^{2}}+\frac{6 i c^{2} d a x}{b}+\frac{6 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}-\frac{2 d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 i a^{4} d^{3}}{2 b^{4}}+i c \,d^{2} x^{3}+\frac{3 i c^{2} d \,x^{2}}{2}-\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}-\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}-\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}-\frac{6 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i d^{3} a^{2}}{b^{4}}+\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{6 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-i c^{3} x +\frac{i d^{3} x^{4}}{4}-\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{2 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{2 b \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+6 b c \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+6 b \,c^{2} d x \,{\mathrm e}^{2 i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{2 i \left(b x +a \right)}+3 i d^{3} x^{2}+2 b \,c^{3} {\mathrm e}^{2 i \left(b x +a \right)}+6 i c \,d^{2} x +3 i c^{2} d}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{3 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{3 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i d^{3} x^{2}}{b^{2}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{6 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 i c^{2} d \,a^{2}}{b^{2}}+\frac{2 i a^{3} d^{3} x}{b^{3}}-\frac{4 i c \,d^{2} a^{3}}{b^{3}}+\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{3 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{6 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 i d^{3} a x}{b^{3}}"," ",0,"1/4*I*d^3*x^4+I*c*d^2*x^3-I*c^3*x+3*I/b^2*a^2*c^2*d+3*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))+3*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2-4*I/b^3*a^3*c*d^2+2*I/b^3*d^3*a^3*x+1/b^4*d^3*a^3*ln(exp(I*(b*x+a))-1)-2/b^4*d^3*a^3*ln(exp(I*(b*x+a)))-6/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))-6/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))-6/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x-6/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x-3*I*d^3*polylog(2,exp(I*(b*x+a)))/b^4-6*I*d^3*polylog(4,-exp(I*(b*x+a)))/b^4-1/b*c^3*ln(exp(I*(b*x+a))-1)-1/b*c^3*ln(exp(I*(b*x+a))+1)+2/b*c^3*ln(exp(I*(b*x+a)))+6*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x+(2*b*d^3*x^3*exp(2*I*(b*x+a))-3*I*d^3*x^2*exp(2*I*(b*x+a))+6*b*c*d^2*x^2*exp(2*I*(b*x+a))-6*I*c*d^2*x*exp(2*I*(b*x+a))+6*b*c^2*d*x*exp(2*I*(b*x+a))-3*I*c^2*d*exp(2*I*(b*x+a))+3*I*d^3*x^2+2*b*c^3*exp(2*I*(b*x+a))+6*I*c*d^2*x+3*I*c^2*d)/b^2/(exp(2*I*(b*x+a))-1)^2+3/2*I*c^2*d*x^2+3/b^3*d^2*c*ln(exp(I*(b*x+a))-1)+3/b^3*d^2*c*ln(exp(I*(b*x+a))+1)-6/b^3*d^2*c*ln(exp(I*(b*x+a)))+3/b^3*d^3*ln(exp(I*(b*x+a))+1)*x+3/b^3*d^3*ln(1-exp(I*(b*x+a)))*x+3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a-3/b^4*d^3*a*ln(exp(I*(b*x+a))-1)+6/b^4*d^3*a*ln(exp(I*(b*x+a)))-3*I/b^2*d^3*x^2-3*I/b^4*d^3*a^2-3*I/b^4*d^3*polylog(2,-exp(I*(b*x+a)))+3*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+3*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-3/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))-1)+6/b^3*c*d^2*a^2*ln(exp(I*(b*x+a)))-3/b*c^2*d*ln(exp(I*(b*x+a))+1)*x-3/b*c^2*d*ln(1-exp(I*(b*x+a)))*x-3/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a+3/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))-3/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2-3/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2+3/b^2*c^2*d*a*ln(exp(I*(b*x+a))-1)-6/b^2*c^2*d*a*ln(exp(I*(b*x+a)))-1/b*d^3*ln(1-exp(I*(b*x+a)))*x^3-1/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3-1/b*d^3*ln(exp(I*(b*x+a))+1)*x^3-6*I/b^2*a^2*c*d^2*x+6*I/b*a*c^2*d*x+6*I/b^2*polylog(2,exp(I*(b*x+a)))*c*d^2*x-6*I/b^3*d^3*a*x-6*I/b^4*d^3*polylog(4,exp(I*(b*x+a)))+3/2*I/b^4*d^3*a^4","B"
180,1,635,152,0.112000," ","int((d*x+c)^2*cot(b*x+a)^3,x)","-\frac{d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{2 d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}-\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{4 i d^{2} a^{3}}{3 b^{3}}+i c d \,x^{2}+\frac{4 i c d a x}{b}+\frac{2 b \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+4 b c d x \,{\mathrm e}^{2 i \left(b x +a \right)}+2 b \,c^{2} {\mathrm e}^{2 i \left(b x +a \right)}-2 i d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}-2 i c d \,{\mathrm e}^{2 i \left(b x +a \right)}+2 i d^{2} x +2 i d c}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}-i c^{2} x +\frac{2 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{i d^{2} x^{3}}{3}-\frac{2 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{4 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{2 i d^{2} a^{2} x}{b^{2}}+\frac{2 i c d \,a^{2}}{b^{2}}+\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}"," ",0,"-4/3*I/b^3*a^3*d^2-1/b^3*d^2*a^2*ln(exp(I*(b*x+a))-1)+2/b^3*d^2*a^2*ln(exp(I*(b*x+a)))-1/b*d^2*ln(1-exp(I*(b*x+a)))*x^2+1/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2-1/b*d^2*ln(exp(I*(b*x+a))+1)*x^2+4*I/b*a*c*d*x+1/3*I*d^2*x^3+I*c*d*x^2-2*d^2*polylog(3,-exp(I*(b*x+a)))/b^3-2*d^2*polylog(3,exp(I*(b*x+a)))/b^3+2/b*c^2*ln(exp(I*(b*x+a)))-1/b*c^2*ln(exp(I*(b*x+a))-1)-1/b*c^2*ln(exp(I*(b*x+a))+1)-I*c^2*x-2/b*c*d*ln(1-exp(I*(b*x+a)))*x-2/b^2*c*d*ln(1-exp(I*(b*x+a)))*a-2/b*c*d*ln(exp(I*(b*x+a))+1)*x-4/b^2*c*d*a*ln(exp(I*(b*x+a)))+2/b^2*c*d*a*ln(exp(I*(b*x+a))-1)+2*(b*d^2*x^2*exp(2*I*(b*x+a))+2*b*c*d*x*exp(2*I*(b*x+a))+b*c^2*exp(2*I*(b*x+a))-I*d^2*x*exp(2*I*(b*x+a))-I*c*d*exp(2*I*(b*x+a))+I*d^2*x+I*d*c)/b^2/(exp(2*I*(b*x+a))-1)^2+1/b^3*d^2*ln(exp(I*(b*x+a))+1)-2/b^3*d^2*ln(exp(I*(b*x+a)))+1/b^3*d^2*ln(exp(I*(b*x+a))-1)+2*I/b^2*polylog(2,exp(I*(b*x+a)))*d^2*x+2*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))-2*I/b^2*a^2*d^2*x+2*I/b^2*a^2*c*d+2*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x+2*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))","B"
181,1,281,93,0.086000," ","int((d*x+c)*cot(b*x+a)^3,x)","\frac{i d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-i c x +\frac{2 b d x \,{\mathrm e}^{2 i \left(b x +a \right)}+2 b c \,{\mathrm e}^{2 i \left(b x +a \right)}-i d \,{\mathrm e}^{2 i \left(b x +a \right)}+i d}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}-\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{2 c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{i d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{i d \,x^{2}}{2}+\frac{i d \,a^{2}}{b^{2}}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{2 i d a x}{b}-\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{2 d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"I*d*polylog(2,-exp(I*(b*x+a)))/b^2-I*c*x+(2*b*d*x*exp(2*I*(b*x+a))+2*b*c*exp(2*I*(b*x+a))-I*d*exp(2*I*(b*x+a))+I*d)/b^2/(exp(2*I*(b*x+a))-1)^2-1/b*c*ln(exp(I*(b*x+a))-1)-1/b*c*ln(exp(I*(b*x+a))+1)+2/b*c*ln(exp(I*(b*x+a)))+I/b^2*d*polylog(2,exp(I*(b*x+a)))+1/2*I*d*x^2+I/b^2*d*a^2-1/b*d*ln(exp(I*(b*x+a))+1)*x+2*I/b*d*a*x-1/b*d*ln(1-exp(I*(b*x+a)))*x-1/b^2*d*ln(1-exp(I*(b*x+a)))*a+1/b^2*d*a*ln(exp(I*(b*x+a))-1)-2/b^2*d*a*ln(exp(I*(b*x+a)))","B"
182,0,0,18,2.646000," ","int(cot(b*x+a)^3/(d*x+c),x)","\int \frac{\cot^{3}\left(b x +a \right)}{d x +c}\, dx"," ",0,"int(cot(b*x+a)^3/(d*x+c),x)","F"
183,0,0,18,4.187000," ","int(cot(b*x+a)^3/(d*x+c)^2,x)","\int \frac{\cot^{3}\left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(cot(b*x+a)^3/(d*x+c)^2,x)","F"
184,1,470,315,0.045000," ","int((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{4 b}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{8 b}\right)}{32 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(5/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+5/16/b*d*(1/4/b*d*(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-3/4/b*d*(-1/4/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/64/b*d*(d*x+c)^(5/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+5/64/b*d*(1/8/b*d*(d*x+c)^(3/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-3/8/b*d*(-1/8/b*d*(d*x+c)^(1/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
185,1,376,267,0.039000," ","int((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{32 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/16/b*d*(1/4/b*d*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/64/b*d*(d*x+c)^(3/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+3/64/b*d*(1/8/b*d*(d*x+c)^(1/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
186,1,286,223,0.038000," ","int((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a),x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{16 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{128 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/32/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/64/b*d*(d*x+c)^(1/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+1/256/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
187,1,286,223,0.000000," ","int((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a),x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{16 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{128 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/32/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/64/b*d*(d*x+c)^(1/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+1/256/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
188,1,376,267,0.001000," ","int((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{32 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/16/b*d*(1/4/b*d*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/64/b*d*(d*x+c)^(3/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+3/64/b*d*(1/8/b*d*(d*x+c)^(1/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
189,1,470,315,0.000000," ","int((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{8 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{4 b}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{32 b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{4 \left(d x +c \right) b}{d}+\frac{4 d a -4 c b}{d}\right)}{8 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{4 d a -4 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{4 d a -4 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{32 b \sqrt{\frac{b}{d}}}\right)}{8 b}\right)}{32 b}}{d}"," ",0,"2/d*(-1/16/b*d*(d*x+c)^(5/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+5/16/b*d*(1/4/b*d*(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-3/4/b*d*(-1/4/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/64/b*d*(d*x+c)^(5/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+5/64/b*d*(1/8/b*d*(d*x+c)^(3/2)*sin(4/d*(d*x+c)*b+4*(a*d-b*c)/d)-3/8/b*d*(-1/8/b*d*(d*x+c)^(1/2)*cos(4/d*(d*x+c)*b+4*(a*d-b*c)/d)+1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos(4*(a*d-b*c)/d)*FresnelC(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(4*(a*d-b*c)/d)*FresnelS(2*2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
190,1,716,471,0.068000," ","int((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^2,x)","\frac{\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}-\frac{5 d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{5 d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{48 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}+\frac{d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{100 b \sqrt{\frac{b}{d}}}\right)}{10 b}\right)}{16 b}}{d}"," ",0,"2/d*(1/16/b*d*(d*x+c)^(5/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-5/16/b*d*(-1/2/b*d*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/2/b*d*(1/2/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/96/b*d*(d*x+c)^(5/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+5/96/b*d*(-1/6/b*d*(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/2/b*d*(1/6/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/160/b*d*(d*x+c)^(5/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+1/32/b*d*(-1/10/b*d*(d*x+c)^(3/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+3/10/b*d*(1/10/b*d*(d*x+c)^(1/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-1/100/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
191,1,583,402,0.065000," ","int((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^2,x)","\frac{\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{16 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}+\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{100 b \sqrt{\frac{b}{d}}}\right)}{80 b}}{d}"," ",0,"2/d*(1/16/b*d*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/16/b*d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/96/b*d*(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/32/b*d*(-1/6/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/160/b*d*(d*x+c)^(3/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+3/160/b*d*(-1/10/b*d*(d*x+c)^(1/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+1/100/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
192,1,444,339,0.062000," ","int((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^2,x)","\frac{\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{16 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{288 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{800 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(1/16/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/96/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/576/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/160/b*d*(d*x+c)^(1/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+1/1600/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
193,1,444,339,0.000000," ","int((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^2,x)","\frac{\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{16 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{288 b \sqrt{\frac{b}{d}}}-\frac{d \sqrt{d x +c}\, \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{800 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(1/16/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/32/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/96/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/576/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/160/b*d*(d*x+c)^(1/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+1/1600/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
194,1,583,402,0.000000," ","int((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^2,x)","\frac{\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{16 b}-\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}+\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{100 b \sqrt{\frac{b}{d}}}\right)}{80 b}}{d}"," ",0,"2/d*(1/16/b*d*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/16/b*d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/96/b*d*(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/32/b*d*(-1/6/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/160/b*d*(d*x+c)^(3/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+3/160/b*d*(-1/10/b*d*(d*x+c)^(1/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+1/100/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
195,1,716,471,0.002000," ","int((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^2,x)","\frac{\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{8 b}-\frac{5 d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{8 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{48 b}+\frac{5 d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{48 b}-\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{80 b}+\frac{d \left(-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}+\frac{3 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{5 \left(d x +c \right) b}{d}+\frac{5 d a -5 c b}{d}\right)}{10 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \left(\cos \left(\frac{5 d a -5 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{5 d a -5 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{100 b \sqrt{\frac{b}{d}}}\right)}{10 b}\right)}{16 b}}{d}"," ",0,"2/d*(1/16/b*d*(d*x+c)^(5/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-5/16/b*d*(-1/2/b*d*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/2/b*d*(1/2/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/96/b*d*(d*x+c)^(5/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+5/96/b*d*(-1/6/b*d*(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/2/b*d*(1/6/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/160/b*d*(d*x+c)^(5/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+1/32/b*d*(-1/10/b*d*(d*x+c)^(3/2)*cos(5/d*(d*x+c)*b+5*(a*d-b*c)/d)+3/10/b*d*(1/10/b*d*(d*x+c)^(1/2)*sin(5/d*(d*x+c)*b+5*(a*d-b*c)/d)-1/100/b*d*2^(1/2)*Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(cos(5*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(5*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
196,1,477,315,0.046000," ","int((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^3,x)","\frac{-\frac{3 d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{64 b}+\frac{15 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{4 b}\right)}{64 b}+\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{192 b}-\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{12 b}-\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{12 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{6}\, \left(\cos \left(\frac{6 d a -6 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{6 d a -6 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{144 b \sqrt{\frac{b}{d}}}\right)}{4 b}\right)}{192 b}}{d}"," ",0,"2/d*(-3/128/b*d*(d*x+c)^(5/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+15/128/b*d*(1/4/b*d*(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-3/4/b*d*(-1/4/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))+1/384/b*d*(d*x+c)^(5/2)*cos(6/d*(d*x+c)*b+6*(a*d-b*c)/d)-5/384/b*d*(1/12/b*d*(d*x+c)^(3/2)*sin(6/d*(d*x+c)*b+6*(a*d-b*c)/d)-1/4/b*d*(-1/12/b*d*(d*x+c)^(1/2)*cos(6/d*(d*x+c)*b+6*(a*d-b*c)/d)+1/144/b*d*2^(1/2)*Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(cos(6*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(6*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
197,1,383,267,0.045000," ","int((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^3,x)","\frac{-\frac{3 d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{64 b}+\frac{9 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{64 b}+\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{192 b}-\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{12 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{6}\, \left(\cos \left(\frac{6 d a -6 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{6 d a -6 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{144 b \sqrt{\frac{b}{d}}}\right)}{64 b}}{d}"," ",0,"2/d*(-3/128/b*d*(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+9/128/b*d*(1/4/b*d*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))+1/384/b*d*(d*x+c)^(3/2)*cos(6/d*(d*x+c)*b+6*(a*d-b*c)/d)-1/128/b*d*(1/12/b*d*(d*x+c)^(1/2)*sin(6/d*(d*x+c)*b+6*(a*d-b*c)/d)-1/144/b*d*2^(1/2)*Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(cos(6*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(6*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
198,1,293,223,0.043000," ","int((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^3,x)","\frac{-\frac{3 d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{64 b}+\frac{3 d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{128 b \sqrt{\frac{b}{d}}}+\frac{d \sqrt{d x +c}\, \cos \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{192 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{6}\, \left(\cos \left(\frac{6 d a -6 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{6 d a -6 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{2304 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-3/128/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/256/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))+1/384/b*d*(d*x+c)^(1/2)*cos(6/d*(d*x+c)*b+6*(a*d-b*c)/d)-1/4608/b*d*2^(1/2)*Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(cos(6*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(6*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
199,1,293,223,0.000000," ","int((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^3,x)","\frac{-\frac{3 d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{64 b}+\frac{3 d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{128 b \sqrt{\frac{b}{d}}}+\frac{d \sqrt{d x +c}\, \cos \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{192 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{6}\, \left(\cos \left(\frac{6 d a -6 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{6 d a -6 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{2304 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-3/128/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/256/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))+1/384/b*d*(d*x+c)^(1/2)*cos(6/d*(d*x+c)*b+6*(a*d-b*c)/d)-1/4608/b*d*2^(1/2)*Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(cos(6*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(6*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
200,1,383,267,0.000000," ","int((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^3,x)","\frac{-\frac{3 d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{64 b}+\frac{9 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{64 b}+\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{192 b}-\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{12 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{6}\, \left(\cos \left(\frac{6 d a -6 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{6 d a -6 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{144 b \sqrt{\frac{b}{d}}}\right)}{64 b}}{d}"," ",0,"2/d*(-3/128/b*d*(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+9/128/b*d*(1/4/b*d*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))+1/384/b*d*(d*x+c)^(3/2)*cos(6/d*(d*x+c)*b+6*(a*d-b*c)/d)-1/128/b*d*(1/12/b*d*(d*x+c)^(1/2)*sin(6/d*(d*x+c)*b+6*(a*d-b*c)/d)-1/144/b*d*2^(1/2)*Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(cos(6*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(6*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
201,1,477,315,0.000000," ","int((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^3,x)","\frac{-\frac{3 d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{64 b}+\frac{15 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{4 b}+\frac{d \sqrt{\pi}\, \left(\cos \left(\frac{2 d a -2 c b}{d}\right) \FresnelC \left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{2 d a -2 c b}{d}\right) \mathrm{S}\left(\frac{2 \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}\right)}{4 b}\right)}{64 b}+\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{192 b}-\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{12 b}-\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{6 \left(d x +c \right) b}{d}+\frac{6 d a -6 c b}{d}\right)}{12 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{6}\, \left(\cos \left(\frac{6 d a -6 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{6 d a -6 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{144 b \sqrt{\frac{b}{d}}}\right)}{4 b}\right)}{192 b}}{d}"," ",0,"2/d*(-3/128/b*d*(d*x+c)^(5/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+15/128/b*d*(1/4/b*d*(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-3/4/b*d*(-1/4/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))+1/384/b*d*(d*x+c)^(5/2)*cos(6/d*(d*x+c)*b+6*(a*d-b*c)/d)-5/384/b*d*(1/12/b*d*(d*x+c)^(3/2)*sin(6/d*(d*x+c)*b+6*(a*d-b*c)/d)-1/4/b*d*(-1/12/b*d*(d*x+c)^(1/2)*cos(6/d*(d*x+c)*b+6*(a*d-b*c)/d)+1/144/b*d*2^(1/2)*Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(cos(6*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(6*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*6^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
202,1,150,90,0.122000," ","int(x^3*cos(x)^2*cot(x)^2,x)","-\frac{3 x^{4}}{8}+\frac{i \left(4 x^{3}+6 i x^{2}-6 x -3 i\right) {\mathrm e}^{2 i x}}{32}-\frac{i \left(4 x^{3}-6 i x^{2}-6 x +3 i\right) {\mathrm e}^{-2 i x}}{32}-\frac{2 i x^{3}}{{\mathrm e}^{2 i x}-1}-2 i x^{3}+3 x^{2} \ln \left(1+{\mathrm e}^{i x}\right)-6 i x \polylog \left(2, -{\mathrm e}^{i x}\right)+6 \polylog \left(3, -{\mathrm e}^{i x}\right)+3 x^{2} \ln \left(1-{\mathrm e}^{i x}\right)-6 i x \polylog \left(2, {\mathrm e}^{i x}\right)+6 \polylog \left(3, {\mathrm e}^{i x}\right)"," ",0,"-3/8*x^4+1/32*I*(6*I*x^2+4*x^3-3*I-6*x)*exp(2*I*x)-1/32*I*(-6*I*x^2+4*x^3+3*I-6*x)*exp(-2*I*x)-2*I*x^3/(exp(2*I*x)-1)-2*I*x^3+3*x^2*ln(1+exp(I*x))-6*I*x*polylog(2,-exp(I*x))+6*polylog(3,-exp(I*x))+3*x^2*ln(1-exp(I*x))-6*I*x*polylog(2,exp(I*x))+6*polylog(3,exp(I*x))","A"
203,1,112,67,0.111000," ","int(x^2*cos(x)^2*cot(x)^2,x)","-\frac{x^{3}}{2}+\frac{i \left(2 x^{2}+2 i x -1\right) {\mathrm e}^{2 i x}}{16}-\frac{i \left(2 x^{2}-2 i x -1\right) {\mathrm e}^{-2 i x}}{16}-\frac{2 i x^{2}}{{\mathrm e}^{2 i x}-1}+2 x \ln \left(1+{\mathrm e}^{i x}\right)+2 x \ln \left(1-{\mathrm e}^{i x}\right)-2 i x^{2}-2 i \polylog \left(2, -{\mathrm e}^{i x}\right)-2 i \polylog \left(2, {\mathrm e}^{i x}\right)"," ",0,"-1/2*x^3+1/16*I*(2*I*x+2*x^2-1)*exp(2*I*x)-1/16*I*(-2*I*x+2*x^2-1)*exp(-2*I*x)-2*I*x^2/(exp(2*I*x)-1)+2*x*ln(1+exp(I*x))+2*x*ln(1-exp(I*x))-2*I*x^2-2*I*polylog(2,-exp(I*x))-2*I*polylog(2,exp(I*x))","A"
204,1,76,27,0.115000," ","int(x*cos(x)^2*cot(x)^2,x)","\frac{-x -\frac{x^{2} \tan \left(x \right)}{2}}{2 \tan \left(x \right)}-\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{2}+\ln \left(\tan \left(x \right)\right)+\frac{-\frac{\tan \left(x \right)}{2}-x -2 x \left(\tan^{2}\left(x \right)\right)-x^{2} \tan \left(x \right)-x^{2} \left(\tan^{3}\left(x \right)\right)}{2 \tan \left(x \right) \left(1+\tan^{2}\left(x \right)\right)}"," ",0,"1/2*(-x-1/2*x^2*tan(x))/tan(x)-1/2*ln(1+tan(x)^2)+ln(tan(x))+1/2*(-1/2*tan(x)-x-2*x*tan(x)^2-x^2*tan(x)-x^2*tan(x)^3)/tan(x)/(1+tan(x)^2)","B"
205,1,240,139,0.157000," ","int(x^3*cos(x)^2*cot(x)^3,x)","6 i x^{2} \polylog \left(2, {\mathrm e}^{i x}\right)-\frac{\left(4 x^{3}+6 i x^{2}-6 x -3 i\right) {\mathrm e}^{2 i x}}{32}-\frac{\left(4 x^{3}-6 i x^{2}-6 x +3 i\right) {\mathrm e}^{-2 i x}}{32}+\frac{x^{2} \left(2 x \,{\mathrm e}^{2 i x}-3 i {\mathrm e}^{2 i x}+3 i\right)}{\left({\mathrm e}^{2 i x}-1\right)^{2}}-2 x^{3} \ln \left(1+{\mathrm e}^{i x}\right)-2 x^{3} \ln \left(1-{\mathrm e}^{i x}\right)-12 i \polylog \left(4, -{\mathrm e}^{i x}\right)-12 x \polylog \left(3, {\mathrm e}^{i x}\right)+3 x \ln \left(1+{\mathrm e}^{i x}\right)+3 x \ln \left(1-{\mathrm e}^{i x}\right)-12 x \polylog \left(3, -{\mathrm e}^{i x}\right)-3 i x^{2}-3 i \polylog \left(2, -{\mathrm e}^{i x}\right)+6 i x^{2} \polylog \left(2, -{\mathrm e}^{i x}\right)-12 i \polylog \left(4, {\mathrm e}^{i x}\right)-3 i \polylog \left(2, {\mathrm e}^{i x}\right)+\frac{i x^{4}}{2}"," ",0,"-3*I*polylog(2,-exp(I*x))-1/32*(6*I*x^2+4*x^3-3*I-6*x)*exp(2*I*x)-1/32*(-6*I*x^2+4*x^3+3*I-6*x)*exp(-2*I*x)+x^2*(2*x*exp(2*I*x)-3*I*exp(2*I*x)+3*I)/(exp(2*I*x)-1)^2-2*x^3*ln(1+exp(I*x))-2*x^3*ln(1-exp(I*x))-12*I*polylog(4,-exp(I*x))-12*x*polylog(3,exp(I*x))+3*x*ln(1+exp(I*x))+3*x*ln(1-exp(I*x))-12*x*polylog(3,-exp(I*x))+6*I*x^2*polylog(2,exp(I*x))-3*I*x^2+6*I*x^2*polylog(2,-exp(I*x))-3*I*polylog(2,exp(I*x))+1/2*I*x^4-12*I*polylog(4,exp(I*x))","A"
206,1,170,86,0.164000," ","int(x^2*cos(x)^2*cot(x)^3,x)","\frac{2 i x^{3}}{3}-\frac{\left(2 x^{2}+2 i x -1\right) {\mathrm e}^{2 i x}}{16}-\frac{\left(2 x^{2}-2 i x -1\right) {\mathrm e}^{-2 i x}}{16}+\frac{2 x \left(x \,{\mathrm e}^{2 i x}-i {\mathrm e}^{2 i x}+i\right)}{\left({\mathrm e}^{2 i x}-1\right)^{2}}+\ln \left(1+{\mathrm e}^{i x}\right)+\ln \left({\mathrm e}^{i x}-1\right)-2 \ln \left({\mathrm e}^{i x}\right)-2 x^{2} \ln \left(1+{\mathrm e}^{i x}\right)+4 i x \polylog \left(2, -{\mathrm e}^{i x}\right)-4 \polylog \left(3, -{\mathrm e}^{i x}\right)-2 x^{2} \ln \left(1-{\mathrm e}^{i x}\right)+4 i x \polylog \left(2, {\mathrm e}^{i x}\right)-4 \polylog \left(3, {\mathrm e}^{i x}\right)"," ",0,"2/3*I*x^3-1/16*(2*I*x+2*x^2-1)*exp(2*I*x)-1/16*(-2*I*x+2*x^2-1)*exp(-2*I*x)+2*x*(x*exp(2*I*x)-I*exp(2*I*x)+I)/(exp(2*I*x)-1)^2+ln(1+exp(I*x))+ln(exp(I*x)-1)-2*ln(exp(I*x))-2*x^2*ln(1+exp(I*x))+4*I*x*polylog(2,-exp(I*x))-4*polylog(3,-exp(I*x))-2*x^2*ln(1-exp(I*x))+4*I*x*polylog(2,exp(I*x))-4*polylog(3,exp(I*x))","A"
207,1,109,57,0.138000," ","int(x*cos(x)^2*cot(x)^3,x)","i x^{2}-\frac{\left(i+2 x \right) {\mathrm e}^{2 i x}}{16}-\frac{\left(2 x -i\right) {\mathrm e}^{-2 i x}}{16}+\frac{2 x \,{\mathrm e}^{2 i x}-i {\mathrm e}^{2 i x}+i}{\left({\mathrm e}^{2 i x}-1\right)^{2}}-2 x \ln \left(1+{\mathrm e}^{i x}\right)-2 x \ln \left(1-{\mathrm e}^{i x}\right)+2 i \polylog \left(2, -{\mathrm e}^{i x}\right)+2 i \polylog \left(2, {\mathrm e}^{i x}\right)"," ",0,"I*x^2-1/16*(I+2*x)*exp(2*I*x)-1/16*(2*x-I)*exp(-2*I*x)+(2*x*exp(2*I*x)-I*exp(2*I*x)+I)/(exp(2*I*x)-1)^2-2*x*ln(1+exp(I*x))-2*x*ln(1-exp(I*x))+2*I*polylog(2,-exp(I*x))+2*I*polylog(2,exp(I*x))","A"
208,0,0,16,0.131000," ","int((d*x+c)^m*sec(b*x+a)*sin(b*x+a),x)","\int \left(d x +c \right)^{m} \sec \left(b x +a \right) \sin \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*sec(b*x+a)*sin(b*x+a),x)","F"
209,1,616,141,0.109000," ","int((d*x+c)^4*sec(b*x+a)*sin(b*x+a),x)","-\frac{3 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 d^{4} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{d^{4} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{4}}{b}-i c^{4} x +\frac{2 c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{i d^{4} x^{5}}{5}+\frac{6 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{6 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{8 i d^{4} a^{5}}{5 b^{5}}+i c \,d^{3} x^{4}+2 i c^{2} d^{2} x^{3}+2 i c^{3} d \,x^{2}-\frac{c^{4} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{3 d^{4} \polylog \left(5, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{5}}-\frac{4 c^{3} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{6 c^{2} d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}-\frac{4 c \,d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}-\frac{6 c \,d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}-\frac{3 i d^{4} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{4}}+\frac{2 i d^{4} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{3 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{4}}+\frac{2 i c^{3} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i d^{4} a^{4} x}{b^{4}}+\frac{4 i c^{3} d \,a^{2}}{b^{2}}-\frac{8 i c^{2} d^{2} a^{3}}{b^{3}}+\frac{6 i c \,d^{3} a^{4}}{b^{4}}-\frac{8 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{8 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{12 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{8 i c \,d^{3} a^{3} x}{b^{3}}-\frac{12 i c^{2} d^{2} a^{2} x}{b^{2}}+\frac{8 i c^{3} d a x}{b}"," ",0,"3/2*d^4*polylog(5,-exp(2*I*(b*x+a)))/b^5+2/b^5*d^4*a^4*ln(exp(I*(b*x+a)))-3/b^3*c^2*d^2*polylog(3,-exp(2*I*(b*x+a)))-3/b^3*d^4*polylog(3,-exp(2*I*(b*x+a)))*x^2+1/5*I*d^4*x^5+I*c*d^3*x^4+8*I/b*a*c^3*d*x-12*I/b^2*a^2*c^2*d^2*x+8*I/b^3*c*d^3*a^3*x+6*I/b^4*c*d^3*a^4-8*I/b^3*a^3*c^2*d^2-2*I/b^4*d^4*a^4*x+4*I/b^2*a^2*c^3*d-4/b*c*d^3*ln(1+exp(2*I*(b*x+a)))*x^3+6*I/b^2*c*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2+6*I/b^2*c^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x-I*c^4*x-1/b*c^4*ln(1+exp(2*I*(b*x+a)))+2/b*c^4*ln(exp(I*(b*x+a)))-1/b*d^4*ln(1+exp(2*I*(b*x+a)))*x^4-8/b^2*c^3*d*a*ln(exp(I*(b*x+a)))-8/b^4*c*d^3*a^3*ln(exp(I*(b*x+a)))+12/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a)))+2*I*c^2*d^2*x^3+2*I*c^3*d*x^2-4/b*c^3*d*ln(1+exp(2*I*(b*x+a)))*x-6/b^3*c*d^3*polylog(3,-exp(2*I*(b*x+a)))*x-6/b*c^2*d^2*ln(1+exp(2*I*(b*x+a)))*x^2-8/5*I/b^5*d^4*a^5-3*I/b^4*d^4*polylog(4,-exp(2*I*(b*x+a)))*x+2*I/b^2*d^4*polylog(2,-exp(2*I*(b*x+a)))*x^3-3*I/b^4*c*d^3*polylog(4,-exp(2*I*(b*x+a)))+2*I/b^2*c^3*d*polylog(2,-exp(2*I*(b*x+a)))","B"
210,1,423,113,0.079000," ","int((d*x+c)^3*sec(b*x+a)*sin(b*x+a),x)","\frac{3 i c^{2} d \,a^{2}}{b^{2}}+\frac{3 i c^{2} d \,x^{2}}{2}+\frac{2 i a^{3} d^{3} x}{b^{3}}-i c^{3} x -\frac{4 i c \,d^{2} a^{3}}{b^{3}}-\frac{3 i d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{4 b^{4}}-\frac{c^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{2 d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 c \,d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{2 b^{3}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}+\frac{2 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{i d^{3} x^{4}}{4}-\frac{6 i c \,d^{2} a^{2} x}{b^{2}}+\frac{6 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}+\frac{3 i a^{4} d^{3}}{2 b^{4}}+\frac{6 i c^{2} d a x}{b}+i c \,d^{2} x^{3}+\frac{3 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{3 c^{2} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{3 c \,d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}"," ",0,"1/4*I*d^3*x^4+I*c*d^2*x^3-I*c^3*x+3*I/b^2*a^2*c^2*d-4*I/b^3*a^3*c*d^2+2*I/b^3*d^3*a^3*x-1/b*c^3*ln(1+exp(2*I*(b*x+a)))-2/b^4*d^3*a^3*ln(exp(I*(b*x+a)))-3/2/b^3*c*d^2*polylog(3,-exp(2*I*(b*x+a)))-3/2/b^3*d^3*polylog(3,-exp(2*I*(b*x+a)))*x-3/4*I*d^3*polylog(4,-exp(2*I*(b*x+a)))/b^4+2/b*c^3*ln(exp(I*(b*x+a)))+3*I/b^2*c*d^2*polylog(2,-exp(2*I*(b*x+a)))*x+3/2*I*c^2*d*x^2+6/b^3*c*d^2*a^2*ln(exp(I*(b*x+a)))-6/b^2*c^2*d*a*ln(exp(I*(b*x+a)))-1/b*d^3*ln(1+exp(2*I*(b*x+a)))*x^3+3/2*I/b^2*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2-6*I/b^2*a^2*c*d^2*x+6*I/b*a*c^2*d*x+3/2*I/b^2*c^2*d*polylog(2,-exp(2*I*(b*x+a)))+3/2*I/b^4*d^3*a^4-3/b*c^2*d*ln(1+exp(2*I*(b*x+a)))*x-3/b*c*d^2*ln(1+exp(2*I*(b*x+a)))*x^2","B"
211,1,257,84,0.064000," ","int((d*x+c)^2*sec(b*x+a)*sin(b*x+a),x)","\frac{i d^{2} x^{3}}{3}-\frac{4 i d^{2} a^{3}}{3 b^{3}}+\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}-\frac{c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{2 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{2 d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+i c d \,x^{2}-\frac{2 i d^{2} a^{2} x}{b^{2}}+\frac{2 i c d \,a^{2}}{b^{2}}-\frac{d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}+\frac{4 i c d a x}{b}-\frac{d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{4 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-i c^{2} x +\frac{i c d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 c d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}"," ",0,"1/3*I*d^2*x^3+I/b^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x-2*I/b^2*a^2*d^2*x-1/b*c^2*ln(1+exp(2*I*(b*x+a)))+2/b*c^2*ln(exp(I*(b*x+a)))+2/b^3*d^2*a^2*ln(exp(I*(b*x+a)))+2*I/b^2*a^2*c*d-I*c^2*x-4/3*I/b^3*a^3*d^2-1/b*d^2*ln(1+exp(2*I*(b*x+a)))*x^2+I*c*d*x^2-1/2*d^2*polylog(3,-exp(2*I*(b*x+a)))/b^3-4/b^2*c*d*a*ln(exp(I*(b*x+a)))+I/b^2*c*d*polylog(2,-exp(2*I*(b*x+a)))+4*I/b*a*c*d*x-2/b*c*d*ln(1+exp(2*I*(b*x+a)))*x","B"
212,1,123,56,0.071000," ","int((d*x+c)*sec(b*x+a)*sin(b*x+a),x)","\frac{i d \,x^{2}}{2}-i c x -\frac{c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{2 c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{2 i d a x}{b}+\frac{i d \,a^{2}}{b^{2}}-\frac{d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{i d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{2 d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"1/2*I*d*x^2-I*c*x-1/b*c*ln(1+exp(2*I*(b*x+a)))+2/b*c*ln(exp(I*(b*x+a)))+2*I/b*d*a*x+I/b^2*d*a^2-1/b*d*ln(1+exp(2*I*(b*x+a)))*x+1/2*I*d*polylog(2,-exp(2*I*(b*x+a)))/b^2-2/b^2*d*a*ln(exp(I*(b*x+a)))","B"
213,0,0,16,0.128000," ","int(sec(b*x+a)*sin(b*x+a)/(d*x+c),x)","\int \frac{\sec \left(b x +a \right) \sin \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)*sin(b*x+a)/(d*x+c),x)","F"
214,0,0,16,0.135000," ","int(sec(b*x+a)*sin(b*x+a)/(d*x+c)^2,x)","\int \frac{\sec \left(b x +a \right) \sin \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(sec(b*x+a)*sin(b*x+a)/(d*x+c)^2,x)","F"
215,0,0,135,0.270000," ","int((d*x+c)^m*sec(b*x+a)*sin(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \sec \left(b x +a \right) \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*sec(b*x+a)*sin(b*x+a)^2,x)","F"
216,1,901,250,0.362000," ","int((d*x+c)^3*sec(b*x+a)*sin(b*x+a)^2,x)","-\frac{6 i d^{2} c \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i d^{2} c \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 i d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{3 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{3 c^{2} d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 c^{2} d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{3 a^{2} c \,d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 c^{2} d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{3 c^{2} d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 a^{2} c \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 i d^{3} a^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 i c^{2} d \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i c^{2} d \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{i \left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}+3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x +6 i b^{2} c \,d^{2} x +b^{3} c^{3}+3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b -6 i d^{3}\right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{4}}-\frac{i \left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}-3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x -6 i b^{2} c \,d^{2} x +b^{3} c^{3}-3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b +6 i d^{3}\right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{4}}-\frac{6 i c \,d^{2} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i c^{2} d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{a^{3} d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}-\frac{d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{a^{3} d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{2 i c^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{6 i d^{3} \polylog \left(4, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i d^{3} \polylog \left(4, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{2} c \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 d^{2} c \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"1/2*I*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3+3*I*b^2*d^3*x^2-6*b*d^3*x+6*I*b^2*c*d^2*x-6*c*d^2*b+3*I*b^2*c^2*d-6*I*d^3)/b^4*exp(I*(b*x+a))+6*I*d^3*polylog(4,I*exp(I*(b*x+a)))/b^4-6*I*d^3*polylog(4,-I*exp(I*(b*x+a)))/b^4-1/b^4*a^3*d^3*ln(1+I*exp(I*(b*x+a)))+6/b^3*d^3*polylog(3,I*exp(I*(b*x+a)))*x+1/b*d^3*ln(1-I*exp(I*(b*x+a)))*x^3-1/b*d^3*ln(1+I*exp(I*(b*x+a)))*x^3-6/b^3*d^3*polylog(3,-I*exp(I*(b*x+a)))*x+6/b^3*d^2*c*polylog(3,I*exp(I*(b*x+a)))-6/b^3*d^2*c*polylog(3,-I*exp(I*(b*x+a)))+1/b^4*a^3*d^3*ln(1-I*exp(I*(b*x+a)))-2*I/b*c^3*arctan(exp(I*(b*x+a)))+3/b*d^2*c*ln(1-I*exp(I*(b*x+a)))*x^2-3/b*d^2*c*ln(1+I*exp(I*(b*x+a)))*x^2+3/b*c^2*d*ln(1-I*exp(I*(b*x+a)))*x+3/b^2*c^2*d*ln(1-I*exp(I*(b*x+a)))*a+3/b^3*a^2*c*d^2*ln(1+I*exp(I*(b*x+a)))-3/b*c^2*d*ln(1+I*exp(I*(b*x+a)))*x-3/b^2*c^2*d*ln(1+I*exp(I*(b*x+a)))*a-3/b^3*a^2*c*d^2*ln(1-I*exp(I*(b*x+a)))+3*I/b^2*c^2*d*polylog(2,-I*exp(I*(b*x+a)))+2*I/b^4*d^3*a^3*arctan(exp(I*(b*x+a)))-3*I/b^2*c^2*d*polylog(2,I*exp(I*(b*x+a)))-3*I/b^2*d^3*polylog(2,I*exp(I*(b*x+a)))*x^2+3*I/b^2*d^3*polylog(2,-I*exp(I*(b*x+a)))*x^2-1/2*I*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3-3*I*b^2*d^3*x^2-6*b*d^3*x-6*I*b^2*c*d^2*x-6*c*d^2*b-3*I*b^2*c^2*d+6*I*d^3)/b^4*exp(-I*(b*x+a))-6*I/b^2*d^2*c*polylog(2,I*exp(I*(b*x+a)))*x-6*I/b^3*c*d^2*a^2*arctan(exp(I*(b*x+a)))+6*I/b^2*c^2*d*a*arctan(exp(I*(b*x+a)))+6*I/b^2*d^2*c*polylog(2,-I*exp(I*(b*x+a)))*x","B"
217,1,512,169,0.260000," ","int((d*x+c)^2*sec(b*x+a)*sin(b*x+a)^2,x)","\frac{i \left(d^{2} x^{2} b^{2}+2 b^{2} c d x +2 i b \,d^{2} x +b^{2} c^{2}+2 i b c d -2 d^{2}\right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{3}}+\frac{4 i c d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 c d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{2 d^{2} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{i \left(d^{2} x^{2} b^{2}+2 b^{2} c d x -2 i b \,d^{2} x +b^{2} c^{2}-2 i b c d -2 d^{2}\right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{3}}-\frac{2 i c^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{2 i c d \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{2 d^{2} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i d^{2} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 c d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{2 c d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 i d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 c d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{a^{2} d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i d^{2} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 i c d \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{a^{2} d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"1/2*I*(d^2*x^2*b^2+2*b^2*c*d*x+b^2*c^2+2*I*b*d^2*x-2*d^2+2*I*b*c*d)/b^3*exp(I*(b*x+a))+4*I/b^2*c*d*a*arctan(exp(I*(b*x+a)))-2/b*c*d*ln(1+I*exp(I*(b*x+a)))*x-2*d^2*polylog(3,-I*exp(I*(b*x+a)))/b^3-1/2*I*(d^2*x^2*b^2+2*b^2*c*d*x+b^2*c^2-2*I*b*d^2*x-2*d^2-2*I*b*c*d)/b^3*exp(-I*(b*x+a))-2*I/b^2*c*d*polylog(2,I*exp(I*(b*x+a)))-2*I/b*c^2*arctan(exp(I*(b*x+a)))-1/b*d^2*ln(1+I*exp(I*(b*x+a)))*x^2+2*d^2*polylog(3,I*exp(I*(b*x+a)))/b^3-2*I/b^2*d^2*polylog(2,I*exp(I*(b*x+a)))*x+2/b^2*c*d*ln(1-I*exp(I*(b*x+a)))*a+2/b*c*d*ln(1-I*exp(I*(b*x+a)))*x+2*I/b^2*d^2*polylog(2,-I*exp(I*(b*x+a)))*x-2/b^2*c*d*ln(1+I*exp(I*(b*x+a)))*a+1/b^3*a^2*d^2*ln(1+I*exp(I*(b*x+a)))-2*I/b^3*d^2*a^2*arctan(exp(I*(b*x+a)))+2*I/b^2*c*d*polylog(2,-I*exp(I*(b*x+a)))+1/b*d^2*ln(1-I*exp(I*(b*x+a)))*x^2-1/b^3*a^2*d^2*ln(1-I*exp(I*(b*x+a)))","B"
218,1,209,92,0.057000," ","int((d*x+c)*sec(b*x+a)*sin(b*x+a)^2,x)","-\frac{d \sin \left(b x +a \right) x}{b}-\frac{d \cos \left(b x +a \right)}{b^{2}}-\frac{c \sin \left(b x +a \right)}{b}-\frac{d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{i d \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{i d \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d a \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b^{2}}+\frac{c \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b}"," ",0,"-1/b*d*sin(b*x+a)*x-d*cos(b*x+a)/b^2-1/b*c*sin(b*x+a)-1/b*d*ln(1+I*exp(I*(b*x+a)))*x+1/b*d*ln(1-I*exp(I*(b*x+a)))*x-I/b^2*d*dilog(1-I*exp(I*(b*x+a)))-1/b^2*d*ln(1+I*exp(I*(b*x+a)))*a+1/b^2*d*ln(1-I*exp(I*(b*x+a)))*a+I/b^2*d*dilog(1+I*exp(I*(b*x+a)))-1/b^2*d*a*ln(sec(b*x+a)+tan(b*x+a))+1/b*c*ln(sec(b*x+a)+tan(b*x+a))","B"
219,0,0,68,0.269000," ","int(sec(b*x+a)*sin(b*x+a)^2/(d*x+c),x)","\int \frac{\sec \left(b x +a \right) \left(\sin^{2}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)*sin(b*x+a)^2/(d*x+c),x)","F"
220,0,0,86,0.422000," ","int(sec(b*x+a)*sin(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\sec \left(b x +a \right) \left(\sin^{2}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(sec(b*x+a)*sin(b*x+a)^2/(d*x+c)^2,x)","F"
221,0,0,145,0.252000," ","int((d*x+c)^m*sec(b*x+a)*sin(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \sec \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*sec(b*x+a)*sin(b*x+a)^3,x)","F"
222,1,641,220,0.218000," ","int((d*x+c)^3*sec(b*x+a)*sin(b*x+a)^3,x)","-\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{2 b^{3}}-\frac{d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}-\frac{6 i c \,d^{2} a^{2} x}{b^{2}}+\frac{6 i c^{2} d a x}{b}-\frac{2 d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 i a^{4} d^{3}}{2 b^{4}}+i c \,d^{2} x^{3}+\frac{3 i c^{2} d \,x^{2}}{2}-\frac{3 c \,d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{3 i d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{4 b^{4}}-\frac{c^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{3 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}-i c^{3} x +\frac{i d^{3} x^{4}}{4}+\frac{2 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{6 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 i c^{2} d \,a^{2}}{b^{2}}+\frac{2 i a^{3} d^{3} x}{b^{3}}-\frac{4 i c \,d^{2} a^{3}}{b^{3}}-\frac{6 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{3 c^{2} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{3 c \,d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}+\frac{\left(4 d^{3} x^{3} b^{3}+12 b^{3} c \,d^{2} x^{2}+6 i b^{2} d^{3} x^{2}+12 b^{3} c^{2} d x +12 i b^{2} c \,d^{2} x +4 b^{3} c^{3}+6 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b -3 i d^{3}\right) {\mathrm e}^{2 i \left(b x +a \right)}}{32 b^{4}}+\frac{\left(4 d^{3} x^{3} b^{3}+12 b^{3} c \,d^{2} x^{2}-6 i b^{2} d^{3} x^{2}+12 b^{3} c^{2} d x -12 i b^{2} c \,d^{2} x +4 b^{3} c^{3}-6 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b +3 i d^{3}\right) {\mathrm e}^{-2 i \left(b x +a \right)}}{32 b^{4}}"," ",0,"1/4*I*d^3*x^4+I*c*d^2*x^3-I*c^3*x+3*I/b^2*a^2*c^2*d-4*I/b^3*a^3*c*d^2+2*I/b^3*d^3*a^3*x-1/b*c^3*ln(1+exp(2*I*(b*x+a)))-2/b^4*d^3*a^3*ln(exp(I*(b*x+a)))+1/32*(4*d^3*x^3*b^3+6*I*b^2*d^3*x^2+12*b^3*c*d^2*x^2+12*I*b^2*c*d^2*x+12*b^3*c^2*d*x+6*I*b^2*c^2*d+4*b^3*c^3-6*b*d^3*x-3*I*d^3-6*c*d^2*b)/b^4*exp(2*I*(b*x+a))+1/32*(4*d^3*x^3*b^3-6*I*b^2*d^3*x^2+12*b^3*c*d^2*x^2-12*I*b^2*c*d^2*x+12*b^3*c^2*d*x-6*I*b^2*c^2*d+4*b^3*c^3-6*b*d^3*x+3*I*d^3-6*c*d^2*b)/b^4*exp(-2*I*(b*x+a))-3/2/b^3*c*d^2*polylog(3,-exp(2*I*(b*x+a)))-3/2/b^3*d^3*polylog(3,-exp(2*I*(b*x+a)))*x-3/4*I*d^3*polylog(4,-exp(2*I*(b*x+a)))/b^4+2/b*c^3*ln(exp(I*(b*x+a)))+3*I/b^2*c*d^2*polylog(2,-exp(2*I*(b*x+a)))*x+3/2*I*c^2*d*x^2+6/b^3*c*d^2*a^2*ln(exp(I*(b*x+a)))-6/b^2*c^2*d*a*ln(exp(I*(b*x+a)))-1/b*d^3*ln(1+exp(2*I*(b*x+a)))*x^3+3/2*I/b^2*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2-6*I/b^2*a^2*c*d^2*x+6*I/b*a*c^2*d*x+3/2*I/b^2*c^2*d*polylog(2,-exp(2*I*(b*x+a)))+3/2*I/b^4*d^3*a^4-3/b*c^2*d*ln(1+exp(2*I*(b*x+a)))*x-3/b*c*d^2*ln(1+exp(2*I*(b*x+a)))*x^2","B"
223,1,379,162,0.327000," ","int((d*x+c)^2*sec(b*x+a)*sin(b*x+a)^3,x)","\frac{i d^{2} x^{3}}{3}-\frac{2 i d^{2} a^{2} x}{b^{2}}+\frac{2 i c d \,a^{2}}{b^{2}}+\frac{\left(2 d^{2} x^{2} b^{2}+4 b^{2} c d x +2 i b \,d^{2} x +2 b^{2} c^{2}+2 i b c d -d^{2}\right) {\mathrm e}^{2 i \left(b x +a \right)}}{16 b^{3}}+\frac{\left(2 d^{2} x^{2} b^{2}+4 b^{2} c d x -2 i b \,d^{2} x +2 b^{2} c^{2}-2 i b c d -d^{2}\right) {\mathrm e}^{-2 i \left(b x +a \right)}}{16 b^{3}}-\frac{c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{2 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{2 d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{4 i c d a x}{b}-i c^{2} x +i c d \,x^{2}-\frac{d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}-\frac{4 i d^{2} a^{3}}{3 b^{3}}-\frac{d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{4 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{i c d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}+\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 c d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}"," ",0,"I/b^2*c*d*polylog(2,-exp(2*I*(b*x+a)))+1/3*I*d^2*x^3-2*I/b^2*a^2*d^2*x+1/16*(2*d^2*x^2*b^2+2*I*b*d^2*x+4*b^2*c*d*x+2*I*b*c*d+2*b^2*c^2-d^2)/b^3*exp(2*I*(b*x+a))+1/16*(2*d^2*x^2*b^2-2*I*b*d^2*x+4*b^2*c*d*x-2*I*b*c*d+2*b^2*c^2-d^2)/b^3*exp(-2*I*(b*x+a))-1/b*c^2*ln(1+exp(2*I*(b*x+a)))+2/b*c^2*ln(exp(I*(b*x+a)))+2/b^3*d^2*a^2*ln(exp(I*(b*x+a)))+I/b^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x+2*I/b^2*a^2*c*d+4*I/b*a*c*d*x-1/b*d^2*ln(1+exp(2*I*(b*x+a)))*x^2-I*c^2*x-1/2*d^2*polylog(3,-exp(2*I*(b*x+a)))/b^3-4/b^2*c*d*a*ln(exp(I*(b*x+a)))+I*c*d*x^2-4/3*I/b^3*a^3*d^2-2/b*c*d*ln(1+exp(2*I*(b*x+a)))*x","B"
224,1,179,99,0.339000," ","int((d*x+c)*sec(b*x+a)*sin(b*x+a)^3,x)","\frac{i d \,x^{2}}{2}-i c x +\frac{\left(2 b d x +2 c b +i d \right) {\mathrm e}^{2 i \left(b x +a \right)}}{16 b^{2}}+\frac{\left(2 b d x +2 c b -i d \right) {\mathrm e}^{-2 i \left(b x +a \right)}}{16 b^{2}}-\frac{c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{2 c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{2 i d a x}{b}+\frac{i d \,a^{2}}{b^{2}}-\frac{d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{i d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{2 d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"1/2*I*d*x^2-I*c*x+1/16*(2*b*d*x+I*d+2*c*b)/b^2*exp(2*I*(b*x+a))+1/16*(2*b*d*x-I*d+2*c*b)/b^2*exp(-2*I*(b*x+a))-1/b*c*ln(1+exp(2*I*(b*x+a)))+2/b*c*ln(exp(I*(b*x+a)))+2*I/b*d*a*x+I/b^2*d*a^2-1/b*d*ln(1+exp(2*I*(b*x+a)))*x+1/2*I*d*polylog(2,-exp(2*I*(b*x+a)))/b^2-2/b^2*d*a*ln(exp(I*(b*x+a)))","A"
225,0,0,77,0.453000," ","int(sec(b*x+a)*sin(b*x+a)^3/(d*x+c),x)","\int \frac{\sec \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)*sin(b*x+a)^3/(d*x+c),x)","F"
226,0,0,99,0.693000," ","int(sec(b*x+a)*sin(b*x+a)^3/(d*x+c)^2,x)","\int \frac{\sec \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(sec(b*x+a)*sin(b*x+a)^3/(d*x+c)^2,x)","F"
227,0,0,22,0.060000," ","int((d*x+c)^m*csc(b*x+a)*sec(b*x+a),x)","\int \left(d x +c \right)^{m} \csc \left(b x +a \right) \sec \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a)*sec(b*x+a),x)","F"
228,1,1242,221,0.170000," ","int((d*x+c)^4*csc(b*x+a)*sec(b*x+a),x)","-\frac{d^{4} a^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{12 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 c^{2} d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{12 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{4}}{b}+\frac{d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{4}}{b}-\frac{3 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 d^{4} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{d^{4} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{4}}{b}+\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{6 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{6 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{5}}-\frac{c^{4} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{3 d^{4} \polylog \left(5, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{5}}-\frac{24 d^{4} \polylog \left(5, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 d^{4} \polylog \left(5, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{4 c^{3} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{6 c^{2} d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}-\frac{4 c \,d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}-\frac{6 c \,d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}-\frac{3 i d^{4} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{4}}+\frac{2 i d^{4} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{3 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{4}}+\frac{2 i c^{3} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}+\frac{4 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{24 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{4 i c^{3} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 i c^{3} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{24 c \,d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 c \,d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 i c \,d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{4 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{24 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{4 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{4 c^{3} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{6 c^{2} d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{6 c^{2} d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{12 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{12 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c^{2} d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c \,d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{4 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{6 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{4 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}"," ",0,"3/2*d^4*polylog(5,-exp(2*I*(b*x+a)))/b^5+1/b^5*d^4*a^4*ln(exp(I*(b*x+a))-1)+12/b^3*c^2*d^2*polylog(3,-exp(I*(b*x+a)))+12/b^3*c^2*d^2*polylog(3,exp(I*(b*x+a)))-1/b^5*d^4*a^4*ln(1-exp(I*(b*x+a)))+12/b^3*d^4*polylog(3,exp(I*(b*x+a)))*x^2+12/b^3*d^4*polylog(3,-exp(I*(b*x+a)))*x^2-3/b^3*c^2*d^2*polylog(3,-exp(2*I*(b*x+a)))-3/b^3*d^4*polylog(3,-exp(2*I*(b*x+a)))*x^2-24*d^4*polylog(5,-exp(I*(b*x+a)))/b^5-24*d^4*polylog(5,exp(I*(b*x+a)))/b^5-4/b*c*d^3*ln(1+exp(2*I*(b*x+a)))*x^3+6*I/b^2*c*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2+6*I/b^2*c^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x-1/b*c^4*ln(1+exp(2*I*(b*x+a)))+1/b*c^4*ln(exp(I*(b*x+a))+1)+1/b*c^4*ln(exp(I*(b*x+a))-1)-1/b*d^4*ln(1+exp(2*I*(b*x+a)))*x^4+4/b*c^3*d*ln(exp(I*(b*x+a))+1)*x+4/b*c^3*d*ln(1-exp(I*(b*x+a)))*x+4/b^2*c^3*d*ln(1-exp(I*(b*x+a)))*a+6/b*c^2*d^2*ln(exp(I*(b*x+a))+1)*x^2+24/b^3*c*d^3*polylog(3,-exp(I*(b*x+a)))*x-6/b^3*c^2*d^2*a^2*ln(1-exp(I*(b*x+a)))+6/b*c^2*d^2*ln(1-exp(I*(b*x+a)))*x^2+24/b^3*c*d^3*polylog(3,exp(I*(b*x+a)))*x+24*I/b^4*c*d^3*polylog(4,-exp(I*(b*x+a)))+24*I/b^4*c*d^3*polylog(4,exp(I*(b*x+a)))-4*I/b^2*d^4*polylog(2,exp(I*(b*x+a)))*x^3+24*I/b^4*d^4*polylog(4,exp(I*(b*x+a)))*x-4*I/b^2*d^4*polylog(2,-exp(I*(b*x+a)))*x^3+24*I/b^4*d^4*polylog(4,-exp(I*(b*x+a)))*x-4*I/b^2*c^3*d*polylog(2,-exp(I*(b*x+a)))-4*I/b^2*c^3*d*polylog(2,exp(I*(b*x+a)))-4/b^4*c*d^3*a^3*ln(exp(I*(b*x+a))-1)+6/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a))-1)-4/b^2*c^3*d*a*ln(exp(I*(b*x+a))-1)+1/b*d^4*ln(1-exp(I*(b*x+a)))*x^4+1/b*d^4*ln(exp(I*(b*x+a))+1)*x^4-12*I/b^2*c*d^3*polylog(2,-exp(I*(b*x+a)))*x^2-12*I/b^2*c^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-12*I/b^2*c^2*d^2*polylog(2,exp(I*(b*x+a)))*x-12*I/b^2*c*d^3*polylog(2,exp(I*(b*x+a)))*x^2+4/b*c*d^3*ln(exp(I*(b*x+a))+1)*x^3+4/b*c*d^3*ln(1-exp(I*(b*x+a)))*x^3+4/b^4*c*d^3*ln(1-exp(I*(b*x+a)))*a^3-4/b*c^3*d*ln(1+exp(2*I*(b*x+a)))*x-6/b^3*c*d^3*polylog(3,-exp(2*I*(b*x+a)))*x-6/b*c^2*d^2*ln(1+exp(2*I*(b*x+a)))*x^2-3*I/b^4*d^4*polylog(4,-exp(2*I*(b*x+a)))*x+2*I/b^2*d^4*polylog(2,-exp(2*I*(b*x+a)))*x^3-3*I/b^4*c*d^3*polylog(4,-exp(2*I*(b*x+a)))+2*I/b^2*c^3*d*polylog(2,-exp(2*I*(b*x+a)))","B"
229,1,816,167,0.119000," ","int((d*x+c)^3*csc(b*x+a)*sec(b*x+a),x)","-\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{2 b^{3}}-\frac{d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}-\frac{6 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{6 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{6 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 c \,d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{3 i d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{4 b^{4}}-\frac{c^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{3 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{3 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{3 c^{2} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{3 c \,d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}"," ",0,"-6*I/b^2*c*d^2*polylog(2,exp(I*(b*x+a)))*x-6*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x+6*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4-1/b*c^3*ln(1+exp(2*I*(b*x+a)))-1/b^4*d^3*a^3*ln(exp(I*(b*x+a))-1)+6/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+6/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))+6/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x+6/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x+6*I/b^4*d^3*polylog(4,-exp(I*(b*x+a)))-3/2/b^3*c*d^2*polylog(3,-exp(2*I*(b*x+a)))-3/2/b^3*d^3*polylog(3,-exp(2*I*(b*x+a)))*x-3/4*I*d^3*polylog(4,-exp(2*I*(b*x+a)))/b^4+1/b*c^3*ln(exp(I*(b*x+a))-1)+1/b*c^3*ln(exp(I*(b*x+a))+1)+3*I/b^2*c*d^2*polylog(2,-exp(2*I*(b*x+a)))*x+3/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))-1)-3*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))-3*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-3*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2-3*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+3/b*c^2*d*ln(exp(I*(b*x+a))+1)*x+3/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+3/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-3/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+3/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2+3/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2-3/b^2*c^2*d*a*ln(exp(I*(b*x+a))-1)+1/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+1/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3+1/b*d^3*ln(exp(I*(b*x+a))+1)*x^3-1/b*d^3*ln(1+exp(2*I*(b*x+a)))*x^3+3/2*I/b^2*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2+3/2*I/b^2*c^2*d*polylog(2,-exp(2*I*(b*x+a)))-3/b*c^2*d*ln(1+exp(2*I*(b*x+a)))*x-3/b*c*d^2*ln(1+exp(2*I*(b*x+a)))*x^2","B"
230,1,469,111,0.093000," ","int((d*x+c)^2*csc(b*x+a)*sec(b*x+a),x)","-\frac{d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{2 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}+\frac{i c d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 c d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{2 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}"," ",0,"-1/2*d^2*polylog(3,-exp(2*I*(b*x+a)))/b^3+1/b^3*d^2*a^2*ln(exp(I*(b*x+a))-1)+1/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-1/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2+1/b*d^2*ln(exp(I*(b*x+a))+1)*x^2+2*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+2*d^2*polylog(3,exp(I*(b*x+a)))/b^3-1/b*c^2*ln(1+exp(2*I*(b*x+a)))+1/b*c^2*ln(exp(I*(b*x+a))-1)+1/b*c^2*ln(exp(I*(b*x+a))+1)-1/b*d^2*ln(1+exp(2*I*(b*x+a)))*x^2-2*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-2*I/b^2*d^2*polylog(2,exp(I*(b*x+a)))*x-2/b*c*d*ln(1+exp(2*I*(b*x+a)))*x+2/b*c*d*ln(1-exp(I*(b*x+a)))*x+2/b^2*c*d*ln(1-exp(I*(b*x+a)))*a+2/b*c*d*ln(exp(I*(b*x+a))+1)*x-2/b^2*c*d*a*ln(exp(I*(b*x+a))-1)-2*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))+I/b^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x+I/b^2*c*d*polylog(2,-exp(2*I*(b*x+a)))-2*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))","B"
231,1,208,59,0.081000," ","int((d*x+c)*csc(b*x+a)*sec(b*x+a),x)","\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{i d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{i d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{i d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}"," ",0,"1/b*c*ln(exp(I*(b*x+a))-1)-1/b*c*ln(1+exp(2*I*(b*x+a)))+1/b*c*ln(exp(I*(b*x+a))+1)-1/b*d*ln(1+exp(2*I*(b*x+a)))*x+1/2*I*d*polylog(2,-exp(2*I*(b*x+a)))/b^2+1/b*d*ln(exp(I*(b*x+a))+1)*x-I*d*polylog(2,-exp(I*(b*x+a)))/b^2+1/b*d*ln(1-exp(I*(b*x+a)))*x+1/b^2*d*ln(1-exp(I*(b*x+a)))*a-I*d*polylog(2,exp(I*(b*x+a)))/b^2-1/b^2*d*a*ln(exp(I*(b*x+a))-1)","B"
232,0,0,21,0.099000," ","int(csc(b*x+a)*sec(b*x+a)/(d*x+c),x)","\int \frac{\csc \left(b x +a \right) \sec \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)*sec(b*x+a)/(d*x+c),x)","F"
233,0,0,21,0.099000," ","int(csc(b*x+a)*sec(b*x+a)/(d*x+c)^2,x)","\int \frac{\csc \left(b x +a \right) \sec \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)*sec(b*x+a)/(d*x+c)^2,x)","F"
234,0,0,24,0.082000," ","int((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a),x)","\int \left(d x +c \right)^{m} \left(\csc^{2}\left(b x +a \right)\right) \sec \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a),x)","F"
235,1,1158,313,0.501000," ","int((d*x+c)^3*csc(b*x+a)^2*sec(b*x+a),x)","-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}+\frac{3 d^{3} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}-\frac{6 c \,d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{6 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a x}{b^{3}}+\frac{6 i d^{2} c \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{6 i d^{3} a \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{4}}+\frac{6 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{6 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}+\frac{6 i \dilog \left({\mathrm e}^{i \left(b x +a \right)}\right) c \,d^{2}}{b^{3}}-\frac{6 i \dilog \left({\mathrm e}^{i \left(b x +a \right)}\right) d^{3} a}{b^{4}}-\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i d^{2} c \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i d^{2} c \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 i d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{6 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{2 i \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right) {\mathrm e}^{i \left(b x +a \right)}}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}-\frac{6 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}+\frac{3 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{3 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{3 c^{2} d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 c^{2} d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{3 a^{2} c \,d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 c^{2} d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{3 c^{2} d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 a^{2} c \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 i d^{3} a^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 i c^{2} d \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i c^{2} d \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 i c \,d^{2} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i c^{2} d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{a^{3} d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}-\frac{d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{a^{3} d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{2 i c^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{6 i d^{3} \polylog \left(4, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i d^{3} \polylog \left(4, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{2} c \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 d^{2} c \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"6*I*d^3*polylog(4,I*exp(I*(b*x+a)))/b^4-6*d^3*polylog(3,-exp(I*(b*x+a)))/b^4+6*d^3*polylog(3,exp(I*(b*x+a)))/b^4+3/b^2*c^2*d*ln(exp(I*(b*x+a))-1)-3/b^2*c^2*d*ln(exp(I*(b*x+a))+1)+3/b^4*d^3*a^2*ln(exp(I*(b*x+a))-1)-3/b^2*d^3*ln(exp(I*(b*x+a))+1)*x^2+3/b^2*d^3*ln(1-exp(I*(b*x+a)))*x^2+3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^2-6*I*d^3*polylog(4,-I*exp(I*(b*x+a)))/b^4-1/b^4*a^3*d^3*ln(1+I*exp(I*(b*x+a)))+6/b^3*d^3*polylog(3,I*exp(I*(b*x+a)))*x+1/b*d^3*ln(1-I*exp(I*(b*x+a)))*x^3-1/b*d^3*ln(1+I*exp(I*(b*x+a)))*x^3-6/b^3*d^3*polylog(3,-I*exp(I*(b*x+a)))*x+6/b^3*d^2*c*polylog(3,I*exp(I*(b*x+a)))-6/b^3*d^2*c*polylog(3,-I*exp(I*(b*x+a)))+1/b^4*a^3*d^3*ln(1-I*exp(I*(b*x+a)))-2*I/b*c^3*arctan(exp(I*(b*x+a)))+3/b*d^2*c*ln(1-I*exp(I*(b*x+a)))*x^2-3/b*d^2*c*ln(1+I*exp(I*(b*x+a)))*x^2+3/b*c^2*d*ln(1-I*exp(I*(b*x+a)))*x+3/b^2*c^2*d*ln(1-I*exp(I*(b*x+a)))*a+3/b^3*a^2*c*d^2*ln(1+I*exp(I*(b*x+a)))-3/b*c^2*d*ln(1+I*exp(I*(b*x+a)))*x-3/b^2*c^2*d*ln(1+I*exp(I*(b*x+a)))*a-3/b^3*a^2*c*d^2*ln(1-I*exp(I*(b*x+a)))+3*I/b^2*c^2*d*polylog(2,-I*exp(I*(b*x+a)))+2*I/b^4*d^3*a^3*arctan(exp(I*(b*x+a)))-3*I/b^2*c^2*d*polylog(2,I*exp(I*(b*x+a)))-3*I/b^2*d^3*polylog(2,I*exp(I*(b*x+a)))*x^2+3*I/b^2*d^3*polylog(2,-I*exp(I*(b*x+a)))*x^2-2*I*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)*exp(I*(b*x+a))/b/(exp(2*I*(b*x+a))-1)-6/b^3*c*d^2*a*ln(exp(I*(b*x+a))-1)+6/b^3*d^3*ln(1-exp(I*(b*x+a)))*a*x+6*I/b^3*d^2*c*dilog(exp(I*(b*x+a))+1)-6*I/b^4*d^3*a*dilog(exp(I*(b*x+a))+1)+6*I/b^4*d^3*polylog(2,-exp(I*(b*x+a)))*a-6*I/b^4*d^3*polylog(2,exp(I*(b*x+a)))*a+6*I/b^3*dilog(exp(I*(b*x+a)))*c*d^2-6*I/b^4*dilog(exp(I*(b*x+a)))*d^3*a-6*I/b^3*d^3*polylog(2,exp(I*(b*x+a)))*x-6/b^2*d^2*c*ln(exp(I*(b*x+a))+1)*x+6*I/b^3*d^3*polylog(2,-exp(I*(b*x+a)))*x-6*I/b^2*d^2*c*polylog(2,I*exp(I*(b*x+a)))*x-6*I/b^3*c*d^2*a^2*arctan(exp(I*(b*x+a)))+6*I/b^2*c^2*d*a*arctan(exp(I*(b*x+a)))+6*I/b^2*d^2*c*polylog(2,-I*exp(I*(b*x+a)))*x","B"
236,1,556,201,0.277000," ","int((d*x+c)^2*csc(b*x+a)^2*sec(b*x+a),x)","\frac{4 i c d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{2 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}+\frac{2 i \dilog \left({\mathrm e}^{i \left(b x +a \right)}\right) d^{2}}{b^{3}}-\frac{2 i {\mathrm e}^{i \left(b x +a \right)} \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}+\frac{2 i d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 i d^{2} \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{2 i c^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{2 i d^{2} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 i c d \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{a^{2} d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{2 c d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{a^{2} d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{2 d^{2} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i c d \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}+\frac{2 c d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{2 c d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}"," ",0,"4*I/b^2*c*d*a*arctan(exp(I*(b*x+a)))+2/b^2*d*c*ln(exp(I*(b*x+a))-1)-2/b^2*d*c*ln(exp(I*(b*x+a))+1)-2*I*exp(I*(b*x+a))*(d^2*x^2+2*c*d*x+c^2)/b/(exp(2*I*(b*x+a))-1)+2*I/b^3*dilog(exp(I*(b*x+a)))*d^2-2*I/b^2*d^2*polylog(2,I*exp(I*(b*x+a)))*x+2*I/b^3*d^2*dilog(exp(I*(b*x+a))+1)-2*I/b*c^2*arctan(exp(I*(b*x+a)))-2*I/b^3*d^2*a^2*arctan(exp(I*(b*x+a)))+2*I/b^2*c*d*polylog(2,-I*exp(I*(b*x+a)))+2*I/b^2*d^2*polylog(2,-I*exp(I*(b*x+a)))*x-1/b^3*a^2*d^2*ln(1-I*exp(I*(b*x+a)))-1/b*d^2*ln(1+I*exp(I*(b*x+a)))*x^2-2/b^2*c*d*ln(1+I*exp(I*(b*x+a)))*a+1/b^3*a^2*d^2*ln(1+I*exp(I*(b*x+a)))+2*d^2*polylog(3,I*exp(I*(b*x+a)))/b^3-2/b^3*d^2*a*ln(exp(I*(b*x+a))-1)-2*d^2*polylog(3,-I*exp(I*(b*x+a)))/b^3-2*I/b^2*c*d*polylog(2,I*exp(I*(b*x+a)))-2/b^2*d^2*ln(exp(I*(b*x+a))+1)*x+2/b*c*d*ln(1-I*exp(I*(b*x+a)))*x+2/b^2*c*d*ln(1-I*exp(I*(b*x+a)))*a-2/b*c*d*ln(1+I*exp(I*(b*x+a)))*x+1/b*d^2*ln(1-I*exp(I*(b*x+a)))*x^2","B"
237,1,235,120,0.129000," ","int((d*x+c)*csc(b*x+a)^2*sec(b*x+a),x)","-\frac{2 i {\mathrm e}^{i \left(b x +a \right)} \left(d x +c \right)}{b \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}+\frac{2 i d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{2 i c \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{i d \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{i d \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}"," ",0,"-2*I*exp(I*(b*x+a))*(d*x+c)/b/(exp(2*I*(b*x+a))-1)+2*I/b^2*d*a*arctan(exp(I*(b*x+a)))+d/b^2*ln(exp(I*(b*x+a))-1)-d/b^2*ln(exp(I*(b*x+a))+1)-2*I/b*c*arctan(exp(I*(b*x+a)))-I/b^2*d*dilog(1-I*exp(I*(b*x+a)))+I/b^2*d*dilog(1+I*exp(I*(b*x+a)))-1/b*d*ln(1+I*exp(I*(b*x+a)))*x-1/b^2*d*ln(1+I*exp(I*(b*x+a)))*a+1/b*d*ln(1-I*exp(I*(b*x+a)))*x+1/b^2*d*ln(1-I*exp(I*(b*x+a)))*a","A"
238,0,0,24,2.634000," ","int(csc(b*x+a)^2*sec(b*x+a)/(d*x+c),x)","\int \frac{\left(\csc^{2}\left(b x +a \right)\right) \sec \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)^2*sec(b*x+a)/(d*x+c),x)","F"
239,0,0,24,3.124000," ","int(csc(b*x+a)^2*sec(b*x+a)/(d*x+c)^2,x)","\int \frac{\left(\csc^{2}\left(b x +a \right)\right) \sec \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)^2*sec(b*x+a)/(d*x+c)^2,x)","F"
240,0,0,24,0.111000," ","int((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a),x)","\int \left(d x +c \right)^{m} \left(\csc^{3}\left(b x +a \right)\right) \sec \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a),x)","F"
241,1,1223,279,0.187000," ","int((d*x+c)^3*csc(b*x+a)^3*sec(b*x+a),x)","-\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{2 b^{3}}-\frac{d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}-\frac{6 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{6 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{6 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 c \,d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{3 i d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{4 b^{4}}-\frac{c^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{3 i d^{3} a^{2}}{b^{4}}+\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{6 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{2 b \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+6 b c \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+6 b \,c^{2} d x \,{\mathrm e}^{2 i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{2 i \left(b x +a \right)}+3 i d^{3} x^{2}+2 b \,c^{3} {\mathrm e}^{2 i \left(b x +a \right)}+6 i c \,d^{2} x +3 i c^{2} d}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{3 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{3 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i d^{3} x^{2}}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{3 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{3 c^{2} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{3 c \,d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}-\frac{6 i d^{3} a x}{b^{3}}"," ",0,"-6*I/b^2*c*d^2*polylog(2,exp(I*(b*x+a)))*x-6*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x+6*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4-1/b*c^3*ln(1+exp(2*I*(b*x+a)))-1/b^4*d^3*a^3*ln(exp(I*(b*x+a))-1)+6/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+6/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))+6/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x+6/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x+6*I/b^4*d^3*polylog(4,-exp(I*(b*x+a)))-3*I*d^3*polylog(2,exp(I*(b*x+a)))/b^4-3/2/b^3*c*d^2*polylog(3,-exp(2*I*(b*x+a)))-3/2/b^3*d^3*polylog(3,-exp(2*I*(b*x+a)))*x-3/4*I*d^3*polylog(4,-exp(2*I*(b*x+a)))/b^4+1/b*c^3*ln(exp(I*(b*x+a))-1)+1/b*c^3*ln(exp(I*(b*x+a))+1)+3*I/b^2*c*d^2*polylog(2,-exp(2*I*(b*x+a)))*x+(2*b*d^3*x^3*exp(2*I*(b*x+a))-3*I*d^3*x^2*exp(2*I*(b*x+a))+6*b*c*d^2*x^2*exp(2*I*(b*x+a))-6*I*c*d^2*x*exp(2*I*(b*x+a))+6*b*c^2*d*x*exp(2*I*(b*x+a))-3*I*c^2*d*exp(2*I*(b*x+a))+3*I*d^3*x^2+2*b*c^3*exp(2*I*(b*x+a))+6*I*c*d^2*x+3*I*c^2*d)/b^2/(exp(2*I*(b*x+a))-1)^2+3/b^3*d^2*c*ln(exp(I*(b*x+a))-1)+3/b^3*d^2*c*ln(exp(I*(b*x+a))+1)-6/b^3*d^2*c*ln(exp(I*(b*x+a)))+3/b^3*d^3*ln(exp(I*(b*x+a))+1)*x+3/b^3*d^3*ln(1-exp(I*(b*x+a)))*x+3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a-3/b^4*d^3*a*ln(exp(I*(b*x+a))-1)+6/b^4*d^3*a*ln(exp(I*(b*x+a)))-3*I/b^2*d^3*x^2-3*I/b^4*d^3*a^2-3*I/b^4*d^3*polylog(2,-exp(I*(b*x+a)))+3/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))-1)-3*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))-3*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-3*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2-3*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+3/b*c^2*d*ln(exp(I*(b*x+a))+1)*x+3/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+3/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-3/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+3/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2+3/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2-3/b^2*c^2*d*a*ln(exp(I*(b*x+a))-1)+1/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+1/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3+1/b*d^3*ln(exp(I*(b*x+a))+1)*x^3-1/b*d^3*ln(1+exp(2*I*(b*x+a)))*x^3+3/2*I/b^2*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2-6*I/b^3*d^3*a*x+3/2*I/b^2*c^2*d*polylog(2,-exp(2*I*(b*x+a)))-3/b*c^2*d*ln(1+exp(2*I*(b*x+a)))*x-3/b*c*d^2*ln(1+exp(2*I*(b*x+a)))*x^2","B"
242,1,632,181,0.164000," ","int((d*x+c)^2*csc(b*x+a)^3*sec(b*x+a),x)","\frac{d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{2 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}+\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{i c d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 c d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{2 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 b \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+4 b c d x \,{\mathrm e}^{2 i \left(b x +a \right)}+2 b \,c^{2} {\mathrm e}^{2 i \left(b x +a \right)}-2 i d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}-2 i c d \,{\mathrm e}^{2 i \left(b x +a \right)}+2 i d^{2} x +2 i d c}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}"," ",0,"-1/2*d^2*polylog(3,-exp(2*I*(b*x+a)))/b^3+1/b^3*d^2*a^2*ln(exp(I*(b*x+a))-1)+1/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-1/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2+1/b*d^2*ln(exp(I*(b*x+a))+1)*x^2+2*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+2*d^2*polylog(3,exp(I*(b*x+a)))/b^3-1/b*c^2*ln(1+exp(2*I*(b*x+a)))+1/b*c^2*ln(exp(I*(b*x+a))-1)+1/b*c^2*ln(exp(I*(b*x+a))+1)-1/b*d^2*ln(1+exp(2*I*(b*x+a)))*x^2+I/b^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x+I/b^2*c*d*polylog(2,-exp(2*I*(b*x+a)))-2/b*c*d*ln(1+exp(2*I*(b*x+a)))*x+2/b*c*d*ln(1-exp(I*(b*x+a)))*x+2/b^2*c*d*ln(1-exp(I*(b*x+a)))*a+2/b*c*d*ln(exp(I*(b*x+a))+1)*x-2/b^2*c*d*a*ln(exp(I*(b*x+a))-1)-2*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-2*I/b^2*d^2*polylog(2,exp(I*(b*x+a)))*x-2*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))-2*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))+2*(b*d^2*x^2*exp(2*I*(b*x+a))+2*b*c*d*x*exp(2*I*(b*x+a))+b*c^2*exp(2*I*(b*x+a))-I*d^2*x*exp(2*I*(b*x+a))-I*c*d*exp(2*I*(b*x+a))+I*d^2*x+I*d*c)/b^2/(exp(2*I*(b*x+a))-1)^2+1/b^3*d^2*ln(exp(I*(b*x+a))+1)-2/b^3*d^2*ln(exp(I*(b*x+a)))+1/b^3*d^2*ln(exp(I*(b*x+a))-1)","B"
243,1,270,123,0.125000," ","int((d*x+c)*csc(b*x+a)^3*sec(b*x+a),x)","\frac{2 b d x \,{\mathrm e}^{2 i \left(b x +a \right)}+2 b c \,{\mathrm e}^{2 i \left(b x +a \right)}-i d \,{\mathrm e}^{2 i \left(b x +a \right)}+i d}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{i d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{i d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{i d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}"," ",0,"(2*b*d*x*exp(2*I*(b*x+a))+2*b*c*exp(2*I*(b*x+a))-I*d*exp(2*I*(b*x+a))+I*d)/b^2/(exp(2*I*(b*x+a))-1)^2+1/b*c*ln(exp(I*(b*x+a))-1)-1/b*c*ln(1+exp(2*I*(b*x+a)))+1/b*c*ln(exp(I*(b*x+a))+1)-1/b*d*ln(1+exp(2*I*(b*x+a)))*x+1/2*I*d*polylog(2,-exp(2*I*(b*x+a)))/b^2+1/b*d*ln(exp(I*(b*x+a))+1)*x-I*d*polylog(2,-exp(I*(b*x+a)))/b^2+1/b*d*ln(1-exp(I*(b*x+a)))*x+1/b^2*d*ln(1-exp(I*(b*x+a)))*a-I*d*polylog(2,exp(I*(b*x+a)))/b^2-1/b^2*d*a*ln(exp(I*(b*x+a))-1)","B"
244,0,0,24,3.382000," ","int(csc(b*x+a)^3*sec(b*x+a)/(d*x+c),x)","\int \frac{\left(\csc^{3}\left(b x +a \right)\right) \sec \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)^3*sec(b*x+a)/(d*x+c),x)","F"
245,0,0,24,5.592000," ","int(csc(b*x+a)^3*sec(b*x+a)/(d*x+c)^2,x)","\int \frac{\left(\csc^{3}\left(b x +a \right)\right) \sec \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)^3*sec(b*x+a)/(d*x+c)^2,x)","F"
246,0,0,22,0.080000," ","int((d*x+c)^m*sec(b*x+a)*tan(b*x+a),x)","\int \left(d x +c \right)^{m} \sec \left(b x +a \right) \tan \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*sec(b*x+a)*tan(b*x+a),x)","F"
247,1,767,202,0.196000," ","int((d*x+c)^4*sec(b*x+a)*tan(b*x+a),x)","\frac{24 i d^{3} c \,a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{24 i d^{2} c^{2} a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{24 i d^{3} c \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 i d^{3} c \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{2 \,{\mathrm e}^{i \left(b x +a \right)} \left(d^{4} x^{4}+4 c \,d^{3} x^{3}+6 c^{2} d^{2} x^{2}+4 c^{3} d x +c^{4}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}+\frac{4 d^{4} a^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{4 d^{4} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{4 d^{4} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{4 d^{4} a^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{24 i d^{4} \polylog \left(4, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 i d^{4} \polylog \left(4, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{24 d^{4} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{24 d^{4} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{24 d^{3} c \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{24 d^{3} c \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{12 d^{3} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{12 d^{3} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{12 d^{3} a^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 d^{2} c^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 d^{2} c^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{12 d^{3} a^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{12 d^{2} c^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{12 d^{2} c^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{8 i d^{4} a^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{8 i d \,c^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{12 i d^{4} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{12 i d^{4} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{12 i d^{2} c^{2} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{12 i d^{2} c^{2} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"24*I*d^4*polylog(4,-I*exp(I*(b*x+a)))/b^5-24*I*d^4*polylog(4,I*exp(I*(b*x+a)))/b^5+12/b^2*d^3*c*ln(1+I*exp(I*(b*x+a)))*x^2-12/b^2*d^3*c*ln(1-I*exp(I*(b*x+a)))*x^2+12/b^4*d^3*a^2*c*ln(1-I*exp(I*(b*x+a)))-12/b^2*d^2*c^2*ln(1-I*exp(I*(b*x+a)))*x-12/b^3*d^2*c^2*ln(1-I*exp(I*(b*x+a)))*a-12/b^4*d^3*a^2*c*ln(1+I*exp(I*(b*x+a)))+12/b^2*d^2*c^2*ln(1+I*exp(I*(b*x+a)))*x+12/b^3*d^2*c^2*ln(1+I*exp(I*(b*x+a)))*a-12*I/b^3*d^4*polylog(2,-I*exp(I*(b*x+a)))*x^2+12*I/b^3*d^4*polylog(2,I*exp(I*(b*x+a)))*x^2+12*I/b^3*d^2*c^2*polylog(2,I*exp(I*(b*x+a)))-8*I/b^5*d^4*a^3*arctan(exp(I*(b*x+a)))-12*I/b^3*d^2*c^2*polylog(2,-I*exp(I*(b*x+a)))+8*I/b^2*d*c^3*arctan(exp(I*(b*x+a)))-24*I/b^3*d^3*c*polylog(2,-I*exp(I*(b*x+a)))*x+24*I/b^3*d^3*c*polylog(2,I*exp(I*(b*x+a)))*x+24*I/b^4*d^3*c*a^2*arctan(exp(I*(b*x+a)))-24*I/b^3*d^2*c^2*a*arctan(exp(I*(b*x+a)))+2*exp(I*(b*x+a))*(d^4*x^4+4*c*d^3*x^3+6*c^2*d^2*x^2+4*c^3*d*x+c^4)/b/(1+exp(2*I*(b*x+a)))+24/b^4*d^4*polylog(3,-I*exp(I*(b*x+a)))*x-24/b^4*d^4*polylog(3,I*exp(I*(b*x+a)))*x+4/b^5*d^4*a^3*ln(1+I*exp(I*(b*x+a)))+24/b^4*d^3*c*polylog(3,-I*exp(I*(b*x+a)))-24/b^4*d^3*c*polylog(3,I*exp(I*(b*x+a)))+4/b^2*d^4*ln(1+I*exp(I*(b*x+a)))*x^3-4/b^2*d^4*ln(1-I*exp(I*(b*x+a)))*x^3-4/b^5*d^4*a^3*ln(1-I*exp(I*(b*x+a)))","B"
248,1,463,142,0.128000," ","int((d*x+c)^3*sec(b*x+a)*tan(b*x+a),x)","\frac{2 \,{\mathrm e}^{i \left(b x +a \right)} \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}-\frac{6 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{3 d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{6 i d \,c^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{6 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{6 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{3 d^{3} a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{6 i c \,d^{2} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 d^{3} a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 i d^{3} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 i d^{2} c a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{3} x \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i d^{3} x \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{6 i c \,d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"2*exp(I*(b*x+a))*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/b/(1+exp(2*I*(b*x+a)))-6/b^3*d^2*c*ln(1-I*exp(I*(b*x+a)))*a+3/b^2*d^3*ln(1+I*exp(I*(b*x+a)))*x^2+6*I/b^2*d*c^2*arctan(exp(I*(b*x+a)))+6/b^3*d^2*c*ln(1+I*exp(I*(b*x+a)))*a-6/b^2*d^2*c*ln(1-I*exp(I*(b*x+a)))*x-3/b^4*d^3*a^2*ln(1+I*exp(I*(b*x+a)))-3/b^2*d^3*ln(1-I*exp(I*(b*x+a)))*x^2-6*I*c*d^2*polylog(2,-I*exp(I*(b*x+a)))/b^3+3/b^4*d^3*a^2*ln(1-I*exp(I*(b*x+a)))+6*d^3*polylog(3,-I*exp(I*(b*x+a)))/b^4+6*I/b^4*d^3*a^2*arctan(exp(I*(b*x+a)))-12*I/b^3*d^2*c*a*arctan(exp(I*(b*x+a)))-6*I*d^3*x*polylog(2,-I*exp(I*(b*x+a)))/b^3+6*I*c*d^2*polylog(2,I*exp(I*(b*x+a)))/b^3-6*d^3*polylog(3,I*exp(I*(b*x+a)))/b^4+6/b^2*d^2*c*ln(1+I*exp(I*(b*x+a)))*x+6*I*d^3*x*polylog(2,I*exp(I*(b*x+a)))/b^3","B"
249,1,239,86,0.023000," ","int((d*x+c)^2*sec(b*x+a)*tan(b*x+a),x)","\frac{d^{2} x^{2}}{b \cos \left(b x +a \right)}+\frac{2 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{2 i d^{2} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i d^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 a \,d^{2} \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b^{3}}+\frac{2 c d x}{b \cos \left(b x +a \right)}-\frac{2 c d \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b^{2}}+\frac{c^{2}}{b \cos \left(b x +a \right)}"," ",0,"1/b*d^2/cos(b*x+a)*x^2+2/b^2*d^2*ln(1+I*exp(I*(b*x+a)))*x+2/b^3*d^2*ln(1+I*exp(I*(b*x+a)))*a-2/b^2*d^2*ln(1-I*exp(I*(b*x+a)))*x-2/b^3*d^2*ln(1-I*exp(I*(b*x+a)))*a+2*I/b^3*d^2*dilog(1-I*exp(I*(b*x+a)))-2*I/b^3*d^2*dilog(1+I*exp(I*(b*x+a)))+2/b^3*a*d^2*ln(sec(b*x+a)+tan(b*x+a))+2/b*c*d/cos(b*x+a)*x-2/b^2*c*d*ln(sec(b*x+a)+tan(b*x+a))+1/b/cos(b*x+a)*c^2","B"
250,1,49,29,0.021000," ","int((d*x+c)*sec(b*x+a)*tan(b*x+a),x)","\frac{d x}{b \cos \left(b x +a \right)}-\frac{d \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b^{2}}+\frac{c}{b \cos \left(b x +a \right)}"," ",0,"1/b*d/cos(b*x+a)*x-1/b^2*d*ln(sec(b*x+a)+tan(b*x+a))+1/b*c/cos(b*x+a)","A"
251,0,0,22,0.169000," ","int(sec(b*x+a)*tan(b*x+a)/(d*x+c),x)","\int \frac{\sec \left(b x +a \right) \tan \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)*tan(b*x+a)/(d*x+c),x)","F"
252,0,0,22,0.237000," ","int(sec(b*x+a)*tan(b*x+a)/(d*x+c)^2,x)","\int \frac{\sec \left(b x +a \right) \tan \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(sec(b*x+a)*tan(b*x+a)/(d*x+c)^2,x)","F"
253,0,0,18,0.083000," ","int((d*x+c)^m*tan(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \left(\tan^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*tan(b*x+a)^2,x)","F"
254,1,348,116,0.131000," ","int((d*x+c)^3*tan(b*x+a)^2,x)","-\frac{d^{3} x^{4}}{4}-c \,d^{2} x^{3}-\frac{3 c^{2} d \,x^{2}}{2}-c^{3} x -\frac{6 i d^{2} c \,a^{2}}{b^{3}}+\frac{3 d \,c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 d \,c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 d^{3} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i d^{2} c \,x^{2}}{b}+\frac{6 i d^{3} a^{2} x}{b^{3}}+\frac{2 i \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}+\frac{3 d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{4 i d^{3} a^{3}}{b^{4}}+\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{4}}+\frac{12 d^{2} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i d^{2} c \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}-\frac{2 i d^{3} x^{3}}{b}+\frac{6 d^{2} c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i d^{2} c a x}{b^{2}}"," ",0,"-1/4*d^3*x^4-c*d^2*x^3-3/2*c^2*d*x^2-c^3*x-6*I*d^2/b^3*c*a^2+3*d/b^2*c^2*ln(1+exp(2*I*(b*x+a)))-6*d/b^2*c^2*ln(exp(I*(b*x+a)))-6*d^3/b^4*a^2*ln(exp(I*(b*x+a)))-6*I*d^2/b*c*x^2+6*I*d^3/b^3*a^2*x+2*I*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/b/(1+exp(2*I*(b*x+a)))+3*d^3/b^2*ln(1+exp(2*I*(b*x+a)))*x^2+4*I*d^3/b^4*a^3+3/2*d^3*polylog(3,-exp(2*I*(b*x+a)))/b^4+12*d^2/b^3*c*a*ln(exp(I*(b*x+a)))-3*I*d^3/b^3*polylog(2,-exp(2*I*(b*x+a)))*x-2*I*d^3/b*x^3-3*I*d^2/b^3*c*polylog(2,-exp(2*I*(b*x+a)))+6*d^2/b^2*c*ln(1+exp(2*I*(b*x+a)))*x-12*I*d^2/b^2*c*a*x","B"
255,1,191,88,0.089000," ","int((d*x+c)^2*tan(b*x+a)^2,x)","-\frac{d^{2} x^{3}}{3}-c d \,x^{2}-c^{2} x +\frac{2 i \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}+\frac{2 d c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i d^{2} x^{2}}{b}-\frac{4 i d^{2} a x}{b^{2}}-\frac{2 i d^{2} a^{2}}{b^{3}}+\frac{2 d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}-\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{4 d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"-1/3*d^2*x^3-c*d*x^2-c^2*x+2*I*(d^2*x^2+2*c*d*x+c^2)/b/(1+exp(2*I*(b*x+a)))+2*d/b^2*c*ln(1+exp(2*I*(b*x+a)))-4/b^2*d*c*ln(exp(I*(b*x+a)))-2*I/b*d^2*x^2-4*I/b^2*d^2*a*x-2*I/b^3*d^2*a^2+2*d^2/b^2*ln(1+exp(2*I*(b*x+a)))*x-I*d^2*polylog(2,-exp(2*I*(b*x+a)))/b^3+4/b^3*d^2*a*ln(exp(I*(b*x+a)))","B"
256,1,47,38,0.053000," ","int((d*x+c)*tan(b*x+a)^2,x)","-\frac{d \,x^{2}}{2}-c x +\frac{d \tan \left(b x +a \right) x}{b}+\frac{d \ln \left(\cos \left(b x +a \right)\right)}{b^{2}}+\frac{c \tan \left(b x +a \right)}{b}"," ",0,"-1/2*d*x^2-c*x+1/b*d*tan(b*x+a)*x+d*ln(cos(b*x+a))/b^2+1/b*c*tan(b*x+a)","A"
257,0,0,18,0.168000," ","int(tan(b*x+a)^2/(d*x+c),x)","\int \frac{\tan^{2}\left(b x +a \right)}{d x +c}\, dx"," ",0,"int(tan(b*x+a)^2/(d*x+c),x)","F"
258,0,0,18,0.235000," ","int(tan(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\tan^{2}\left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(tan(b*x+a)^2/(d*x+c)^2,x)","F"
259,0,0,139,0.090000," ","int((d*x+c)^m*sin(b*x+a)*tan(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \sin \left(b x +a \right) \left(\tan^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*sin(b*x+a)*tan(b*x+a)^2,x)","F"
260,1,677,211,0.125000," ","int((d*x+c)^3*sin(b*x+a)*tan(b*x+a)^2,x)","\frac{\left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}+3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x +6 i b^{2} c \,d^{2} x +b^{3} c^{3}+3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b -6 i d^{3}\right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{4}}+\frac{\left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}-3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x -6 i b^{2} c \,d^{2} x +b^{3} c^{3}-3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b +6 i d^{3}\right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{4}}+\frac{2 \,{\mathrm e}^{i \left(b x +a \right)} \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}+\frac{3 d^{3} a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{6 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{6 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i d^{3} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 i d^{3} x \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{3 d^{3} a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i d^{3} x \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i d \,c^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{6 i c \,d^{2} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i c \,d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{6 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 i d^{2} c a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"1/2*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3+3*I*b^2*d^3*x^2-6*b*d^3*x+6*I*b^2*c*d^2*x-6*c*d^2*b+3*I*b^2*c^2*d-6*I*d^3)/b^4*exp(I*(b*x+a))+1/2*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3-3*I*b^2*d^3*x^2-6*b*d^3*x-6*I*b^2*c*d^2*x-6*c*d^2*b-3*I*b^2*c^2*d+6*I*d^3)/b^4*exp(-I*(b*x+a))+2*exp(I*(b*x+a))*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/b/(1+exp(2*I*(b*x+a)))+3/b^4*d^3*a^2*ln(1-I*exp(I*(b*x+a)))+3/b^2*d^3*ln(1+I*exp(I*(b*x+a)))*x^2-6/b^3*d^2*c*ln(1-I*exp(I*(b*x+a)))*a-6/b^2*d^2*c*ln(1-I*exp(I*(b*x+a)))*x+6*I*c*d^2*polylog(2,I*exp(I*(b*x+a)))/b^3+6*I/b^4*d^3*a^2*arctan(exp(I*(b*x+a)))+6/b^3*d^2*c*ln(1+I*exp(I*(b*x+a)))*a-3/b^4*d^3*a^2*ln(1+I*exp(I*(b*x+a)))+6*I*d^3*x*polylog(2,I*exp(I*(b*x+a)))/b^3+6*I/b^2*d*c^2*arctan(exp(I*(b*x+a)))-6*I*c*d^2*polylog(2,-I*exp(I*(b*x+a)))/b^3-12*I/b^3*d^2*c*a*arctan(exp(I*(b*x+a)))-3/b^2*d^3*ln(1-I*exp(I*(b*x+a)))*x^2-6*d^3*polylog(3,I*exp(I*(b*x+a)))/b^4-6*I*d^3*x*polylog(2,-I*exp(I*(b*x+a)))/b^3+6/b^2*d^2*c*ln(1+I*exp(I*(b*x+a)))*x+6*d^3*polylog(3,-I*exp(I*(b*x+a)))/b^4","B"
261,1,345,134,0.126000," ","int((d*x+c)^2*sin(b*x+a)*tan(b*x+a)^2,x)","\frac{\left(d^{2} x^{2} b^{2}+2 b^{2} c d x +2 i b \,d^{2} x +b^{2} c^{2}+2 i b c d -2 d^{2}\right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{3}}+\frac{\left(d^{2} x^{2} b^{2}+2 b^{2} c d x -2 i b \,d^{2} x +b^{2} c^{2}-2 i b c d -2 d^{2}\right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{3}}+\frac{2 \,{\mathrm e}^{i \left(b x +a \right)} \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}+\frac{4 i d c \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 i d^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 i d^{2} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{4 i d^{2} a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"1/2*(d^2*x^2*b^2+2*b^2*c*d*x+b^2*c^2+2*I*b*d^2*x-2*d^2+2*I*b*c*d)/b^3*exp(I*(b*x+a))+1/2*(d^2*x^2*b^2+2*b^2*c*d*x+b^2*c^2-2*I*b*d^2*x-2*d^2-2*I*b*c*d)/b^3*exp(-I*(b*x+a))+2*exp(I*(b*x+a))*(d^2*x^2+2*c*d*x+c^2)/b/(1+exp(2*I*(b*x+a)))+4*I*d/b^2*c*arctan(exp(I*(b*x+a)))+2/b^2*d^2*ln(1+I*exp(I*(b*x+a)))*x+2/b^3*d^2*ln(1+I*exp(I*(b*x+a)))*a-2/b^2*d^2*ln(1-I*exp(I*(b*x+a)))*x-2/b^3*d^2*ln(1-I*exp(I*(b*x+a)))*a-2*I/b^3*d^2*dilog(1+I*exp(I*(b*x+a)))+2*I/b^3*d^2*dilog(1-I*exp(I*(b*x+a)))-4*I*d^2/b^3*a*arctan(exp(I*(b*x+a)))","B"
262,1,123,56,0.158000," ","int((d*x+c)*sin(b*x+a)*tan(b*x+a)^2,x)","\frac{\left(b d x +c b +i d \right) {\mathrm e}^{i \left(b x +a \right)}}{2 b^{2}}+\frac{\left(b d x +c b -i d \right) {\mathrm e}^{-i \left(b x +a \right)}}{2 b^{2}}+\frac{2 \,{\mathrm e}^{i \left(b x +a \right)} \left(d x +c \right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+i\right)}{b^{2}}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}-i\right)}{b^{2}}"," ",0,"1/2*(b*d*x+c*b+I*d)/b^2*exp(I*(b*x+a))+1/2*(b*d*x+c*b-I*d)/b^2*exp(-I*(b*x+a))+2*exp(I*(b*x+a))*(d*x+c)/b/(1+exp(2*I*(b*x+a)))-d/b^2*ln(exp(I*(b*x+a))+I)+d/b^2*ln(exp(I*(b*x+a))-I)","C"
263,0,0,75,0.186000," ","int(sin(b*x+a)*tan(b*x+a)^2/(d*x+c),x)","\int \frac{\sin \left(b x +a \right) \left(\tan^{2}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(sin(b*x+a)*tan(b*x+a)^2/(d*x+c),x)","F"
264,0,0,93,0.280000," ","int(sin(b*x+a)*tan(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\sin \left(b x +a \right) \left(\tan^{2}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(sin(b*x+a)*tan(b*x+a)^2/(d*x+c)^2,x)","F"
265,0,0,24,0.082000," ","int((d*x+c)^m*csc(b*x+a)*sec(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \csc \left(b x +a \right) \left(\sec^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a)*sec(b*x+a)^2,x)","F"
266,1,1866,422,0.599000," ","int((d*x+c)^4*csc(b*x+a)*sec(b*x+a)^2,x)","-\frac{d^{4} a^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{12 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 c^{2} d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{12 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{4}}{b}-\frac{d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{4}}{b}+\frac{12 i a^{2} d^{4} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{12 i a^{2} d^{4} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{12 i c^{2} d^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 i c^{2} d^{2} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{12 i a^{2} d^{4} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{12 i a^{2} d^{4} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{24 i d^{3} c \,a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{24 i d^{2} c^{2} a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{24 i d^{3} c \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 i d^{3} c \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{5}}+\frac{24 d^{4} \polylog \left(5, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 d^{4} \polylog \left(5, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{2 \,{\mathrm e}^{i \left(b x +a \right)} \left(d^{4} x^{4}+4 c \,d^{3} x^{3}+6 c^{2} d^{2} x^{2}+4 c^{3} d x +c^{4}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}+\frac{4 d^{4} a^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{4 d^{4} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{4 d^{4} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{4 d^{4} a^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{24 i d^{4} \polylog \left(4, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 i d^{4} \polylog \left(4, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{24 d^{4} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{24 d^{4} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{24 d^{3} c \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{24 d^{3} c \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{4 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}-\frac{24 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{4 i c^{3} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 i c^{3} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{24 c \,d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 c \,d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{24 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 i c \,d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{4 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{24 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}+\frac{4 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{4 c^{3} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{6 c^{2} d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{6 c^{2} d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{12 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{12 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c^{2} d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c \,d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{4 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{6 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{4 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{12 d^{3} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{12 d^{3} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{12 d^{3} a^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 d^{2} c^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 d^{2} c^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{12 d^{3} a^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{12 d^{2} c^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{12 d^{2} c^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{8 i d^{4} a^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{8 i d \,c^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{12 i d^{4} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{12 i d^{4} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{24 i c \,d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}+\frac{24 i a c \,d^{3} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{24 i a c \,d^{3} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 i c \,d^{3} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}"," ",0,"1/b^5*d^4*a^4*ln(exp(I*(b*x+a))-1)-12/b^3*c^2*d^2*polylog(3,-exp(I*(b*x+a)))+12/b^3*c^2*d^2*polylog(3,exp(I*(b*x+a)))-1/b^5*d^4*a^4*ln(1-exp(I*(b*x+a)))+12/b^3*d^4*polylog(3,exp(I*(b*x+a)))*x^2-12/b^3*d^4*polylog(3,-exp(I*(b*x+a)))*x^2+24*I*d^4*polylog(4,-I*exp(I*(b*x+a)))/b^5+24*d^4*polylog(5,-exp(I*(b*x+a)))/b^5-24*d^4*polylog(5,exp(I*(b*x+a)))/b^5-24*I*d^4*polylog(4,I*exp(I*(b*x+a)))/b^5+12*I/b^3*c^2*d^2*dilog(1-I*exp(I*(b*x+a)))-12*I/b^5*a^2*d^4*polylog(2,I*exp(I*(b*x+a)))-12*I/b^5*a^2*d^4*dilog(1+I*exp(I*(b*x+a)))+12*I/b^5*a^2*d^4*dilog(1-I*exp(I*(b*x+a)))+12*I/b^5*a^2*d^4*polylog(2,-I*exp(I*(b*x+a)))-12*I/b^3*c^2*d^2*dilog(1+I*exp(I*(b*x+a)))+12/b^2*d^3*c*ln(1+I*exp(I*(b*x+a)))*x^2-12/b^2*d^3*c*ln(1-I*exp(I*(b*x+a)))*x^2+12/b^4*d^3*a^2*c*ln(1-I*exp(I*(b*x+a)))-12/b^2*d^2*c^2*ln(1-I*exp(I*(b*x+a)))*x-12/b^3*d^2*c^2*ln(1-I*exp(I*(b*x+a)))*a-12/b^4*d^3*a^2*c*ln(1+I*exp(I*(b*x+a)))+12/b^2*d^2*c^2*ln(1+I*exp(I*(b*x+a)))*x+12/b^3*d^2*c^2*ln(1+I*exp(I*(b*x+a)))*a-12*I/b^3*d^4*polylog(2,-I*exp(I*(b*x+a)))*x^2+12*I/b^3*d^4*polylog(2,I*exp(I*(b*x+a)))*x^2-8*I/b^5*d^4*a^3*arctan(exp(I*(b*x+a)))+8*I/b^2*d*c^3*arctan(exp(I*(b*x+a)))-24*I/b^3*d^3*c*polylog(2,-I*exp(I*(b*x+a)))*x+24*I/b^3*d^3*c*polylog(2,I*exp(I*(b*x+a)))*x+24*I/b^4*d^3*c*a^2*arctan(exp(I*(b*x+a)))-24*I/b^3*d^2*c^2*a*arctan(exp(I*(b*x+a)))-1/b*c^4*ln(exp(I*(b*x+a))+1)+1/b*c^4*ln(exp(I*(b*x+a))-1)+2*exp(I*(b*x+a))*(d^4*x^4+4*c*d^3*x^3+6*c^2*d^2*x^2+4*c^3*d*x+c^4)/b/(1+exp(2*I*(b*x+a)))-24*I/b^4*d^4*polylog(4,-exp(I*(b*x+a)))*x-24*I/b^4*c*d^3*polylog(4,-exp(I*(b*x+a)))+4*I/b^2*c^3*d*polylog(2,-exp(I*(b*x+a)))+4*I/b^2*d^4*polylog(2,-exp(I*(b*x+a)))*x^3+24/b^4*d^4*polylog(3,-I*exp(I*(b*x+a)))*x-24/b^4*d^4*polylog(3,I*exp(I*(b*x+a)))*x+4/b^5*d^4*a^3*ln(1+I*exp(I*(b*x+a)))+24/b^4*d^3*c*polylog(3,-I*exp(I*(b*x+a)))-24/b^4*d^3*c*polylog(3,I*exp(I*(b*x+a)))+4/b^2*d^4*ln(1+I*exp(I*(b*x+a)))*x^3-4/b^2*d^4*ln(1-I*exp(I*(b*x+a)))*x^3-4/b^5*d^4*a^3*ln(1-I*exp(I*(b*x+a)))-4/b*c^3*d*ln(exp(I*(b*x+a))+1)*x+4/b*c^3*d*ln(1-exp(I*(b*x+a)))*x+4/b^2*c^3*d*ln(1-exp(I*(b*x+a)))*a-6/b*c^2*d^2*ln(exp(I*(b*x+a))+1)*x^2-24/b^3*c*d^3*polylog(3,-exp(I*(b*x+a)))*x-6/b^3*c^2*d^2*a^2*ln(1-exp(I*(b*x+a)))+6/b*c^2*d^2*ln(1-exp(I*(b*x+a)))*x^2+24/b^3*c*d^3*polylog(3,exp(I*(b*x+a)))*x+24*I/b^4*c*d^3*polylog(4,exp(I*(b*x+a)))-4*I/b^2*d^4*polylog(2,exp(I*(b*x+a)))*x^3+24*I/b^4*d^4*polylog(4,exp(I*(b*x+a)))*x-4*I/b^2*c^3*d*polylog(2,exp(I*(b*x+a)))-4/b^4*c*d^3*a^3*ln(exp(I*(b*x+a))-1)+6/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a))-1)-4/b^2*c^3*d*a*ln(exp(I*(b*x+a))-1)+1/b*d^4*ln(1-exp(I*(b*x+a)))*x^4-1/b*d^4*ln(exp(I*(b*x+a))+1)*x^4-12*I/b^2*c^2*d^2*polylog(2,exp(I*(b*x+a)))*x-12*I/b^2*c*d^3*polylog(2,exp(I*(b*x+a)))*x^2-4/b*c*d^3*ln(exp(I*(b*x+a))+1)*x^3+4/b*c*d^3*ln(1-exp(I*(b*x+a)))*x^3+4/b^4*c*d^3*ln(1-exp(I*(b*x+a)))*a^3+12*I/b^2*c*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+12*I/b^2*c^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-24*I/b^4*c*d^3*polylog(2,-I*exp(I*(b*x+a)))*a+24*I/b^4*a*c*d^3*dilog(1+I*exp(I*(b*x+a)))-24*I/b^4*a*c*d^3*dilog(1-I*exp(I*(b*x+a)))+24*I/b^4*c*d^3*polylog(2,I*exp(I*(b*x+a)))*a","B"
267,1,1152,308,0.467000," ","int((d*x+c)^3*csc(b*x+a)*sec(b*x+a)^2,x)","-\frac{6 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i d^{2} c a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{2} c \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i d^{2} c \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i a \,d^{3} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i a \,d^{3} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 i d^{3} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{6 i d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}-\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{6 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{3 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{6 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{6 i d \,c^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{6 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{6 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i d^{3} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i d^{3} x \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i d^{3} x \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 \,{\mathrm e}^{i \left(b x +a \right)} \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}+\frac{3 d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 d^{3} a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 d^{3} a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"6*d^3*polylog(3,-I*exp(I*(b*x+a)))/b^4-6*d^3*polylog(3,I*exp(I*(b*x+a)))/b^4-6*I/b^2*c*d^2*polylog(2,exp(I*(b*x+a)))*x-12*I/b^3*d^2*c*a*arctan(exp(I*(b*x+a)))+6*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4+6*I*d^3*x*polylog(2,I*exp(I*(b*x+a)))/b^3-6*I*d^3*x*polylog(2,-I*exp(I*(b*x+a)))/b^3-1/b^4*d^3*a^3*ln(exp(I*(b*x+a))-1)-6/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+6/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))+6/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x-6/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x-6*I*d^3*polylog(4,-exp(I*(b*x+a)))/b^4-6*I/b^3*d^2*c*dilog(1+I*exp(I*(b*x+a)))+6*I/b^3*d^2*c*dilog(1-I*exp(I*(b*x+a)))+6*I/b^4*a*d^3*dilog(1+I*exp(I*(b*x+a)))-6*I/b^4*a*d^3*dilog(1-I*exp(I*(b*x+a)))+6*I/b^4*d^3*polylog(2,I*exp(I*(b*x+a)))*a-6*I/b^4*d^3*polylog(2,-I*exp(I*(b*x+a)))*a+1/b*c^3*ln(exp(I*(b*x+a))-1)-1/b*c^3*ln(exp(I*(b*x+a))+1)+2*exp(I*(b*x+a))*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/b/(1+exp(2*I*(b*x+a)))+6*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x+6/b^2*d^2*c*ln(1+I*exp(I*(b*x+a)))*x+6*I/b^4*d^3*a^2*arctan(exp(I*(b*x+a)))+6*I/b^2*d*c^2*arctan(exp(I*(b*x+a)))+3*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+3*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-6/b^3*d^2*c*ln(1-I*exp(I*(b*x+a)))*a+6/b^3*d^2*c*ln(1+I*exp(I*(b*x+a)))*a-6/b^2*d^2*c*ln(1-I*exp(I*(b*x+a)))*x+3/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))-1)-3*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))-3*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2-3/b*c^2*d*ln(exp(I*(b*x+a))+1)*x+3/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+3/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-3/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+3/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2-3/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2-3/b^2*c^2*d*a*ln(exp(I*(b*x+a))-1)+1/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+1/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3-1/b*d^3*ln(exp(I*(b*x+a))+1)*x^3+3/b^2*d^3*ln(1+I*exp(I*(b*x+a)))*x^2-3/b^4*d^3*a^2*ln(1+I*exp(I*(b*x+a)))-3/b^2*d^3*ln(1-I*exp(I*(b*x+a)))*x^2+3/b^4*d^3*a^2*ln(1-I*exp(I*(b*x+a)))","B"
268,1,568,196,0.266000," ","int((d*x+c)^2*csc(b*x+a)*sec(b*x+a)^2,x)","\frac{d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}-\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{2 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{2 i d^{2} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i d^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{2 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{2 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{4 i d c \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 i d^{2} a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 \,{\mathrm e}^{i \left(b x +a \right)} \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}"," ",0,"1/b^3*d^2*a^2*ln(exp(I*(b*x+a))-1)+1/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-1/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2-1/b*d^2*ln(exp(I*(b*x+a))+1)*x^2-2*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+2*d^2*polylog(3,exp(I*(b*x+a)))/b^3-2/b^3*d^2*ln(1-I*exp(I*(b*x+a)))*a+2*I/b^3*d^2*dilog(1-I*exp(I*(b*x+a)))-2*I/b^3*d^2*dilog(1+I*exp(I*(b*x+a)))+2/b^2*d^2*ln(1+I*exp(I*(b*x+a)))*x+2/b^3*d^2*ln(1+I*exp(I*(b*x+a)))*a-2/b^2*d^2*ln(1-I*exp(I*(b*x+a)))*x+1/b*c^2*ln(exp(I*(b*x+a))-1)-1/b*c^2*ln(exp(I*(b*x+a))+1)+2/b*c*d*ln(1-exp(I*(b*x+a)))*x+2/b^2*c*d*ln(1-exp(I*(b*x+a)))*a-2/b*c*d*ln(exp(I*(b*x+a))+1)*x-2/b^2*c*d*a*ln(exp(I*(b*x+a))-1)-2*I/b^2*d^2*polylog(2,exp(I*(b*x+a)))*x-2*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))+4*I*d/b^2*c*arctan(exp(I*(b*x+a)))-4*I*d^2/b^3*a*arctan(exp(I*(b*x+a)))+2*exp(I*(b*x+a))*(d^2*x^2+2*c*d*x+c^2)/b/(1+exp(2*I*(b*x+a)))+2*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x+2*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))","B"
269,1,160,105,0.106000," ","int((d*x+c)*csc(b*x+a)*sec(b*x+a)^2,x)","\frac{2 \,{\mathrm e}^{i \left(b x +a \right)} \left(d x +c \right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}+\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{2 i d \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{i d \dilog \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{i d \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}"," ",0,"2*exp(I*(b*x+a))*(d*x+c)/b/(1+exp(2*I*(b*x+a)))+1/b*c*ln(exp(I*(b*x+a))-1)-1/b*c*ln(exp(I*(b*x+a))+1)+2*I/b^2*d*arctan(exp(I*(b*x+a)))+I/b^2*d*dilog(exp(I*(b*x+a)))+I/b^2*d*dilog(exp(I*(b*x+a))+1)-1/b*d*ln(exp(I*(b*x+a))+1)*x-1/b^2*d*a*ln(exp(I*(b*x+a))-1)","A"
270,0,0,24,2.332000," ","int(csc(b*x+a)*sec(b*x+a)^2/(d*x+c),x)","\int \frac{\csc \left(b x +a \right) \left(\sec^{2}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)*sec(b*x+a)^2/(d*x+c),x)","F"
271,0,0,24,2.560000," ","int(csc(b*x+a)*sec(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\csc \left(b x +a \right) \left(\sec^{2}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)*sec(b*x+a)^2/(d*x+c)^2,x)","F"
272,0,0,26,0.076000," ","int((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \left(\csc^{2}\left(b x +a \right)\right) \left(\sec^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a)^2,x)","F"
273,1,687,106,0.133000," ","int((d*x+c)^3*csc(b*x+a)^2*sec(b*x+a)^2,x)","-\frac{24 i d^{2} c a x}{b^{2}}+\frac{3 d \,c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{12 d \,c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{12 d^{3} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{8 i d^{3} a^{3}}{b^{4}}-\frac{4 i d^{3} x^{3}}{b}+\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}+\frac{3 d^{3} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}-\frac{6 c \,d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{4}}-\frac{4 i \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}-\frac{6 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 i d^{2} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{2} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{2} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 d^{2} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}+\frac{24 d^{2} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i d^{2} c \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{2} c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i d^{2} c \,a^{2}}{b^{3}}-\frac{12 i d^{2} c \,x^{2}}{b}+\frac{12 i d^{3} a^{2} x}{b^{3}}"," ",0,"3/2*d^3*polylog(3,-exp(2*I*(b*x+a)))/b^4+6*d^3*polylog(3,-exp(I*(b*x+a)))/b^4+6*d^3*polylog(3,exp(I*(b*x+a)))/b^4+3*d/b^2*c^2*ln(1+exp(2*I*(b*x+a)))-12*d/b^2*c^2*ln(exp(I*(b*x+a)))-12*d^3/b^4*a^2*ln(exp(I*(b*x+a)))+3*d^3/b^2*ln(1+exp(2*I*(b*x+a)))*x^2+3/b^2*c^2*d*ln(exp(I*(b*x+a))-1)+3/b^2*c^2*d*ln(exp(I*(b*x+a))+1)+3/b^4*d^3*a^2*ln(exp(I*(b*x+a))-1)+3/b^2*d^3*ln(exp(I*(b*x+a))+1)*x^2+3/b^2*d^3*ln(1-exp(I*(b*x+a)))*x^2-3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^2-6/b^3*c*d^2*a*ln(exp(I*(b*x+a))-1)+8*I*d^3/b^4*a^3-4*I*d^3/b*x^3-6*I*d^2/b^3*c*polylog(2,-exp(I*(b*x+a)))+12*I*d^3/b^3*a^2*x-12*I*d^2/b*c*x^2-12*I*d^2/b^3*c*a^2-6*I*d^3/b^3*polylog(2,-exp(I*(b*x+a)))*x-6*I/b^3*d^3*polylog(2,exp(I*(b*x+a)))*x+6/b^2*d^2*c*ln(exp(I*(b*x+a))+1)*x-6*I/b^3*d^2*c*polylog(2,exp(I*(b*x+a)))-24*I*d^2/b^2*c*a*x-4*I*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/b/(1+exp(2*I*(b*x+a)))/(exp(2*I*(b*x+a))-1)+6/b^2*d^2*c*ln(1-exp(I*(b*x+a)))*x+6/b^3*d^2*c*ln(1-exp(I*(b*x+a)))*a+24*d^2/b^3*c*a*ln(exp(I*(b*x+a)))+6*d^2/b^2*c*ln(1+exp(2*I*(b*x+a)))*x-3*I*d^3/b^3*polylog(2,-exp(2*I*(b*x+a)))*x-3*I*d^2/b^3*c*polylog(2,-exp(2*I*(b*x+a)))","B"
274,1,351,80,0.119000," ","int((d*x+c)^2*csc(b*x+a)^2*sec(b*x+a)^2,x)","-\frac{4 i \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}+\frac{2 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{2 d c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{8 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 i d^{2} a^{2}}{b^{3}}+\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}-\frac{4 i d^{2} x^{2}}{b}-\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{8 i d^{2} a x}{b^{2}}-\frac{2 d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{8 d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"-2*I/b^3*d^2*polylog(2,-exp(I*(b*x+a)))+2/b^2*d*c*ln(exp(I*(b*x+a))-1)+2*d/b^2*c*ln(1+exp(2*I*(b*x+a)))+2/b^2*d*c*ln(exp(I*(b*x+a))+1)-8/b^2*d*c*ln(exp(I*(b*x+a)))-2*I*d^2*polylog(2,exp(I*(b*x+a)))/b^3+2/b^2*d^2*ln(exp(I*(b*x+a))+1)*x-4*I*(d^2*x^2+2*c*d*x+c^2)/b/(1+exp(2*I*(b*x+a)))/(exp(2*I*(b*x+a))-1)-4*I*d^2/b^3*a^2+2*d^2/b^2*ln(1+exp(2*I*(b*x+a)))*x+2/b^2*d^2*ln(1-exp(I*(b*x+a)))*x+2/b^3*d^2*ln(1-exp(I*(b*x+a)))*a-I*d^2*polylog(2,-exp(2*I*(b*x+a)))/b^3-4*I*d^2/b*x^2-8*I*d^2/b^2*a*x-2/b^3*d^2*a*ln(exp(I*(b*x+a))-1)+8/b^3*d^2*a*ln(exp(I*(b*x+a)))","B"
275,1,182,35,0.088000," ","int((d*x+c)*csc(b*x+a)^2*sec(b*x+a)^2,x)","\frac{\frac{c}{2 b}+\frac{d x}{2 b}-\frac{3 c \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{b}+\frac{c \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2 b}-\frac{3 d x \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{b}+\frac{d x \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2 b}}{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}+\frac{d \ln \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{2}}+\frac{d \ln \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}{b^{2}}+\frac{d \ln \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}{b^{2}}-\frac{2 d \ln \left(1+\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{2}}"," ",0,"(1/2*c/b+1/2*d*x/b-3*c/b*tan(1/2*b*x+1/2*a)^2+1/2*c/b*tan(1/2*b*x+1/2*a)^4-3/b*d*x*tan(1/2*b*x+1/2*a)^2+1/2/b*d*x*tan(1/2*b*x+1/2*a)^4)/tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1)+d/b^2*ln(tan(1/2*b*x+1/2*a))+d/b^2*ln(tan(1/2*b*x+1/2*a)-1)+d/b^2*ln(tan(1/2*b*x+1/2*a)+1)-2*d/b^2*ln(1+tan(1/2*b*x+1/2*a)^2)","B"
276,0,0,23,0.431000," ","int(csc(b*x+a)^2*sec(b*x+a)^2/(d*x+c),x)","\int \frac{\left(\csc^{2}\left(b x +a \right)\right) \left(\sec^{2}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)^2*sec(b*x+a)^2/(d*x+c),x)","F"
277,0,0,23,0.776000," ","int(csc(b*x+a)^2*sec(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\left(\csc^{2}\left(b x +a \right)\right) \left(\sec^{2}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)^2*sec(b*x+a)^2/(d*x+c)^2,x)","F"
278,0,0,26,0.136000," ","int((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \left(\csc^{3}\left(b x +a \right)\right) \left(\sec^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a)^2,x)","F"
279,1,1613,535,0.540000," ","int((d*x+c)^3*csc(b*x+a)^3*sec(b*x+a)^2,x)","-\frac{9 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{9 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i d^{2} c a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{2} c \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i d^{2} c \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i a \,d^{3} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i a \,d^{3} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 i d^{3} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{6 i d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{3 d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{2 b^{4}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{2 b}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{2 b^{4}}-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{2 b}+\frac{9 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{9 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{9 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{9 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{9 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{9 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{2 b}-\frac{3 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{2 b}+\frac{3 d^{3} x^{3} b \,{\mathrm e}^{5 i \left(b x +a \right)}+9 c \,d^{2} x^{2} b \,{\mathrm e}^{5 i \left(b x +a \right)}+9 c^{2} d x b \,{\mathrm e}^{5 i \left(b x +a \right)}-2 d^{3} x^{3} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 c^{3} b \,{\mathrm e}^{5 i \left(b x +a \right)}-6 c \,d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{5 i \left(b x +a \right)}-6 c^{2} d x b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 d^{3} x^{3} b \,{\mathrm e}^{i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{5 i \left(b x +a \right)}-2 c^{3} b \,{\mathrm e}^{3 i \left(b x +a \right)}+9 c \,d^{2} x^{2} b \,{\mathrm e}^{i \left(b x +a \right)}+6 i c \,d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}+9 c^{2} d x b \,{\mathrm e}^{i \left(b x +a \right)}+3 c^{3} b \,{\mathrm e}^{i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{5 i \left(b x +a \right)}+3 i c^{2} d \,{\mathrm e}^{i \left(b x +a \right)}+3 i d^{3} x^{2} {\mathrm e}^{i \left(b x +a \right)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}+\frac{3 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{3 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{3 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{9 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}+\frac{9 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{2 b^{3}}-\frac{9 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{9 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{9 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}-\frac{9 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{2 b}+\frac{9 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}+\frac{9 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}-\frac{9 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{9 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}-\frac{9 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{2 b}-\frac{9 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{2 b^{2}}-\frac{6 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{6 i d \,c^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{6 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{6 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i d^{3} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i d^{3} x \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i d^{3} x \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 d^{3} a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 d^{3} a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"6*d^3*polylog(3,-I*exp(I*(b*x+a)))/b^4-6*d^3*polylog(3,I*exp(I*(b*x+a)))/b^4-12*I/b^3*d^2*c*a*arctan(exp(I*(b*x+a)))+3*I*d^3*polylog(2,-exp(I*(b*x+a)))/b^4+6*I*d^3*x*polylog(2,I*exp(I*(b*x+a)))/b^3+9*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4-6*I*d^3*x*polylog(2,-I*exp(I*(b*x+a)))/b^3-3/2/b^4*d^3*a^3*ln(exp(I*(b*x+a))-1)-9/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+9/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))+9/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x-9/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x-3*I*d^3*polylog(2,exp(I*(b*x+a)))/b^4-9*I*d^3*polylog(4,-exp(I*(b*x+a)))/b^4+1/b^2/(exp(2*I*(b*x+a))-1)^2/(1+exp(2*I*(b*x+a)))*(3*d^3*x^3*b*exp(5*I*(b*x+a))+9*c*d^2*x^2*b*exp(5*I*(b*x+a))+9*c^2*d*x*b*exp(5*I*(b*x+a))-2*d^3*x^3*b*exp(3*I*(b*x+a))+3*c^3*b*exp(5*I*(b*x+a))-6*c*d^2*x^2*b*exp(3*I*(b*x+a))-3*I*c^2*d*exp(5*I*(b*x+a))-6*c^2*d*x*b*exp(3*I*(b*x+a))+3*d^3*x^3*b*exp(I*(b*x+a))-3*I*d^3*x^2*exp(5*I*(b*x+a))-2*c^3*b*exp(3*I*(b*x+a))+9*c*d^2*x^2*b*exp(I*(b*x+a))+6*I*c*d^2*x*exp(I*(b*x+a))+9*c^2*d*x*b*exp(I*(b*x+a))+3*c^3*b*exp(I*(b*x+a))-6*I*c*d^2*x*exp(5*I*(b*x+a))+3*I*c^2*d*exp(I*(b*x+a))+3*I*d^3*x^2*exp(I*(b*x+a)))-6*I/b^3*d^2*c*dilog(1+I*exp(I*(b*x+a)))+6*I/b^3*d^2*c*dilog(1-I*exp(I*(b*x+a)))+6*I/b^4*a*d^3*dilog(1+I*exp(I*(b*x+a)))-6*I/b^4*a*d^3*dilog(1-I*exp(I*(b*x+a)))+6*I/b^4*d^3*polylog(2,I*exp(I*(b*x+a)))*a-6*I/b^4*d^3*polylog(2,-I*exp(I*(b*x+a)))*a+3/2/b*c^3*ln(exp(I*(b*x+a))-1)-3/2/b*c^3*ln(exp(I*(b*x+a))+1)+3/b^3*d^2*c*ln(exp(I*(b*x+a))-1)-3/b^3*d^2*c*ln(exp(I*(b*x+a))+1)-3/b^3*d^3*ln(exp(I*(b*x+a))+1)*x+3/b^3*d^3*ln(1-exp(I*(b*x+a)))*x+3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a-3/b^4*d^3*a*ln(exp(I*(b*x+a))-1)+9/2*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-9/2*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))+9/2*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2-9/2*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2+6/b^2*d^2*c*ln(1+I*exp(I*(b*x+a)))*x+6*I/b^4*d^3*a^2*arctan(exp(I*(b*x+a)))+6*I/b^2*d*c^2*arctan(exp(I*(b*x+a)))-6/b^3*d^2*c*ln(1-I*exp(I*(b*x+a)))*a+6/b^3*d^2*c*ln(1+I*exp(I*(b*x+a)))*a-6/b^2*d^2*c*ln(1-I*exp(I*(b*x+a)))*x+9/2/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))-1)-9/2/b*c^2*d*ln(exp(I*(b*x+a))+1)*x+9/2/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+9/2/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-9/2/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+9/2/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2-9/2/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2-9/2/b^2*c^2*d*a*ln(exp(I*(b*x+a))-1)+3/2/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+3/2/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3-3/2/b*d^3*ln(exp(I*(b*x+a))+1)*x^3+3/b^2*d^3*ln(1+I*exp(I*(b*x+a)))*x^2-3/b^4*d^3*a^2*ln(1+I*exp(I*(b*x+a)))-3/b^2*d^3*ln(1-I*exp(I*(b*x+a)))*x^2+3/b^4*d^3*a^2*ln(1-I*exp(I*(b*x+a)))-9*I/b^2*c*d^2*polylog(2,exp(I*(b*x+a)))*x+9*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x","B"
280,1,802,278,0.307000," ","int((d*x+c)^2*csc(b*x+a)^3*sec(b*x+a)^2,x)","\frac{3 d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{2 b^{3}}+\frac{3 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}-\frac{3 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{2 b^{3}}-\frac{3 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{2 b}+\frac{2 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{2 i d^{2} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i d^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{2 b}-\frac{3 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{2 b}-\frac{3 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 d^{2} x^{2} b \,{\mathrm e}^{5 i \left(b x +a \right)}+6 c d x b \,{\mathrm e}^{5 i \left(b x +a \right)}+3 c^{2} b \,{\mathrm e}^{5 i \left(b x +a \right)}-2 d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}-4 c d x b \,{\mathrm e}^{3 i \left(b x +a \right)}-2 i d^{2} x \,{\mathrm e}^{5 i \left(b x +a \right)}-2 c^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 d^{2} x^{2} b \,{\mathrm e}^{i \left(b x +a \right)}-2 i c d \,{\mathrm e}^{5 i \left(b x +a \right)}+6 c d x b \,{\mathrm e}^{i \left(b x +a \right)}+3 c^{2} b \,{\mathrm e}^{i \left(b x +a \right)}+2 i d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}+2 i d c \,{\mathrm e}^{i \left(b x +a \right)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}-\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{3 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{3 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{3 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{3 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{4 i d c \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 i d^{2} a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"3/2/b^3*d^2*a^2*ln(exp(I*(b*x+a))-1)+3/2/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-3/2/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2-3/2/b*d^2*ln(exp(I*(b*x+a))+1)*x^2-3*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+3*d^2*polylog(3,exp(I*(b*x+a)))/b^3-2/b^3*d^2*ln(1-I*exp(I*(b*x+a)))*a+2*I/b^3*d^2*dilog(1-I*exp(I*(b*x+a)))-2*I/b^3*d^2*dilog(1+I*exp(I*(b*x+a)))+2/b^2*d^2*ln(1+I*exp(I*(b*x+a)))*x+2/b^3*d^2*ln(1+I*exp(I*(b*x+a)))*a-2/b^2*d^2*ln(1-I*exp(I*(b*x+a)))*x+3/2/b*c^2*ln(exp(I*(b*x+a))-1)-3/2/b*c^2*ln(exp(I*(b*x+a))+1)-3*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))+3*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))+3/b*c*d*ln(1-exp(I*(b*x+a)))*x+3/b^2*c*d*ln(1-exp(I*(b*x+a)))*a-3/b*c*d*ln(exp(I*(b*x+a))+1)*x-3/b^2*c*d*a*ln(exp(I*(b*x+a))-1)-1/b^3*d^2*ln(exp(I*(b*x+a))+1)+1/b^3*d^2*ln(exp(I*(b*x+a))-1)+4*I*d/b^2*c*arctan(exp(I*(b*x+a)))-4*I*d^2/b^3*a*arctan(exp(I*(b*x+a)))+3*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-3*I/b^2*polylog(2,exp(I*(b*x+a)))*d^2*x+1/b^2/(exp(2*I*(b*x+a))-1)^2/(1+exp(2*I*(b*x+a)))*(3*d^2*x^2*b*exp(5*I*(b*x+a))+6*c*d*x*b*exp(5*I*(b*x+a))+3*c^2*b*exp(5*I*(b*x+a))-2*d^2*x^2*b*exp(3*I*(b*x+a))-4*c*d*x*b*exp(3*I*(b*x+a))-2*I*d^2*x*exp(5*I*(b*x+a))-2*c^2*b*exp(3*I*(b*x+a))+3*d^2*x^2*b*exp(I*(b*x+a))-2*I*c*d*exp(5*I*(b*x+a))+6*c*d*x*b*exp(I*(b*x+a))+3*c^2*b*exp(I*(b*x+a))+2*I*d^2*x*exp(I*(b*x+a))+2*I*d*c*exp(I*(b*x+a)))","B"
281,1,267,134,0.158000," ","int((d*x+c)*csc(b*x+a)^3*sec(b*x+a)^2,x)","\frac{3 b d x \,{\mathrm e}^{5 i \left(b x +a \right)}+3 c b \,{\mathrm e}^{5 i \left(b x +a \right)}-2 b d x \,{\mathrm e}^{3 i \left(b x +a \right)}-2 c b \,{\mathrm e}^{3 i \left(b x +a \right)}-i d \,{\mathrm e}^{5 i \left(b x +a \right)}+3 b d x \,{\mathrm e}^{i \left(b x +a \right)}+3 c b \,{\mathrm e}^{i \left(b x +a \right)}+i d \,{\mathrm e}^{i \left(b x +a \right)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}+\frac{3 c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{2 b}-\frac{3 c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{2 b}-\frac{3 d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{2 b^{2}}+\frac{2 i d \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 i d \dilog \left({\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{3 i d \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{2 b^{2}}-\frac{3 d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{2 b}"," ",0,"1/b^2/(exp(2*I*(b*x+a))-1)^2/(1+exp(2*I*(b*x+a)))*(3*b*d*x*exp(5*I*(b*x+a))+3*c*b*exp(5*I*(b*x+a))-2*b*d*x*exp(3*I*(b*x+a))-2*c*b*exp(3*I*(b*x+a))-I*d*exp(5*I*(b*x+a))+3*b*d*x*exp(I*(b*x+a))+3*c*b*exp(I*(b*x+a))+I*d*exp(I*(b*x+a)))+3/2/b*c*ln(exp(I*(b*x+a))-1)-3/2/b*c*ln(exp(I*(b*x+a))+1)-3/2/b^2*d*a*ln(exp(I*(b*x+a))-1)+2*I/b^2*d*arctan(exp(I*(b*x+a)))+3/2*I/b^2*d*dilog(exp(I*(b*x+a)))+3/2*I/b^2*d*dilog(exp(I*(b*x+a))+1)-3/2/b*d*ln(exp(I*(b*x+a))+1)*x","A"
282,0,0,26,2.670000," ","int(csc(b*x+a)^3*sec(b*x+a)^2/(d*x+c),x)","\int \frac{\left(\csc^{3}\left(b x +a \right)\right) \left(\sec^{2}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)^3*sec(b*x+a)^2/(d*x+c),x)","F"
283,0,0,26,5.195000," ","int(csc(b*x+a)^3*sec(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\left(\csc^{3}\left(b x +a \right)\right) \left(\sec^{2}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)^3*sec(b*x+a)^2/(d*x+c)^2,x)","F"
284,0,0,22,0.113000," ","int(x^m*csc(b*x+a)^3*sec(b*x+a)^2,x)","\int x^{m} \left(\csc^{3}\left(b x +a \right)\right) \left(\sec^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^m*csc(b*x+a)^3*sec(b*x+a)^2,x)","F"
285,0,0,334,1.624000," ","int(x^3*csc(b*x+a)^3*sec(b*x+a)^2,x)","\int x^{3} \left(\csc^{3}\left(b x +a \right)\right) \left(\sec^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^3*csc(b*x+a)^3*sec(b*x+a)^2,x)","F"
286,1,429,208,0.224000," ","int(x^2*csc(b*x+a)^3*sec(b*x+a)^2,x)","\frac{x \left(3 b x \,{\mathrm e}^{5 i \left(b x +a \right)}-2 b x \,{\mathrm e}^{3 i \left(b x +a \right)}-2 i {\mathrm e}^{5 i \left(b x +a \right)}+3 b x \,{\mathrm e}^{i \left(b x +a \right)}+2 i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}-\frac{3 a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{3 i x \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 i x \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{2 b}-\frac{2 i \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}-\frac{2 \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}+\frac{3 a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{2 b^{3}}+\frac{2 i \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{4 i a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"x/b^2/(exp(2*I*(b*x+a))-1)^2/(1+exp(2*I*(b*x+a)))*(3*b*x*exp(5*I*(b*x+a))-2*b*x*exp(3*I*(b*x+a))-2*I*exp(5*I*(b*x+a))+3*b*x*exp(I*(b*x+a))+2*I*exp(I*(b*x+a)))-3/2/b^3*a^2*ln(1-exp(I*(b*x+a)))-2*I/b^3*dilog(1+I*exp(I*(b*x+a)))+3*polylog(3,exp(I*(b*x+a)))/b^3-3*polylog(3,-exp(I*(b*x+a)))/b^3+2/b^2*ln(1+I*exp(I*(b*x+a)))*x+3*I*x*polylog(2,-exp(I*(b*x+a)))/b^2-3/2/b*ln(exp(I*(b*x+a))+1)*x^2-3*I*x*polylog(2,exp(I*(b*x+a)))/b^2+3/2/b*ln(1-exp(I*(b*x+a)))*x^2-2/b^2*ln(1-I*exp(I*(b*x+a)))*x+2/b^3*ln(1+I*exp(I*(b*x+a)))*a-2/b^3*ln(1-I*exp(I*(b*x+a)))*a+1/b^3*ln(exp(I*(b*x+a))-1)-1/b^3*ln(exp(I*(b*x+a))+1)+3/2/b^3*a^2*ln(exp(I*(b*x+a))-1)-4*I/b^3*a*arctan(exp(I*(b*x+a)))+2*I/b^3*dilog(1-I*exp(I*(b*x+a)))","B"
287,1,182,108,0.141000," ","int(x*csc(b*x+a)^3*sec(b*x+a)^2,x)","\frac{3 b x \,{\mathrm e}^{5 i \left(b x +a \right)}-2 b x \,{\mathrm e}^{3 i \left(b x +a \right)}-i {\mathrm e}^{5 i \left(b x +a \right)}+3 b x \,{\mathrm e}^{i \left(b x +a \right)}+i {\mathrm e}^{i \left(b x +a \right)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}-\frac{3 a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{2 b^{2}}+\frac{2 i \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 i \dilog \left({\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{3 i \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{2 b^{2}}-\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{2 b}"," ",0,"1/b^2/(exp(2*I*(b*x+a))-1)^2/(1+exp(2*I*(b*x+a)))*(3*b*x*exp(5*I*(b*x+a))-2*b*x*exp(3*I*(b*x+a))-I*exp(5*I*(b*x+a))+3*b*x*exp(I*(b*x+a))+I*exp(I*(b*x+a)))-3/2/b^2*a*ln(exp(I*(b*x+a))-1)+2*I/b^2*arctan(exp(I*(b*x+a)))+3/2*I/b^2*dilog(exp(I*(b*x+a)))+3/2*I/b^2*dilog(exp(I*(b*x+a))+1)-3/2/b*ln(exp(I*(b*x+a))+1)*x","A"
288,0,0,22,0.779000," ","int(csc(b*x+a)^3*sec(b*x+a)^2/x,x)","\int \frac{\left(\csc^{3}\left(b x +a \right)\right) \left(\sec^{2}\left(b x +a \right)\right)}{x}\, dx"," ",0,"int(csc(b*x+a)^3*sec(b*x+a)^2/x,x)","F"
289,0,0,22,0.882000," ","int(csc(b*x+a)^3*sec(b*x+a)^2/x^2,x)","\int \frac{\left(\csc^{3}\left(b x +a \right)\right) \left(\sec^{2}\left(b x +a \right)\right)}{x^{2}}\, dx"," ",0,"int(csc(b*x+a)^3*sec(b*x+a)^2/x^2,x)","F"
290,0,0,24,0.095000," ","int((d*x+c)^m*sec(b*x+a)^2*tan(b*x+a),x)","\int \left(d x +c \right)^{m} \left(\sec^{2}\left(b x +a \right)\right) \tan \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*sec(b*x+a)^2*tan(b*x+a),x)","F"
291,1,489,129,0.111000," ","int((d*x+c)^4*sec(b*x+a)^2*tan(b*x+a),x)","\frac{2 b \,d^{4} x^{4} {\mathrm e}^{2 i \left(b x +a \right)}+8 b c \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}+12 b \,c^{2} d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+8 b \,c^{3} d x \,{\mathrm e}^{2 i \left(b x +a \right)}-4 i d^{4} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}+2 b \,c^{4} {\mathrm e}^{2 i \left(b x +a \right)}-12 i c \,d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-12 i c^{2} d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}-4 i d^{4} x^{3}-4 i c^{3} d \,{\mathrm e}^{2 i \left(b x +a \right)}-12 i c \,d^{3} x^{2}-12 i c^{2} d^{2} x -4 i c^{3} d}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}-\frac{6 d^{2} c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{4} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{24 i d^{3} c a x}{b^{3}}+\frac{6 i d^{3} c \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{4}}+\frac{12 i d^{3} c \,a^{2}}{b^{4}}-\frac{12 d^{3} c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 d^{4} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{12 i d^{4} a^{2} x}{b^{4}}-\frac{3 d^{4} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 d^{3} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{12 i d^{3} c \,x^{2}}{b^{2}}-\frac{8 i d^{4} a^{3}}{b^{5}}+\frac{6 i d^{4} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{4}}+\frac{4 i d^{4} x^{3}}{b^{2}}"," ",0,"2*(b*d^4*x^4*exp(2*I*(b*x+a))+4*b*c*d^3*x^3*exp(2*I*(b*x+a))+6*b*c^2*d^2*x^2*exp(2*I*(b*x+a))+4*b*c^3*d*x*exp(2*I*(b*x+a))-2*I*d^4*x^3*exp(2*I*(b*x+a))+b*c^4*exp(2*I*(b*x+a))-6*I*c*d^3*x^2*exp(2*I*(b*x+a))-6*I*c^2*d^2*x*exp(2*I*(b*x+a))-2*I*d^4*x^3-2*I*c^3*d*exp(2*I*(b*x+a))-6*I*c*d^3*x^2-6*I*c^2*d^2*x-2*I*c^3*d)/b^2/(1+exp(2*I*(b*x+a)))^2-6/b^3*d^2*c^2*ln(1+exp(2*I*(b*x+a)))+12/b^3*d^2*c^2*ln(exp(I*(b*x+a)))+12/b^5*d^4*a^2*ln(exp(I*(b*x+a)))+24*I/b^3*d^3*c*a*x+6*I/b^4*d^3*c*polylog(2,-exp(2*I*(b*x+a)))+12*I/b^4*d^3*c*a^2-12/b^3*d^3*c*ln(1+exp(2*I*(b*x+a)))*x-6/b^3*d^4*ln(1+exp(2*I*(b*x+a)))*x^2+6*I/b^4*d^4*polylog(2,-exp(2*I*(b*x+a)))*x-3*d^4*polylog(3,-exp(2*I*(b*x+a)))/b^5-24/b^4*d^3*c*a*ln(exp(I*(b*x+a)))-12*I/b^4*d^4*a^2*x+12*I/b^2*d^3*c*x^2-8*I/b^5*d^4*a^3+4*I/b^2*d^4*x^3","B"
292,1,301,101,0.098000," ","int((d*x+c)^3*sec(b*x+a)^2*tan(b*x+a),x)","\frac{2 b \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+6 b c \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+6 b \,c^{2} d x \,{\mathrm e}^{2 i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{2 i \left(b x +a \right)}-3 i d^{3} x^{2}+2 b \,c^{3} {\mathrm e}^{2 i \left(b x +a \right)}-6 i c \,d^{2} x -3 i c^{2} d}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}-\frac{3 d^{2} c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 i d^{3} x^{2}}{b^{2}}+\frac{6 i d^{3} a x}{b^{3}}+\frac{3 i d^{3} a^{2}}{b^{4}}-\frac{3 d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{4}}-\frac{6 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"(2*b*d^3*x^3*exp(2*I*(b*x+a))-3*I*d^3*x^2*exp(2*I*(b*x+a))+6*b*c*d^2*x^2*exp(2*I*(b*x+a))-6*I*c*d^2*x*exp(2*I*(b*x+a))+6*b*c^2*d*x*exp(2*I*(b*x+a))-3*I*c^2*d*exp(2*I*(b*x+a))-3*I*d^3*x^2+2*b*c^3*exp(2*I*(b*x+a))-6*I*c*d^2*x-3*I*c^2*d)/b^2/(1+exp(2*I*(b*x+a)))^2-3/b^3*d^2*c*ln(1+exp(2*I*(b*x+a)))+6/b^3*d^2*c*ln(exp(I*(b*x+a)))+3*I/b^2*d^3*x^2+6*I/b^3*d^3*a*x+3*I/b^4*d^3*a^2-3/b^3*d^3*ln(1+exp(2*I*(b*x+a)))*x+3/2*I*d^3*polylog(2,-exp(2*I*(b*x+a)))/b^4-6/b^4*d^3*a*ln(exp(I*(b*x+a)))","B"
293,1,95,53,0.030000," ","int((d*x+c)^2*sec(b*x+a)^2*tan(b*x+a),x)","\frac{d^{2} x^{2}}{2 b \cos \left(b x +a \right)^{2}}-\frac{d^{2} \tan \left(b x +a \right) x}{b^{2}}-\frac{d^{2} \ln \left(\cos \left(b x +a \right)\right)}{b^{3}}+\frac{c d x}{b \cos \left(b x +a \right)^{2}}-\frac{c d \tan \left(b x +a \right)}{b^{2}}+\frac{c^{2}}{2 b \cos \left(b x +a \right)^{2}}"," ",0,"1/2/b*d^2/cos(b*x+a)^2*x^2-1/b^2*d^2*tan(b*x+a)*x-d^2*ln(cos(b*x+a))/b^3+1/b*c*d/cos(b*x+a)^2*x-1/b^2*c*d*tan(b*x+a)+1/2/b*c^2/cos(b*x+a)^2","A"
294,1,61,31,0.030000," ","int((d*x+c)*sec(b*x+a)^2*tan(b*x+a),x)","\frac{\frac{d \left(\frac{b x +a}{2 \cos \left(b x +a \right)^{2}}-\frac{\tan \left(b x +a \right)}{2}\right)}{b}-\frac{d a}{2 b \cos \left(b x +a \right)^{2}}+\frac{c}{2 \cos \left(b x +a \right)^{2}}}{b}"," ",0,"1/b*(1/b*d*(1/2*(b*x+a)/cos(b*x+a)^2-1/2*tan(b*x+a))-1/2/b*d*a/cos(b*x+a)^2+1/2*c/cos(b*x+a)^2)","A"
295,0,0,24,0.278000," ","int(sec(b*x+a)^2*tan(b*x+a)/(d*x+c),x)","\int \frac{\left(\sec^{2}\left(b x +a \right)\right) \tan \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)^2*tan(b*x+a)/(d*x+c),x)","F"
296,0,0,24,0.292000," ","int(sec(b*x+a)^2*tan(b*x+a)/(d*x+c)^2,x)","\int \frac{\left(\sec^{2}\left(b x +a \right)\right) \tan \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(sec(b*x+a)^2*tan(b*x+a)/(d*x+c)^2,x)","F"
297,0,0,37,0.090000," ","int((d*x+c)^m*sec(b*x+a)*tan(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \sec \left(b x +a \right) \left(\tan^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*sec(b*x+a)*tan(b*x+a)^2,x)","F"
298,1,1127,293,0.208000," ","int((d*x+c)^3*sec(b*x+a)*tan(b*x+a)^2,x)","\frac{3 i d^{2} c \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{3 i d^{2} c \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{3 d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{3 d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}+\frac{3 i d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i d^{3} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{i \left(d^{3} x^{3} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 c \,d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 c^{2} d x b \,{\mathrm e}^{3 i \left(b x +a \right)}-d^{3} x^{3} b \,{\mathrm e}^{i \left(b x +a \right)}+c^{3} b \,{\mathrm e}^{3 i \left(b x +a \right)}-3 c \,d^{2} x^{2} b \,{\mathrm e}^{i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{3 i \left(b x +a \right)}-3 c^{2} d x b \,{\mathrm e}^{i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{3 i \left(b x +a \right)}-c^{3} b \,{\mathrm e}^{i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{3 i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}+\frac{3 i d^{3} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}-\frac{3 i d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}-\frac{3 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}+\frac{3 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}-\frac{3 c^{2} d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}-\frac{3 c^{2} d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}-\frac{3 a^{2} c \,d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{3 c^{2} d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}+\frac{3 c^{2} d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}+\frac{3 a^{2} c \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{i d^{3} a^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i c^{2} d \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{3 i c^{2} d \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{3 i c \,d^{2} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i c^{2} d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{6 i d^{3} a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i c \,d^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{a^{3} d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{4}}-\frac{d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{2 b}+\frac{d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{2 b}-\frac{a^{3} d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{4}}+\frac{i c^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{3 i d^{3} \polylog \left(4, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 i d^{3} \polylog \left(4, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{3 d^{2} c \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 d^{2} c \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"3*I*d^3*polylog(2,-I*exp(I*(b*x+a)))/b^4+3*I*d^3*polylog(4,-I*exp(I*(b*x+a)))/b^4-3*I*d^3*polylog(2,I*exp(I*(b*x+a)))/b^4-3*I*d^3*polylog(4,I*exp(I*(b*x+a)))/b^4-3/2*I/b^2*d^3*polylog(2,-I*exp(I*(b*x+a)))*x^2+3/2*I/b^2*d^3*polylog(2,I*exp(I*(b*x+a)))*x^2-I/b^4*d^3*a^3*arctan(exp(I*(b*x+a)))+6*I/b^4*d^3*a*arctan(exp(I*(b*x+a)))-3/2*I/b^2*c^2*d*polylog(2,-I*exp(I*(b*x+a)))-6*I/b^3*c*d^2*arctan(exp(I*(b*x+a)))+3/2*I/b^2*c^2*d*polylog(2,I*exp(I*(b*x+a)))+1/2/b^4*a^3*d^3*ln(1+I*exp(I*(b*x+a)))-3/b^3*d^3*polylog(3,I*exp(I*(b*x+a)))*x-1/2/b*d^3*ln(1-I*exp(I*(b*x+a)))*x^3+1/2/b*d^3*ln(1+I*exp(I*(b*x+a)))*x^3+3/b^3*d^3*polylog(3,-I*exp(I*(b*x+a)))*x-3/b^3*d^2*c*polylog(3,I*exp(I*(b*x+a)))+3/b^3*d^2*c*polylog(3,-I*exp(I*(b*x+a)))-1/2/b^4*a^3*d^3*ln(1-I*exp(I*(b*x+a)))-3/2/b*d^2*c*ln(1-I*exp(I*(b*x+a)))*x^2+3/2/b*d^2*c*ln(1+I*exp(I*(b*x+a)))*x^2-3/2/b*c^2*d*ln(1-I*exp(I*(b*x+a)))*x-3/2/b^2*c^2*d*ln(1-I*exp(I*(b*x+a)))*a-3/2/b^3*a^2*c*d^2*ln(1+I*exp(I*(b*x+a)))+3/2/b*c^2*d*ln(1+I*exp(I*(b*x+a)))*x+3/2/b^2*c^2*d*ln(1+I*exp(I*(b*x+a)))*a+3/2/b^3*a^2*c*d^2*ln(1-I*exp(I*(b*x+a)))+I/b*c^3*arctan(exp(I*(b*x+a)))+3/b^3*d^3*ln(1-I*exp(I*(b*x+a)))*x+3/b^4*d^3*ln(1-I*exp(I*(b*x+a)))*a-3/b^3*d^3*ln(1+I*exp(I*(b*x+a)))*x-3/b^4*d^3*ln(1+I*exp(I*(b*x+a)))*a-3*I/b^2*c*d^2*polylog(2,-I*exp(I*(b*x+a)))*x+3*I/b^2*c*d^2*polylog(2,I*exp(I*(b*x+a)))*x+3*I/b^3*c*d^2*a^2*arctan(exp(I*(b*x+a)))-I/b^2/(1+exp(2*I*(b*x+a)))^2*(d^3*x^3*b*exp(3*I*(b*x+a))+3*c*d^2*x^2*b*exp(3*I*(b*x+a))+3*c^2*d*x*b*exp(3*I*(b*x+a))-d^3*x^3*b*exp(I*(b*x+a))+c^3*b*exp(3*I*(b*x+a))-3*c*d^2*x^2*b*exp(I*(b*x+a))-3*I*d^3*x^2*exp(3*I*(b*x+a))-3*c^2*d*x*b*exp(I*(b*x+a))-6*I*c*d^2*x*exp(3*I*(b*x+a))-c^3*b*exp(I*(b*x+a))-3*I*c^2*d*exp(3*I*(b*x+a))-3*I*d^3*x^2*exp(I*(b*x+a))-6*I*c*d^2*x*exp(I*(b*x+a))-3*I*c^2*d*exp(I*(b*x+a)))-3*I/b^2*c^2*d*a*arctan(exp(I*(b*x+a)))","B"
299,1,584,174,0.174000," ","int((d*x+c)^2*sec(b*x+a)*tan(b*x+a)^2,x)","-\frac{i c d \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{c d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{d^{2} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{c d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}-\frac{a^{2} d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}-\frac{i \left(d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+2 c d x b \,{\mathrm e}^{3 i \left(b x +a \right)}+c^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}-d^{2} x^{2} b \,{\mathrm e}^{i \left(b x +a \right)}-2 c d x b \,{\mathrm e}^{i \left(b x +a \right)}-2 i d^{2} x \,{\mathrm e}^{3 i \left(b x +a \right)}-c^{2} b \,{\mathrm e}^{i \left(b x +a \right)}-2 i d c \,{\mathrm e}^{3 i \left(b x +a \right)}-2 i d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}-2 i d c \,{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}-\frac{2 i d^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{i d^{2} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i c d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{i d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{i d^{2} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{c d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{d^{2} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{i c d \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{i c^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{a^{2} d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{c d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}"," ",0,"-I/b^2/(1+exp(2*I*(b*x+a)))^2*(d^2*x^2*b*exp(3*I*(b*x+a))+2*c*d*x*b*exp(3*I*(b*x+a))+c^2*b*exp(3*I*(b*x+a))-d^2*x^2*b*exp(I*(b*x+a))-2*c*d*x*b*exp(I*(b*x+a))-2*I*d^2*x*exp(3*I*(b*x+a))-c^2*b*exp(I*(b*x+a))-2*I*d*c*exp(3*I*(b*x+a))-2*I*d^2*x*exp(I*(b*x+a))-2*I*c*d*exp(I*(b*x+a)))-1/b^2*c*d*ln(1-I*exp(I*(b*x+a)))*a+d^2*polylog(3,-I*exp(I*(b*x+a)))/b^3+1/b^2*c*d*ln(1+I*exp(I*(b*x+a)))*a+1/2/b*d^2*ln(1+I*exp(I*(b*x+a)))*x^2-1/2/b^3*a^2*d^2*ln(1+I*exp(I*(b*x+a)))-1/2/b*d^2*ln(1-I*exp(I*(b*x+a)))*x^2-2*I/b^3*d^2*arctan(exp(I*(b*x+a)))+I/b^2*d^2*polylog(2,I*exp(I*(b*x+a)))*x+I/b^2*c*d*polylog(2,I*exp(I*(b*x+a)))-2*I/b^2*a*c*d*arctan(exp(I*(b*x+a)))-I/b^2*c*d*polylog(2,-I*exp(I*(b*x+a)))+I/b^3*a^2*d^2*arctan(exp(I*(b*x+a)))+1/b*c*d*ln(1+I*exp(I*(b*x+a)))*x-d^2*polylog(3,I*exp(I*(b*x+a)))/b^3-I/b^2*d^2*polylog(2,-I*exp(I*(b*x+a)))*x+I/b*c^2*arctan(exp(I*(b*x+a)))+1/2/b^3*a^2*d^2*ln(1-I*exp(I*(b*x+a)))-1/b*c*d*ln(1-I*exp(I*(b*x+a)))*x","B"
300,1,267,98,0.116000," ","int((d*x+c)*sec(b*x+a)*tan(b*x+a)^2,x)","-\frac{i \left(b d x \,{\mathrm e}^{3 i \left(b x +a \right)}-i d \,{\mathrm e}^{3 i \left(b x +a \right)}+c b \,{\mathrm e}^{3 i \left(b x +a \right)}-b d x \,{\mathrm e}^{i \left(b x +a \right)}-i d \,{\mathrm e}^{i \left(b x +a \right)}-c b \,{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}+\frac{i c \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}+\frac{d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}-\frac{d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}-\frac{d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}-\frac{i d \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{i d \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{i d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"-I/b^2/(1+exp(2*I*(b*x+a)))^2*(b*d*x*exp(3*I*(b*x+a))-I*d*exp(3*I*(b*x+a))+c*b*exp(3*I*(b*x+a))-b*d*x*exp(I*(b*x+a))-I*d*exp(I*(b*x+a))-c*b*exp(I*(b*x+a)))+I/b*c*arctan(exp(I*(b*x+a)))+1/2/b*d*ln(1+I*exp(I*(b*x+a)))*x+1/2/b^2*d*ln(1+I*exp(I*(b*x+a)))*a-1/2/b*d*ln(1-I*exp(I*(b*x+a)))*x-1/2/b^2*d*ln(1-I*exp(I*(b*x+a)))*a-1/2*I/b^2*d*dilog(1+I*exp(I*(b*x+a)))+1/2*I/b^2*d*dilog(1-I*exp(I*(b*x+a)))-I/b^2*d*a*arctan(exp(I*(b*x+a)))","B"
301,0,0,37,1.595000," ","int(sec(b*x+a)*tan(b*x+a)^2/(d*x+c),x)","\int \frac{\sec \left(b x +a \right) \left(\tan^{2}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)*tan(b*x+a)^2/(d*x+c),x)","F"
302,0,0,37,2.605000," ","int(sec(b*x+a)*tan(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\sec \left(b x +a \right) \left(\tan^{2}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(sec(b*x+a)*tan(b*x+a)^2/(d*x+c)^2,x)","F"
303,0,0,18,0.118000," ","int((d*x+c)^m*tan(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \left(\tan^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*tan(b*x+a)^3,x)","F"
304,1,720,224,0.127000," ","int((d*x+c)^3*tan(b*x+a)^3,x)","\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{2 b^{3}}+\frac{d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}+\frac{6 i c \,d^{2} a^{2} x}{b^{2}}-\frac{6 i c^{2} d a x}{b}+\frac{2 d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i a^{4} d^{3}}{2 b^{4}}-i c \,d^{2} x^{3}-\frac{3 i c^{2} d \,x^{2}}{2}+\frac{3 c \,d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{3 i d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{4 b^{4}}+\frac{c^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{3 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+i c^{3} x -\frac{i d^{3} x^{4}}{4}-\frac{2 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{2 b \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+6 b c \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+6 b \,c^{2} d x \,{\mathrm e}^{2 i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{2 i \left(b x +a \right)}-3 i d^{3} x^{2}+2 b \,c^{3} {\mathrm e}^{2 i \left(b x +a \right)}-6 i c \,d^{2} x -3 i c^{2} d}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}-\frac{3 d^{2} c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 i d^{3} x^{2}}{b^{2}}+\frac{3 i d^{3} a^{2}}{b^{4}}-\frac{3 d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{4}}-\frac{6 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i c^{2} d \,a^{2}}{b^{2}}-\frac{2 i a^{3} d^{3} x}{b^{3}}+\frac{4 i c \,d^{2} a^{3}}{b^{3}}+\frac{6 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{6 i d^{3} a x}{b^{3}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}-\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{3 c^{2} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{3 c \,d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}"," ",0,"6*I/b^2*c*d^2*a^2*x-6*I/b*c^2*d*a*x+3/2*I*d^3*polylog(2,-exp(2*I*(b*x+a)))/b^4+3/4*I*d^3*polylog(4,-exp(2*I*(b*x+a)))/b^4+I*c^3*x-3/b^3*d^2*c*ln(1+exp(2*I*(b*x+a)))-3/b^3*d^3*ln(1+exp(2*I*(b*x+a)))*x+1/b*c^3*ln(1+exp(2*I*(b*x+a)))+2/b^4*d^3*a^3*ln(exp(I*(b*x+a)))-3/2*I/b^4*a^4*d^3-I*c*d^2*x^3-3/2*I*c^2*d*x^2+3/2/b^3*c*d^2*polylog(3,-exp(2*I*(b*x+a)))+3/2/b^3*d^3*polylog(3,-exp(2*I*(b*x+a)))*x+(2*b*d^3*x^3*exp(2*I*(b*x+a))-3*I*d^3*x^2*exp(2*I*(b*x+a))+6*b*c*d^2*x^2*exp(2*I*(b*x+a))-6*I*c*d^2*x*exp(2*I*(b*x+a))+6*b*c^2*d*x*exp(2*I*(b*x+a))-3*I*c^2*d*exp(2*I*(b*x+a))-3*I*d^3*x^2+2*b*c^3*exp(2*I*(b*x+a))-6*I*c*d^2*x-3*I*c^2*d)/b^2/(1+exp(2*I*(b*x+a)))^2-1/4*I*d^3*x^4-2/b*c^3*ln(exp(I*(b*x+a)))+3*I/b^2*d^3*x^2+3*I/b^4*d^3*a^2+6/b^3*d^2*c*ln(exp(I*(b*x+a)))-6/b^4*d^3*a*ln(exp(I*(b*x+a)))-3/2*I/b^2*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2-3/2*I/b^2*c^2*d*polylog(2,-exp(2*I*(b*x+a)))-6/b^3*c*d^2*a^2*ln(exp(I*(b*x+a)))-3*I/b^2*c^2*d*a^2-2*I/b^3*a^3*d^3*x+4*I/b^3*c*d^2*a^3+6/b^2*c^2*d*a*ln(exp(I*(b*x+a)))+1/b*d^3*ln(1+exp(2*I*(b*x+a)))*x^3-3*I/b^2*polylog(2,-exp(2*I*(b*x+a)))*c*d^2*x+6*I/b^3*d^3*a*x+3/b*c^2*d*ln(1+exp(2*I*(b*x+a)))*x+3/b*c*d^2*ln(1+exp(2*I*(b*x+a)))*x^2","B"
305,1,400,153,0.098000," ","int((d*x+c)^2*tan(b*x+a)^3,x)","-\frac{i d^{2} x^{3}}{3}-\frac{4 i c d a x}{b}+\frac{4 i d^{2} a^{3}}{3 b^{3}}+\frac{2 b \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-2 i d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+4 b c d x \,{\mathrm e}^{2 i \left(b x +a \right)}-2 i c d \,{\mathrm e}^{2 i \left(b x +a \right)}+2 b \,c^{2} {\mathrm e}^{2 i \left(b x +a \right)}-2 i d^{2} x -2 i c d}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}-\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+i c^{2} x +\frac{2 c d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{2 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{2 i d^{2} a^{2} x}{b^{2}}-\frac{i c d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}+\frac{d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}-i c d \,x^{2}+\frac{4 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i c d \,a^{2}}{b^{2}}"," ",0,"-1/3*I*d^2*x^3-4*I/b*c*d*a*x+4/3*I/b^3*d^2*a^3+2*(b*d^2*x^2*exp(2*I*(b*x+a))-I*d^2*x*exp(2*I*(b*x+a))+2*b*c*d*x*exp(2*I*(b*x+a))-I*c*d*exp(2*I*(b*x+a))+b*c^2*exp(2*I*(b*x+a))-I*d^2*x-I*c*d)/b^2/(1+exp(2*I*(b*x+a)))^2-I/b^2*c*d*polylog(2,-exp(2*I*(b*x+a)))+I*c^2*x+2/b*c*d*ln(1+exp(2*I*(b*x+a)))*x+1/2*d^2*polylog(3,-exp(2*I*(b*x+a)))/b^3-1/b^3*d^2*ln(1+exp(2*I*(b*x+a)))+2/b^3*d^2*ln(exp(I*(b*x+a)))-2/b^3*d^2*a^2*ln(exp(I*(b*x+a)))+1/b*c^2*ln(1+exp(2*I*(b*x+a)))-2/b*c^2*ln(exp(I*(b*x+a)))+2*I/b^2*d^2*a^2*x-I*c*d*x^2+1/b*d^2*ln(1+exp(2*I*(b*x+a)))*x^2-2*I/b^2*c*d*a^2+4/b^2*c*d*a*ln(exp(I*(b*x+a)))-I/b^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x","B"
306,1,183,92,0.076000," ","int((d*x+c)*tan(b*x+a)^3,x)","-\frac{i d \,x^{2}}{2}+i c x +\frac{2 b d x \,{\mathrm e}^{2 i \left(b x +a \right)}+2 b c \,{\mathrm e}^{2 i \left(b x +a \right)}-i d \,{\mathrm e}^{2 i \left(b x +a \right)}-i d}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}+\frac{c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{2 c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{2 i d a x}{b}-\frac{i d \,a^{2}}{b^{2}}+\frac{d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{i d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{2 d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"-1/2*I*d*x^2+I*c*x+(2*b*d*x*exp(2*I*(b*x+a))+2*b*c*exp(2*I*(b*x+a))-I*d*exp(2*I*(b*x+a))-I*d)/b^2/(1+exp(2*I*(b*x+a)))^2+1/b*c*ln(1+exp(2*I*(b*x+a)))-2/b*c*ln(exp(I*(b*x+a)))-2*I/b*d*a*x-I/b^2*d*a^2+1/b*d*ln(1+exp(2*I*(b*x+a)))*x-1/2*I*d*polylog(2,-exp(2*I*(b*x+a)))/b^2+2/b^2*d*a*ln(exp(I*(b*x+a)))","A"
307,0,0,18,1.759000," ","int(tan(b*x+a)^3/(d*x+c),x)","\int \frac{\tan^{3}\left(b x +a \right)}{d x +c}\, dx"," ",0,"int(tan(b*x+a)^3/(d*x+c),x)","F"
308,0,0,18,2.733000," ","int(tan(b*x+a)^3/(d*x+c)^2,x)","\int \frac{\tan^{3}\left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(tan(b*x+a)^3/(d*x+c)^2,x)","F"
309,0,0,24,0.105000," ","int((d*x+c)^m*csc(b*x+a)*sec(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \csc \left(b x +a \right) \left(\sec^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a)*sec(b*x+a)^3,x)","F"
310,1,1729,361,0.247000," ","int((d*x+c)^4*csc(b*x+a)*sec(b*x+a)^3,x)","-\frac{d^{4} a^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{12 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 c^{2} d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{4} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{12 d^{4} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{d^{4} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{4}}{b}+\frac{d^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{4}}{b}-\frac{6 d^{2} c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{2} c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{4} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{6 d^{4} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{8 i d^{4} a^{3}}{b^{5}}+\frac{4 i d^{4} x^{3}}{b^{2}}+\frac{2 b \,d^{4} x^{4} {\mathrm e}^{2 i \left(b x +a \right)}+8 b c \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}+12 b \,c^{2} d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+8 b \,c^{3} d x \,{\mathrm e}^{2 i \left(b x +a \right)}-4 i d^{4} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}+2 b \,c^{4} {\mathrm e}^{2 i \left(b x +a \right)}-12 i c \,d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-12 i c^{2} d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}-4 i d^{4} x^{3}-4 i c^{3} d \,{\mathrm e}^{2 i \left(b x +a \right)}-12 i c \,d^{3} x^{2}-12 i c^{2} d^{2} x -4 i c^{3} d}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}-\frac{3 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 d^{4} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{3}}-\frac{d^{4} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{4}}{b}+\frac{24 i d^{3} c a x}{b^{3}}+\frac{12 i d^{3} c \,x^{2}}{b^{2}}+\frac{6 i d^{4} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{4}}+\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{6 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{6 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{5}}-\frac{3 d^{4} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{5}}-\frac{c^{4} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{3 d^{4} \polylog \left(5, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{5}}-\frac{24 d^{4} \polylog \left(5, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{24 d^{4} \polylog \left(5, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}-\frac{4 c^{3} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{6 c^{2} d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}-\frac{4 c \,d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}-\frac{6 c \,d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}-\frac{3 i d^{4} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{4}}+\frac{2 i d^{4} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b^{2}}-\frac{3 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{4}}+\frac{2 i c^{3} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}+\frac{4 c \,d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{4 c \,d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{24 i d^{4} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{4 i c^{3} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 i c^{3} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{24 c \,d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 c \,d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{24 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{24 i c \,d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{4 i d^{4} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{24 i d^{4} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{4}}-\frac{4 i d^{4} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{4 c^{3} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{4 c^{3} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{6 c^{2} d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{6 c^{2} d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{12 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{12 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c^{2} d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c \,d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{12 i d^{3} c \,a^{2}}{b^{4}}-\frac{12 d^{3} c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}-\frac{12 i d^{4} a^{2} x}{b^{4}}-\frac{24 d^{3} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{4 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{6 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{4 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{6 i d^{3} c \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"3/2*d^4*polylog(5,-exp(2*I*(b*x+a)))/b^5-3*d^4*polylog(3,-exp(2*I*(b*x+a)))/b^5+1/b^5*d^4*a^4*ln(exp(I*(b*x+a))-1)+12/b^3*c^2*d^2*polylog(3,-exp(I*(b*x+a)))+12/b^3*c^2*d^2*polylog(3,exp(I*(b*x+a)))-1/b^5*d^4*a^4*ln(1-exp(I*(b*x+a)))+12/b^3*d^4*polylog(3,exp(I*(b*x+a)))*x^2+12/b^3*d^4*polylog(3,-exp(I*(b*x+a)))*x^2-6/b^3*d^2*c^2*ln(1+exp(2*I*(b*x+a)))-6/b^3*d^4*ln(1+exp(2*I*(b*x+a)))*x^2+4*I/b^2*d^4*x^3-8*I/b^5*d^4*a^3-3/b^3*c^2*d^2*polylog(3,-exp(2*I*(b*x+a)))-3/b^3*d^4*polylog(3,-exp(2*I*(b*x+a)))*x^2+24*I/b^3*d^3*c*a*x-24*d^4*polylog(5,-exp(I*(b*x+a)))/b^5-24*d^4*polylog(5,exp(I*(b*x+a)))/b^5-12/b^3*d^3*c*ln(1+exp(2*I*(b*x+a)))*x+12*I/b^2*d^3*c*x^2+12*I/b^4*d^3*c*a^2+6*I/b^4*d^4*polylog(2,-exp(2*I*(b*x+a)))*x-12*I/b^4*d^4*a^2*x+6*I/b^4*d^3*c*polylog(2,-exp(2*I*(b*x+a)))+2*(b*d^4*x^4*exp(2*I*(b*x+a))+4*b*c*d^3*x^3*exp(2*I*(b*x+a))+6*b*c^2*d^2*x^2*exp(2*I*(b*x+a))+4*b*c^3*d*x*exp(2*I*(b*x+a))-2*I*d^4*x^3*exp(2*I*(b*x+a))+b*c^4*exp(2*I*(b*x+a))-6*I*c*d^3*x^2*exp(2*I*(b*x+a))-6*I*c^2*d^2*x*exp(2*I*(b*x+a))-2*I*d^4*x^3-2*I*c^3*d*exp(2*I*(b*x+a))-6*I*c*d^3*x^2-6*I*c^2*d^2*x-2*I*c^3*d)/b^2/(1+exp(2*I*(b*x+a)))^2-4/b*c*d^3*ln(1+exp(2*I*(b*x+a)))*x^3+6*I/b^2*c*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2+6*I/b^2*c^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x-1/b*c^4*ln(1+exp(2*I*(b*x+a)))+1/b*c^4*ln(exp(I*(b*x+a))+1)+1/b*c^4*ln(exp(I*(b*x+a))-1)+12/b^5*d^4*a^2*ln(exp(I*(b*x+a)))+12/b^3*d^2*c^2*ln(exp(I*(b*x+a)))-1/b*d^4*ln(1+exp(2*I*(b*x+a)))*x^4+4/b*c^3*d*ln(exp(I*(b*x+a))+1)*x+4/b*c^3*d*ln(1-exp(I*(b*x+a)))*x+4/b^2*c^3*d*ln(1-exp(I*(b*x+a)))*a+6/b*c^2*d^2*ln(exp(I*(b*x+a))+1)*x^2+24/b^3*c*d^3*polylog(3,-exp(I*(b*x+a)))*x-6/b^3*c^2*d^2*a^2*ln(1-exp(I*(b*x+a)))+6/b*c^2*d^2*ln(1-exp(I*(b*x+a)))*x^2+24/b^3*c*d^3*polylog(3,exp(I*(b*x+a)))*x+24*I/b^4*c*d^3*polylog(4,-exp(I*(b*x+a)))+24*I/b^4*c*d^3*polylog(4,exp(I*(b*x+a)))-4*I/b^2*d^4*polylog(2,exp(I*(b*x+a)))*x^3+24*I/b^4*d^4*polylog(4,exp(I*(b*x+a)))*x-4*I/b^2*d^4*polylog(2,-exp(I*(b*x+a)))*x^3+24*I/b^4*d^4*polylog(4,-exp(I*(b*x+a)))*x-4*I/b^2*c^3*d*polylog(2,-exp(I*(b*x+a)))-4*I/b^2*c^3*d*polylog(2,exp(I*(b*x+a)))-4/b^4*c*d^3*a^3*ln(exp(I*(b*x+a))-1)+6/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a))-1)-4/b^2*c^3*d*a*ln(exp(I*(b*x+a))-1)+1/b*d^4*ln(1-exp(I*(b*x+a)))*x^4+1/b*d^4*ln(exp(I*(b*x+a))+1)*x^4-12*I/b^2*c*d^3*polylog(2,-exp(I*(b*x+a)))*x^2-12*I/b^2*c^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-12*I/b^2*c^2*d^2*polylog(2,exp(I*(b*x+a)))*x-12*I/b^2*c*d^3*polylog(2,exp(I*(b*x+a)))*x^2+4/b*c*d^3*ln(exp(I*(b*x+a))+1)*x^3+4/b*c*d^3*ln(1-exp(I*(b*x+a)))*x^3+4/b^4*c*d^3*ln(1-exp(I*(b*x+a)))*a^3-24/b^4*d^3*c*a*ln(exp(I*(b*x+a)))-4/b*c^3*d*ln(1+exp(2*I*(b*x+a)))*x-6/b^3*c*d^3*polylog(3,-exp(2*I*(b*x+a)))*x-6/b*c^2*d^2*ln(1+exp(2*I*(b*x+a)))*x^2-3*I/b^4*d^4*polylog(4,-exp(2*I*(b*x+a)))*x+2*I/b^2*d^4*polylog(2,-exp(2*I*(b*x+a)))*x^3-3*I/b^4*c*d^3*polylog(4,-exp(2*I*(b*x+a)))+2*I/b^2*c^3*d*polylog(2,-exp(2*I*(b*x+a)))","B"
311,1,1115,279,0.162000," ","int((d*x+c)^3*csc(b*x+a)*sec(b*x+a)^3,x)","-\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{2 b^{3}}-\frac{d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}-\frac{6 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{6 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{6 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 c \,d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{3 i d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{4 b^{4}}-\frac{c^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{3 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{2 b \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+6 b c \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+6 b \,c^{2} d x \,{\mathrm e}^{2 i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{2 i \left(b x +a \right)}-3 i d^{3} x^{2}+2 b \,c^{3} {\mathrm e}^{2 i \left(b x +a \right)}-6 i c \,d^{2} x -3 i c^{2} d}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}-\frac{3 d^{2} c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 i d^{3} x^{2}}{b^{2}}+\frac{3 i d^{3} a^{2}}{b^{4}}-\frac{3 d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{4}}-\frac{6 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{3 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{6 i d^{3} a x}{b^{3}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{3 c^{2} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{3 c \,d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}"," ",0,"-6*I/b^2*c*d^2*polylog(2,exp(I*(b*x+a)))*x-6*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x+6*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4+3/2*I*d^3*polylog(2,-exp(2*I*(b*x+a)))/b^4-3/b^3*d^2*c*ln(1+exp(2*I*(b*x+a)))-3/b^3*d^3*ln(1+exp(2*I*(b*x+a)))*x-1/b*c^3*ln(1+exp(2*I*(b*x+a)))-1/b^4*d^3*a^3*ln(exp(I*(b*x+a))-1)+6/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+6/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))+6/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x+6/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x+6*I/b^4*d^3*polylog(4,-exp(I*(b*x+a)))-3/2/b^3*c*d^2*polylog(3,-exp(2*I*(b*x+a)))-3/2/b^3*d^3*polylog(3,-exp(2*I*(b*x+a)))*x-3/4*I*d^3*polylog(4,-exp(2*I*(b*x+a)))/b^4+(2*b*d^3*x^3*exp(2*I*(b*x+a))-3*I*d^3*x^2*exp(2*I*(b*x+a))+6*b*c*d^2*x^2*exp(2*I*(b*x+a))-6*I*c*d^2*x*exp(2*I*(b*x+a))+6*b*c^2*d*x*exp(2*I*(b*x+a))-3*I*c^2*d*exp(2*I*(b*x+a))-3*I*d^3*x^2+2*b*c^3*exp(2*I*(b*x+a))-6*I*c*d^2*x-3*I*c^2*d)/b^2/(1+exp(2*I*(b*x+a)))^2+1/b*c^3*ln(exp(I*(b*x+a))-1)+1/b*c^3*ln(exp(I*(b*x+a))+1)+3*I/b^2*c*d^2*polylog(2,-exp(2*I*(b*x+a)))*x+3*I/b^2*d^3*x^2+3*I/b^4*d^3*a^2+6/b^3*d^2*c*ln(exp(I*(b*x+a)))-6/b^4*d^3*a*ln(exp(I*(b*x+a)))+3/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))-1)-3*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))-3*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-3*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2-3*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+3/b*c^2*d*ln(exp(I*(b*x+a))+1)*x+3/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+3/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-3/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+3/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2+3/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2-3/b^2*c^2*d*a*ln(exp(I*(b*x+a))-1)+1/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+1/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3+1/b*d^3*ln(exp(I*(b*x+a))+1)*x^3-1/b*d^3*ln(1+exp(2*I*(b*x+a)))*x^3+3/2*I/b^2*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2+6*I/b^3*d^3*a*x+3/2*I/b^2*c^2*d*polylog(2,-exp(2*I*(b*x+a)))-3/b*c^2*d*ln(1+exp(2*I*(b*x+a)))*x-3/b*c*d^2*ln(1+exp(2*I*(b*x+a)))*x^2","B"
312,1,614,181,0.132000," ","int((d*x+c)^2*csc(b*x+a)*sec(b*x+a)^3,x)","\frac{2 b \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-2 i d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+4 b c d x \,{\mathrm e}^{2 i \left(b x +a \right)}-2 i c d \,{\mathrm e}^{2 i \left(b x +a \right)}+2 b \,c^{2} {\mathrm e}^{2 i \left(b x +a \right)}-2 i d^{2} x -2 i c d}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}+\frac{d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{2 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}+\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{i c d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 c d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{2 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"-1/2*d^2*polylog(3,-exp(2*I*(b*x+a)))/b^3+1/b^3*d^2*a^2*ln(exp(I*(b*x+a))-1)+1/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-1/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2+1/b*d^2*ln(exp(I*(b*x+a))+1)*x^2+2*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+2*d^2*polylog(3,exp(I*(b*x+a)))/b^3-1/b*c^2*ln(1+exp(2*I*(b*x+a)))+1/b*c^2*ln(exp(I*(b*x+a))-1)+1/b*c^2*ln(exp(I*(b*x+a))+1)-1/b*d^2*ln(1+exp(2*I*(b*x+a)))*x^2+2*(b*d^2*x^2*exp(2*I*(b*x+a))-I*d^2*x*exp(2*I*(b*x+a))+2*b*c*d*x*exp(2*I*(b*x+a))-I*c*d*exp(2*I*(b*x+a))+b*c^2*exp(2*I*(b*x+a))-I*d^2*x-I*c*d)/b^2/(1+exp(2*I*(b*x+a)))^2+I/b^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x+I/b^2*c*d*polylog(2,-exp(2*I*(b*x+a)))-2/b*c*d*ln(1+exp(2*I*(b*x+a)))*x+2/b*c*d*ln(1-exp(I*(b*x+a)))*x+2/b^2*c*d*ln(1-exp(I*(b*x+a)))*a+2/b*c*d*ln(exp(I*(b*x+a))+1)*x-2/b^2*c*d*a*ln(exp(I*(b*x+a))-1)-2*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-2*I/b^2*d^2*polylog(2,exp(I*(b*x+a)))*x-2*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))-2*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))-1/b^3*d^2*ln(1+exp(2*I*(b*x+a)))+2/b^3*d^2*ln(exp(I*(b*x+a)))","B"
313,1,270,118,0.109000," ","int((d*x+c)*csc(b*x+a)*sec(b*x+a)^3,x)","\frac{2 b d x \,{\mathrm e}^{2 i \left(b x +a \right)}+2 b c \,{\mathrm e}^{2 i \left(b x +a \right)}-i d \,{\mathrm e}^{2 i \left(b x +a \right)}-i d}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2}}+\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{i d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{i d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{i d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}"," ",0,"(2*b*d*x*exp(2*I*(b*x+a))+2*b*c*exp(2*I*(b*x+a))-I*d*exp(2*I*(b*x+a))-I*d)/b^2/(1+exp(2*I*(b*x+a)))^2+1/b*c*ln(exp(I*(b*x+a))-1)-1/b*c*ln(1+exp(2*I*(b*x+a)))+1/b*c*ln(exp(I*(b*x+a))+1)-1/b*d*ln(1+exp(2*I*(b*x+a)))*x+1/2*I*d*polylog(2,-exp(2*I*(b*x+a)))/b^2+1/b*d*ln(exp(I*(b*x+a))+1)*x-I*d*polylog(2,-exp(I*(b*x+a)))/b^2+1/b*d*ln(1-exp(I*(b*x+a)))*x+1/b^2*d*ln(1-exp(I*(b*x+a)))*a-I*d*polylog(2,exp(I*(b*x+a)))/b^2-1/b^2*d*a*ln(exp(I*(b*x+a))-1)","B"
314,0,0,24,3.352000," ","int(csc(b*x+a)*sec(b*x+a)^3/(d*x+c),x)","\int \frac{\csc \left(b x +a \right) \left(\sec^{3}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)*sec(b*x+a)^3/(d*x+c),x)","F"
315,0,0,24,5.624000," ","int(csc(b*x+a)*sec(b*x+a)^3/(d*x+c)^2,x)","\int \frac{\csc \left(b x +a \right) \left(\sec^{3}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)*sec(b*x+a)^3/(d*x+c)^2,x)","F"
316,0,0,26,0.139000," ","int((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \left(\csc^{2}\left(b x +a \right)\right) \left(\sec^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a)^3,x)","F"
317,1,1629,428,0.560000," ","int((d*x+c)^3*csc(b*x+a)^2*sec(b*x+a)^3,x)","-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}+\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}+\frac{3 d^{3} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}-\frac{6 c \,d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{6 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a x}{b^{3}}+\frac{6 i d^{2} c \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{6 i d^{3} a \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{4}}+\frac{6 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{6 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}+\frac{6 i \dilog \left({\mathrm e}^{i \left(b x +a \right)}\right) c \,d^{2}}{b^{3}}-\frac{6 i \dilog \left({\mathrm e}^{i \left(b x +a \right)}\right) d^{3} a}{b^{4}}-\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{9 i d^{2} c \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{9 i d^{2} c \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{3 d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{3 d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}+\frac{3 i d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i d^{3} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{9 i d^{3} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}+\frac{9 i d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}-\frac{i \left(3 d^{3} x^{3} b \,{\mathrm e}^{5 i \left(b x +a \right)}+9 c \,d^{2} x^{2} b \,{\mathrm e}^{5 i \left(b x +a \right)}+9 c^{2} d x b \,{\mathrm e}^{5 i \left(b x +a \right)}+2 d^{3} x^{3} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 c^{3} b \,{\mathrm e}^{5 i \left(b x +a \right)}+6 c \,d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+6 i c \,d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}+6 c^{2} d x b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 d^{3} x^{3} b \,{\mathrm e}^{i \left(b x +a \right)}-6 i c \,d^{2} x \,{\mathrm e}^{5 i \left(b x +a \right)}+2 c^{3} b \,{\mathrm e}^{3 i \left(b x +a \right)}+9 c \,d^{2} x^{2} b \,{\mathrm e}^{i \left(b x +a \right)}-3 i d^{3} x^{2} {\mathrm e}^{5 i \left(b x +a \right)}+9 c^{2} d x b \,{\mathrm e}^{i \left(b x +a \right)}+3 c^{3} b \,{\mathrm e}^{i \left(b x +a \right)}+3 i c^{2} d \,{\mathrm e}^{i \left(b x +a \right)}+3 i d^{3} x^{2} {\mathrm e}^{i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{5 i \left(b x +a \right)}\right)}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}+\frac{6 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}+\frac{9 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}-\frac{9 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}+\frac{9 c^{2} d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}+\frac{9 c^{2} d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}+\frac{9 a^{2} c \,d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{9 c^{2} d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}-\frac{9 c^{2} d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}-\frac{9 a^{2} c \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{3 i d^{3} a^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{9 i c^{2} d \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{9 i c^{2} d \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{9 i c \,d^{2} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{9 i c^{2} d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{6 i d^{3} a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 i c \,d^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 a^{3} d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{4}}+\frac{3 d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{2 b}-\frac{3 d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{2 b}+\frac{3 a^{3} d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{4}}-\frac{3 i c^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{9 i d^{3} \polylog \left(4, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{9 i d^{3} \polylog \left(4, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{9 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{9 d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{9 d^{2} c \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{9 d^{2} c \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"-9*I*d^3*polylog(4,-I*exp(I*(b*x+a)))/b^4+3*I*d^3*polylog(2,-I*exp(I*(b*x+a)))/b^4+9*I*d^3*polylog(4,I*exp(I*(b*x+a)))/b^4-6*d^3*polylog(3,-exp(I*(b*x+a)))/b^4+6*d^3*polylog(3,exp(I*(b*x+a)))/b^4+3/b^2*c^2*d*ln(exp(I*(b*x+a))-1)-3/b^2*c^2*d*ln(exp(I*(b*x+a))+1)+3/b^4*d^3*a^2*ln(exp(I*(b*x+a))-1)-3*I*d^3*polylog(2,I*exp(I*(b*x+a)))/b^4-3/b^2*d^3*ln(exp(I*(b*x+a))+1)*x^2+3/b^2*d^3*ln(1-exp(I*(b*x+a)))*x^2+3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^2-9*I/b^3*a^2*c*d^2*arctan(exp(I*(b*x+a)))+9*I/b^2*c*d^2*polylog(2,-I*exp(I*(b*x+a)))*x+9*I/b^2*a*c^2*d*arctan(exp(I*(b*x+a)))-9*I/b^2*c*d^2*polylog(2,I*exp(I*(b*x+a)))*x+6*I/b^4*d^3*a*arctan(exp(I*(b*x+a)))-6*I/b^3*c*d^2*arctan(exp(I*(b*x+a)))-3/2/b^4*a^3*d^3*ln(1+I*exp(I*(b*x+a)))+9/b^3*d^3*polylog(3,I*exp(I*(b*x+a)))*x+3/2/b*d^3*ln(1-I*exp(I*(b*x+a)))*x^3-3/2/b*d^3*ln(1+I*exp(I*(b*x+a)))*x^3-9/b^3*d^3*polylog(3,-I*exp(I*(b*x+a)))*x+9/b^3*d^2*c*polylog(3,I*exp(I*(b*x+a)))-9/b^3*d^2*c*polylog(3,-I*exp(I*(b*x+a)))+3/2/b^4*a^3*d^3*ln(1-I*exp(I*(b*x+a)))+9/2/b*d^2*c*ln(1-I*exp(I*(b*x+a)))*x^2-9/2/b*d^2*c*ln(1+I*exp(I*(b*x+a)))*x^2+9/2/b*c^2*d*ln(1-I*exp(I*(b*x+a)))*x+9/2/b^2*c^2*d*ln(1-I*exp(I*(b*x+a)))*a+9/2/b^3*a^2*c*d^2*ln(1+I*exp(I*(b*x+a)))-9/2/b*c^2*d*ln(1+I*exp(I*(b*x+a)))*x-9/2/b^2*c^2*d*ln(1+I*exp(I*(b*x+a)))*a-9/2/b^3*a^2*c*d^2*ln(1-I*exp(I*(b*x+a)))-I/b^2/(1+exp(2*I*(b*x+a)))^2/(exp(2*I*(b*x+a))-1)*(3*d^3*x^3*b*exp(5*I*(b*x+a))+9*c*d^2*x^2*b*exp(5*I*(b*x+a))+9*c^2*d*x*b*exp(5*I*(b*x+a))+2*d^3*x^3*b*exp(3*I*(b*x+a))+3*c^3*b*exp(5*I*(b*x+a))+6*c*d^2*x^2*b*exp(3*I*(b*x+a))+6*I*c*d^2*x*exp(I*(b*x+a))+6*c^2*d*x*b*exp(3*I*(b*x+a))+3*d^3*x^3*b*exp(I*(b*x+a))-6*I*c*d^2*x*exp(5*I*(b*x+a))+2*c^3*b*exp(3*I*(b*x+a))+9*c*d^2*x^2*b*exp(I*(b*x+a))-3*I*d^3*x^2*exp(5*I*(b*x+a))+9*c^2*d*x*b*exp(I*(b*x+a))+3*c^3*b*exp(I*(b*x+a))+3*I*c^2*d*exp(I*(b*x+a))+3*I*d^3*x^2*exp(I*(b*x+a))-3*I*c^2*d*exp(5*I*(b*x+a)))+3/b^3*d^3*ln(1-I*exp(I*(b*x+a)))*x+3/b^4*d^3*ln(1-I*exp(I*(b*x+a)))*a-3/b^3*d^3*ln(1+I*exp(I*(b*x+a)))*x-3/b^4*d^3*ln(1+I*exp(I*(b*x+a)))*a-6/b^3*c*d^2*a*ln(exp(I*(b*x+a))-1)+6/b^3*d^3*ln(1-exp(I*(b*x+a)))*a*x+6*I/b^3*d^2*c*dilog(exp(I*(b*x+a))+1)-6*I/b^4*d^3*a*dilog(exp(I*(b*x+a))+1)+6*I/b^4*d^3*polylog(2,-exp(I*(b*x+a)))*a-6*I/b^4*d^3*polylog(2,exp(I*(b*x+a)))*a+6*I/b^3*dilog(exp(I*(b*x+a)))*c*d^2-6*I/b^4*dilog(exp(I*(b*x+a)))*d^3*a-3*I/b*c^3*arctan(exp(I*(b*x+a)))-6*I/b^3*d^3*polylog(2,exp(I*(b*x+a)))*x-6/b^2*d^2*c*ln(exp(I*(b*x+a))+1)*x+6*I/b^3*d^3*polylog(2,-exp(I*(b*x+a)))*x+3*I/b^4*a^3*d^3*arctan(exp(I*(b*x+a)))-9/2*I/b^2*c^2*d*polylog(2,I*exp(I*(b*x+a)))+9/2*I/b^2*c^2*d*polylog(2,-I*exp(I*(b*x+a)))-9/2*I/b^2*d^3*polylog(2,I*exp(I*(b*x+a)))*x^2+9/2*I/b^2*d^3*polylog(2,-I*exp(I*(b*x+a)))*x^2","B"
318,1,770,310,0.316000," ","int((d*x+c)^2*csc(b*x+a)^2*sec(b*x+a)^3,x)","-\frac{3 c d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{3 i c d \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i d^{2} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 c d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{3 c d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{3 i d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{3 c d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 i d^{2} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 i c d \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}+\frac{2 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{2 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{2 d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{3 i c^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{3 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}+\frac{3 a^{2} d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{3 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}-\frac{3 a^{2} d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}-\frac{3 d^{2} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 d^{2} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i d^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 i \dilog \left({\mathrm e}^{i \left(b x +a \right)}\right) d^{2}}{b^{3}}+\frac{2 i d^{2} \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}+\frac{6 i c d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{i \left(3 d^{2} x^{2} b \,{\mathrm e}^{5 i \left(b x +a \right)}+6 c d x b \,{\mathrm e}^{5 i \left(b x +a \right)}+3 c^{2} b \,{\mathrm e}^{5 i \left(b x +a \right)}+2 d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+4 c d x b \,{\mathrm e}^{3 i \left(b x +a \right)}-2 i d^{2} x \,{\mathrm e}^{5 i \left(b x +a \right)}+2 c^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 d^{2} x^{2} b \,{\mathrm e}^{i \left(b x +a \right)}-2 i c d \,{\mathrm e}^{5 i \left(b x +a \right)}+6 c d x b \,{\mathrm e}^{i \left(b x +a \right)}+3 c^{2} b \,{\mathrm e}^{i \left(b x +a \right)}+2 i d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}+2 i d c \,{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}"," ",0,"-3*d^2*polylog(3,-I*exp(I*(b*x+a)))/b^3+3*d^2*polylog(3,I*exp(I*(b*x+a)))/b^3-2/b^2*d^2*ln(exp(I*(b*x+a))+1)*x+2*I/b^3*d^2*dilog(exp(I*(b*x+a))+1)+2/b^2*d*c*ln(exp(I*(b*x+a))-1)-2/b^2*d*c*ln(exp(I*(b*x+a))+1)-2/b^3*d^2*a*ln(exp(I*(b*x+a))-1)-3*I/b^3*a^2*d^2*arctan(exp(I*(b*x+a)))+3*I/b^2*d^2*polylog(2,-I*exp(I*(b*x+a)))*x-3*I/b^2*c*d*polylog(2,I*exp(I*(b*x+a)))+3*I/b^2*c*d*polylog(2,-I*exp(I*(b*x+a)))-3*I/b^2*d^2*polylog(2,I*exp(I*(b*x+a)))*x-3/b*c*d*ln(1+I*exp(I*(b*x+a)))*x+3/b^2*c*d*ln(1-I*exp(I*(b*x+a)))*a+3/b*c*d*ln(1-I*exp(I*(b*x+a)))*x-3/b^2*c*d*ln(1+I*exp(I*(b*x+a)))*a+6*I/b^2*a*c*d*arctan(exp(I*(b*x+a)))+2*I/b^3*dilog(exp(I*(b*x+a)))*d^2-3/2/b*d^2*ln(1+I*exp(I*(b*x+a)))*x^2+3/2/b^3*a^2*d^2*ln(1+I*exp(I*(b*x+a)))+3/2/b*d^2*ln(1-I*exp(I*(b*x+a)))*x^2-3/2/b^3*a^2*d^2*ln(1-I*exp(I*(b*x+a)))-3*I/b*c^2*arctan(exp(I*(b*x+a)))-2*I/b^3*d^2*arctan(exp(I*(b*x+a)))-I/b^2/(1+exp(2*I*(b*x+a)))^2/(exp(2*I*(b*x+a))-1)*(3*d^2*x^2*b*exp(5*I*(b*x+a))+6*c*d*x*b*exp(5*I*(b*x+a))+3*c^2*b*exp(5*I*(b*x+a))+2*d^2*x^2*b*exp(3*I*(b*x+a))+4*c*d*x*b*exp(3*I*(b*x+a))-2*I*d^2*x*exp(5*I*(b*x+a))+2*c^2*b*exp(3*I*(b*x+a))+3*d^2*x^2*b*exp(I*(b*x+a))-2*I*c*d*exp(5*I*(b*x+a))+6*c*d*x*b*exp(I*(b*x+a))+3*c^2*b*exp(I*(b*x+a))+2*I*d^2*x*exp(I*(b*x+a))+2*I*d*c*exp(I*(b*x+a)))","B"
319,1,344,139,0.164000," ","int((d*x+c)*csc(b*x+a)^2*sec(b*x+a)^3,x)","-\frac{i \left(3 b d x \,{\mathrm e}^{5 i \left(b x +a \right)}+3 c b \,{\mathrm e}^{5 i \left(b x +a \right)}+2 b d x \,{\mathrm e}^{3 i \left(b x +a \right)}+2 c b \,{\mathrm e}^{3 i \left(b x +a \right)}-i d \,{\mathrm e}^{5 i \left(b x +a \right)}+3 b d x \,{\mathrm e}^{i \left(b x +a \right)}+3 c b \,{\mathrm e}^{i \left(b x +a \right)}+i d \,{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)}-\frac{3 i c \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{3 i d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{3 i d \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{3 d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}+\frac{3 d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}+\frac{3 i d \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{3 d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}-\frac{3 d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}"," ",0,"-I/b^2/(1+exp(2*I*(b*x+a)))^2/(exp(2*I*(b*x+a))-1)*(3*b*d*x*exp(5*I*(b*x+a))+3*c*b*exp(5*I*(b*x+a))+2*b*d*x*exp(3*I*(b*x+a))+2*c*b*exp(3*I*(b*x+a))-I*d*exp(5*I*(b*x+a))+3*b*d*x*exp(I*(b*x+a))+3*c*b*exp(I*(b*x+a))+I*d*exp(I*(b*x+a)))-3*I/b*c*arctan(exp(I*(b*x+a)))+3*I/b^2*d*a*arctan(exp(I*(b*x+a)))+d/b^2*ln(exp(I*(b*x+a))-1)-d/b^2*ln(exp(I*(b*x+a))+1)-3/2*I/b^2*d*dilog(1-I*exp(I*(b*x+a)))+3/2/b*d*ln(1-I*exp(I*(b*x+a)))*x+3/2/b^2*d*ln(1-I*exp(I*(b*x+a)))*a+3/2*I/b^2*d*dilog(1+I*exp(I*(b*x+a)))-3/2/b*d*ln(1+I*exp(I*(b*x+a)))*x-3/2/b^2*d*ln(1+I*exp(I*(b*x+a)))*a","B"
320,0,0,26,3.249000," ","int(csc(b*x+a)^2*sec(b*x+a)^3/(d*x+c),x)","\int \frac{\left(\csc^{2}\left(b x +a \right)\right) \left(\sec^{3}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)^2*sec(b*x+a)^3/(d*x+c),x)","F"
321,0,0,26,4.286000," ","int(csc(b*x+a)^2*sec(b*x+a)^3/(d*x+c)^2,x)","\int \frac{\left(\csc^{2}\left(b x +a \right)\right) \left(\sec^{3}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)^2*sec(b*x+a)^3/(d*x+c)^2,x)","F"
322,0,0,26,0.118000," ","int((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \left(\csc^{3}\left(b x +a \right)\right) \left(\sec^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a)^3,x)","F"
323,1,1329,284,0.218000," ","int((d*x+c)^3*csc(b*x+a)^3*sec(b*x+a)^3,x)","-\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}-\frac{2 d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}-\frac{12 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{12 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{2 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{2 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}+\frac{2 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{12 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{12 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{12 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{12 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{12 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 c \,d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{4}}-\frac{2 c^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{2 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{3 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{3 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{3 d^{3} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}-\frac{3 d^{2} c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{4}}-\frac{6 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{6 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}-\frac{6 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{6 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{6 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{6 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{6 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}+\frac{6 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{6 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 c^{2} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{6 c \,d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}+\frac{4 d^{3} x^{3} b \,{\mathrm e}^{6 i \left(b x +a \right)}+12 c \,d^{2} x^{2} b \,{\mathrm e}^{6 i \left(b x +a \right)}+12 c^{2} d x b \,{\mathrm e}^{6 i \left(b x +a \right)}+4 c^{3} b \,{\mathrm e}^{6 i \left(b x +a \right)}-6 i d^{3} x^{2} {\mathrm e}^{6 i \left(b x +a \right)}+4 b \,d^{3} x^{3} {\mathrm e}^{2 i \left(b x +a \right)}-12 i c \,d^{2} x \,{\mathrm e}^{6 i \left(b x +a \right)}+12 b c \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-6 i c^{2} d \,{\mathrm e}^{6 i \left(b x +a \right)}+12 b \,c^{2} d x \,{\mathrm e}^{2 i \left(b x +a \right)}+4 b \,c^{3} {\mathrm e}^{2 i \left(b x +a \right)}+6 i d^{3} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}+12 i c \,d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+6 i c^{2} d \,{\mathrm e}^{2 i \left(b x +a \right)}}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}"," ",0,"-3/2*I*d^3*polylog(4,-exp(2*I*(b*x+a)))/b^4+3/2*I*d^3*polylog(2,-exp(2*I*(b*x+a)))/b^4-3/b^3*d^2*c*ln(1+exp(2*I*(b*x+a)))-3/b^3*d^3*ln(1+exp(2*I*(b*x+a)))*x-2/b*c^3*ln(1+exp(2*I*(b*x+a)))-2/b^4*d^3*a^3*ln(exp(I*(b*x+a))-1)+12/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+12/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))+12/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x+12/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x-3*I*d^3*polylog(2,exp(I*(b*x+a)))/b^4-3/b^3*c*d^2*polylog(3,-exp(2*I*(b*x+a)))-3/b^3*d^3*polylog(3,-exp(2*I*(b*x+a)))*x+2/b*c^3*ln(exp(I*(b*x+a))-1)+2/b*c^3*ln(exp(I*(b*x+a))+1)+3/b^3*d^2*c*ln(exp(I*(b*x+a))-1)+3/b^3*d^2*c*ln(exp(I*(b*x+a))+1)+3/b^3*d^3*ln(exp(I*(b*x+a))+1)*x+3/b^3*d^3*ln(1-exp(I*(b*x+a)))*x+3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a-3/b^4*d^3*a*ln(exp(I*(b*x+a))-1)-3*I/b^4*d^3*polylog(2,-exp(I*(b*x+a)))+2/b^2/(1+exp(2*I*(b*x+a)))^2/(exp(2*I*(b*x+a))-1)^2*(2*d^3*x^3*b*exp(6*I*(b*x+a))+6*c*d^2*x^2*b*exp(6*I*(b*x+a))+6*c^2*d*x*b*exp(6*I*(b*x+a))+2*c^3*b*exp(6*I*(b*x+a))-3*I*d^3*x^2*exp(6*I*(b*x+a))+2*b*d^3*x^3*exp(2*I*(b*x+a))-6*I*c*d^2*x*exp(6*I*(b*x+a))+6*b*c*d^2*x^2*exp(2*I*(b*x+a))-3*I*c^2*d*exp(6*I*(b*x+a))+6*b*c^2*d*x*exp(2*I*(b*x+a))+2*b*c^3*exp(2*I*(b*x+a))+3*I*d^3*x^2*exp(2*I*(b*x+a))+6*I*c*d^2*x*exp(2*I*(b*x+a))+3*I*c^2*d*exp(2*I*(b*x+a)))+12*I/b^4*d^3*polylog(4,exp(I*(b*x+a)))+12*I/b^4*d^3*polylog(4,-exp(I*(b*x+a)))-6*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2-6*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2+3*I/b^2*c^2*d*polylog(2,-exp(2*I*(b*x+a)))+3*I/b^2*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2-6*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))-6*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))+6/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))-1)+6/b*c^2*d*ln(exp(I*(b*x+a))+1)*x+6/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+6/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-6/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+6/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2+6/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2-6/b^2*c^2*d*a*ln(exp(I*(b*x+a))-1)+2/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+2/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3+2/b*d^3*ln(exp(I*(b*x+a))+1)*x^3-2/b*d^3*ln(1+exp(2*I*(b*x+a)))*x^3-6/b*c^2*d*ln(1+exp(2*I*(b*x+a)))*x-6/b*c*d^2*ln(1+exp(2*I*(b*x+a)))*x^2+6*I/b^2*polylog(2,-exp(2*I*(b*x+a)))*c*d^2*x-12*I/b^2*polylog(2,-exp(I*(b*x+a)))*c*d^2*x-12*I/b^2*polylog(2,exp(I*(b*x+a)))*c*d^2*x","B"
324,1,716,178,0.157000," ","int((d*x+c)^2*csc(b*x+a)^3*sec(b*x+a)^3,x)","\frac{2 d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}+\frac{2 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{2 c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}+\frac{2 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}+\frac{4 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{4 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}+\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 i c d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 c d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{4 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{4 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{4 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{4 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}-\frac{4 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{4 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{4 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{4 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{4 d^{2} x^{2} b \,{\mathrm e}^{6 i \left(b x +a \right)}+8 c d x b \,{\mathrm e}^{6 i \left(b x +a \right)}+4 c^{2} b \,{\mathrm e}^{6 i \left(b x +a \right)}-4 i d^{2} x \,{\mathrm e}^{6 i \left(b x +a \right)}+4 b \,d^{2} x^{2} {\mathrm e}^{2 i \left(b x +a \right)}-4 i c d \,{\mathrm e}^{6 i \left(b x +a \right)}+8 b c d x \,{\mathrm e}^{2 i \left(b x +a \right)}+4 b \,c^{2} {\mathrm e}^{2 i \left(b x +a \right)}+4 i d^{2} x \,{\mathrm e}^{2 i \left(b x +a \right)}+4 i c d \,{\mathrm e}^{2 i \left(b x +a \right)}}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}"," ",0,"-d^2*polylog(3,-exp(2*I*(b*x+a)))/b^3+2/b^3*d^2*a^2*ln(exp(I*(b*x+a))-1)+2/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-2/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2+2/b*d^2*ln(exp(I*(b*x+a))+1)*x^2+4*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+4*d^2*polylog(3,exp(I*(b*x+a)))/b^3-2/b*c^2*ln(1+exp(2*I*(b*x+a)))+2/b*c^2*ln(exp(I*(b*x+a))-1)+2/b*c^2*ln(exp(I*(b*x+a))+1)-2/b*d^2*ln(1+exp(2*I*(b*x+a)))*x^2+4/b^2/(1+exp(2*I*(b*x+a)))^2/(exp(2*I*(b*x+a))-1)^2*(d^2*x^2*b*exp(6*I*(b*x+a))+2*c*d*x*b*exp(6*I*(b*x+a))+c^2*b*exp(6*I*(b*x+a))-I*d^2*x*exp(6*I*(b*x+a))+b*d^2*x^2*exp(2*I*(b*x+a))-I*c*d*exp(6*I*(b*x+a))+2*b*c*d*x*exp(2*I*(b*x+a))+b*c^2*exp(2*I*(b*x+a))+I*d^2*x*exp(2*I*(b*x+a))+I*c*d*exp(2*I*(b*x+a)))-4/b*c*d*ln(1+exp(2*I*(b*x+a)))*x+4/b*c*d*ln(1-exp(I*(b*x+a)))*x+4/b^2*c*d*ln(1-exp(I*(b*x+a)))*a+4/b*c*d*ln(exp(I*(b*x+a))+1)*x-4/b^2*c*d*a*ln(exp(I*(b*x+a))-1)-1/b^3*d^2*ln(1+exp(2*I*(b*x+a)))+1/b^3*d^2*ln(exp(I*(b*x+a))+1)+1/b^3*d^2*ln(exp(I*(b*x+a))-1)+2*I/b^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x-4*I/b^2*polylog(2,-exp(I*(b*x+a)))*d^2*x-4*I/b^2*polylog(2,exp(I*(b*x+a)))*d^2*x+2*I/b^2*c*d*polylog(2,-exp(2*I*(b*x+a)))-4*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))-4*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))","B"
325,1,325,102,0.171000," ","int((d*x+c)*csc(b*x+a)^3*sec(b*x+a)^3,x)","\frac{4 b d x \,{\mathrm e}^{6 i \left(b x +a \right)}+4 c b \,{\mathrm e}^{6 i \left(b x +a \right)}-2 i d \,{\mathrm e}^{6 i \left(b x +a \right)}+4 b d x \,{\mathrm e}^{2 i \left(b x +a \right)}+4 b c \,{\mathrm e}^{2 i \left(b x +a \right)}+2 i d \,{\mathrm e}^{2 i \left(b x +a \right)}}{b^{2} \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{2 c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b}-\frac{2 c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}+\frac{2 c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b}-\frac{2 d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{i d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{2 i d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{2 i d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 d a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}"," ",0,"2/b^2/(1+exp(2*I*(b*x+a)))^2/(exp(2*I*(b*x+a))-1)^2*(2*b*d*x*exp(6*I*(b*x+a))+2*c*b*exp(6*I*(b*x+a))-I*d*exp(6*I*(b*x+a))+2*b*d*x*exp(2*I*(b*x+a))+2*b*c*exp(2*I*(b*x+a))+I*d*exp(2*I*(b*x+a)))+2/b*c*ln(exp(I*(b*x+a))-1)-2/b*c*ln(1+exp(2*I*(b*x+a)))+2/b*c*ln(exp(I*(b*x+a))+1)-2/b*d*ln(1+exp(2*I*(b*x+a)))*x+I*d*polylog(2,-exp(2*I*(b*x+a)))/b^2+2/b*d*ln(exp(I*(b*x+a))+1)*x-2*I*d*polylog(2,-exp(I*(b*x+a)))/b^2+2/b*d*ln(1-exp(I*(b*x+a)))*x+2/b^2*d*ln(1-exp(I*(b*x+a)))*a-2*I/b^2*d*polylog(2,exp(I*(b*x+a)))-2/b^2*d*a*ln(exp(I*(b*x+a))-1)","B"
326,0,0,23,1.049000," ","int(csc(b*x+a)^3*sec(b*x+a)^3/(d*x+c),x)","\int \frac{\left(\csc^{3}\left(b x +a \right)\right) \left(\sec^{3}\left(b x +a \right)\right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)^3*sec(b*x+a)^3/(d*x+c),x)","F"
327,0,0,23,3.790000," ","int(csc(b*x+a)^3*sec(b*x+a)^3/(d*x+c)^2,x)","\int \frac{\left(\csc^{3}\left(b x +a \right)\right) \left(\sec^{3}\left(b x +a \right)\right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)^3*sec(b*x+a)^3/(d*x+c)^2,x)","F"
328,0,0,95,0.080000," ","int(x*cos(b*x+a)^(5/2)*sin(b*x+a),x)","\int x \left(\cos^{\frac{5}{2}}\left(b x +a \right)\right) \sin \left(b x +a \right)\, dx"," ",0,"int(x*cos(b*x+a)^(5/2)*sin(b*x+a),x)","F"
329,0,0,76,0.042000," ","int(x*cos(b*x+a)^(3/2)*sin(b*x+a),x)","\int x \left(\cos^{\frac{3}{2}}\left(b x +a \right)\right) \sin \left(b x +a \right)\, dx"," ",0,"int(x*cos(b*x+a)^(3/2)*sin(b*x+a),x)","F"
330,0,0,76,0.039000," ","int(x*sin(b*x+a)*cos(b*x+a)^(1/2),x)","\int x \sin \left(b x +a \right) \left(\sqrt{\cos}\left(b x +a \right)\right)\, dx"," ",0,"int(x*sin(b*x+a)*cos(b*x+a)^(1/2),x)","F"
331,1,310,57,0.156000," ","int(x*sin(b*x+a)/cos(b*x+a)^(1/2),x)","-\frac{\left(b x +2 i\right) \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) \sqrt{2}\, {\mathrm e}^{-i \left(b x +a \right)}}{b^{2} \sqrt{\left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{-i \left(b x +a \right)}}}-\frac{2 i \left(-\frac{2 \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{\sqrt{\left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{i \left(b x +a \right)}}}+\frac{i \sqrt{-i \left({\mathrm e}^{i \left(b x +a \right)}+i\right)}\, \sqrt{2}\, \sqrt{i \left({\mathrm e}^{i \left(b x +a \right)}-i\right)}\, \sqrt{i {\mathrm e}^{i \left(b x +a \right)}}\, \left(-2 i \EllipticE \left(\sqrt{-i \left({\mathrm e}^{i \left(b x +a \right)}+i\right)}, \frac{\sqrt{2}}{2}\right)+i \EllipticF \left(\sqrt{-i \left({\mathrm e}^{i \left(b x +a \right)}+i\right)}, \frac{\sqrt{2}}{2}\right)\right)}{\sqrt{{\mathrm e}^{3 i \left(b x +a \right)}+{\mathrm e}^{i \left(b x +a \right)}}}\right) \sqrt{2}\, \sqrt{\left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{i \left(b x +a \right)}}\, {\mathrm e}^{-i \left(b x +a \right)}}{b^{2} \sqrt{\left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{-i \left(b x +a \right)}}}"," ",0,"-(b*x+2*I)*(exp(I*(b*x+a))^2+1)/b^2*2^(1/2)/((exp(I*(b*x+a))^2+1)/exp(I*(b*x+a)))^(1/2)/exp(I*(b*x+a))-2*I/b^2*(-2*(exp(I*(b*x+a))^2+1)/((exp(I*(b*x+a))^2+1)*exp(I*(b*x+a)))^(1/2)+I*(-I*(exp(I*(b*x+a))+I))^(1/2)*2^(1/2)*(I*(exp(I*(b*x+a))-I))^(1/2)*(I*exp(I*(b*x+a)))^(1/2)/(exp(I*(b*x+a))^3+exp(I*(b*x+a)))^(1/2)*(-2*I*EllipticE((-I*(exp(I*(b*x+a))+I))^(1/2),1/2*2^(1/2))+I*EllipticF((-I*(exp(I*(b*x+a))+I))^(1/2),1/2*2^(1/2))))*2^(1/2)/((exp(I*(b*x+a))^2+1)/exp(I*(b*x+a)))^(1/2)*((exp(I*(b*x+a))^2+1)*exp(I*(b*x+a)))^(1/2)/exp(I*(b*x+a))","C"
332,0,0,57,0.039000," ","int(x*sin(b*x+a)/cos(b*x+a)^(3/2),x)","\int \frac{x \sin \left(b x +a \right)}{\cos \left(b x +a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*sin(b*x+a)/cos(b*x+a)^(3/2),x)","F"
333,0,0,76,0.039000," ","int(x*sin(b*x+a)/cos(b*x+a)^(5/2),x)","\int \frac{x \sin \left(b x +a \right)}{\cos \left(b x +a \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*sin(b*x+a)/cos(b*x+a)^(5/2),x)","F"
334,0,0,76,0.039000," ","int(x*sin(b*x+a)/cos(b*x+a)^(7/2),x)","\int \frac{x \sin \left(b x +a \right)}{\cos \left(b x +a \right)^{\frac{7}{2}}}\, dx"," ",0,"int(x*sin(b*x+a)/cos(b*x+a)^(7/2),x)","F"
335,0,0,95,0.043000," ","int(x*sin(b*x+a)/cos(b*x+a)^(9/2),x)","\int \frac{x \sin \left(b x +a \right)}{\cos \left(b x +a \right)^{\frac{9}{2}}}\, dx"," ",0,"int(x*sin(b*x+a)/cos(b*x+a)^(9/2),x)","F"
336,0,0,111,0.060000," ","int(x*sec(b*x+a)^(9/2)*sin(b*x+a),x)","\int x \left(\sec^{\frac{9}{2}}\left(b x +a \right)\right) \sin \left(b x +a \right)\, dx"," ",0,"int(x*sec(b*x+a)^(9/2)*sin(b*x+a),x)","F"
337,0,0,92,0.048000," ","int(x*sec(b*x+a)^(7/2)*sin(b*x+a),x)","\int x \left(\sec^{\frac{7}{2}}\left(b x +a \right)\right) \sin \left(b x +a \right)\, dx"," ",0,"int(x*sec(b*x+a)^(7/2)*sin(b*x+a),x)","F"
338,0,0,92,0.049000," ","int(x*sec(b*x+a)^(5/2)*sin(b*x+a),x)","\int x \left(\sec^{\frac{5}{2}}\left(b x +a \right)\right) \sin \left(b x +a \right)\, dx"," ",0,"int(x*sec(b*x+a)^(5/2)*sin(b*x+a),x)","F"
339,0,0,73,0.049000," ","int(x*sec(b*x+a)^(3/2)*sin(b*x+a),x)","\int x \left(\sec^{\frac{3}{2}}\left(b x +a \right)\right) \sin \left(b x +a \right)\, dx"," ",0,"int(x*sec(b*x+a)^(3/2)*sin(b*x+a),x)","F"
340,1,310,73,0.083000," ","int(x*sin(b*x+a)*sec(b*x+a)^(1/2),x)","-\frac{\left(b x +2 i\right) \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) \sqrt{2}\, \sqrt{\frac{{\mathrm e}^{i \left(b x +a \right)}}{1+{\mathrm e}^{2 i \left(b x +a \right)}}}\, {\mathrm e}^{-i \left(b x +a \right)}}{b^{2}}-\frac{2 i \left(-\frac{2 \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{\sqrt{\left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{i \left(b x +a \right)}}}+\frac{i \sqrt{-i \left({\mathrm e}^{i \left(b x +a \right)}+i\right)}\, \sqrt{2}\, \sqrt{i \left({\mathrm e}^{i \left(b x +a \right)}-i\right)}\, \sqrt{i {\mathrm e}^{i \left(b x +a \right)}}\, \left(-2 i \EllipticE \left(\sqrt{-i \left({\mathrm e}^{i \left(b x +a \right)}+i\right)}, \frac{\sqrt{2}}{2}\right)+i \EllipticF \left(\sqrt{-i \left({\mathrm e}^{i \left(b x +a \right)}+i\right)}, \frac{\sqrt{2}}{2}\right)\right)}{\sqrt{{\mathrm e}^{3 i \left(b x +a \right)}+{\mathrm e}^{i \left(b x +a \right)}}}\right) \sqrt{2}\, \sqrt{\frac{{\mathrm e}^{i \left(b x +a \right)}}{1+{\mathrm e}^{2 i \left(b x +a \right)}}}\, \sqrt{\left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) {\mathrm e}^{i \left(b x +a \right)}}\, {\mathrm e}^{-i \left(b x +a \right)}}{b^{2}}"," ",0,"-(b*x+2*I)*(exp(I*(b*x+a))^2+1)/b^2*2^(1/2)*(exp(I*(b*x+a))/(exp(I*(b*x+a))^2+1))^(1/2)/exp(I*(b*x+a))-2*I/b^2*(-2*(exp(I*(b*x+a))^2+1)/((exp(I*(b*x+a))^2+1)*exp(I*(b*x+a)))^(1/2)+I*(-I*(exp(I*(b*x+a))+I))^(1/2)*2^(1/2)*(I*(exp(I*(b*x+a))-I))^(1/2)*(I*exp(I*(b*x+a)))^(1/2)/(exp(I*(b*x+a))^3+exp(I*(b*x+a)))^(1/2)*(-2*I*EllipticE((-I*(exp(I*(b*x+a))+I))^(1/2),1/2*2^(1/2))+I*EllipticF((-I*(exp(I*(b*x+a))+I))^(1/2),1/2*2^(1/2))))*2^(1/2)*(exp(I*(b*x+a))/(exp(I*(b*x+a))^2+1))^(1/2)*((exp(I*(b*x+a))^2+1)*exp(I*(b*x+a)))^(1/2)/exp(I*(b*x+a))","C"
341,0,0,92,0.048000," ","int(x*sin(b*x+a)/sec(b*x+a)^(1/2),x)","\int \frac{x \sin \left(b x +a \right)}{\sqrt{\sec \left(b x +a \right)}}\, dx"," ",0,"int(x*sin(b*x+a)/sec(b*x+a)^(1/2),x)","F"
342,0,0,92,0.046000," ","int(x*sin(b*x+a)/sec(b*x+a)^(3/2),x)","\int \frac{x \sin \left(b x +a \right)}{\sec \left(b x +a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*sin(b*x+a)/sec(b*x+a)^(3/2),x)","F"
343,0,0,111,0.045000," ","int(x*sin(b*x+a)/sec(b*x+a)^(5/2),x)","\int \frac{x \sin \left(b x +a \right)}{\sec \left(b x +a \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*sin(b*x+a)/sec(b*x+a)^(5/2),x)","F"
344,0,0,104,0.056000," ","int(x*cos(b*x+a)*sin(b*x+a)^(5/2),x)","\int x \cos \left(b x +a \right) \left(\sin^{\frac{5}{2}}\left(b x +a \right)\right)\, dx"," ",0,"int(x*cos(b*x+a)*sin(b*x+a)^(5/2),x)","F"
345,0,0,85,0.046000," ","int(x*cos(b*x+a)*sin(b*x+a)^(3/2),x)","\int x \cos \left(b x +a \right) \left(\sin^{\frac{3}{2}}\left(b x +a \right)\right)\, dx"," ",0,"int(x*cos(b*x+a)*sin(b*x+a)^(3/2),x)","F"
346,0,0,85,0.041000," ","int(x*cos(b*x+a)*sin(b*x+a)^(1/2),x)","\int x \cos \left(b x +a \right) \left(\sqrt{\sin}\left(b x +a \right)\right)\, dx"," ",0,"int(x*cos(b*x+a)*sin(b*x+a)^(1/2),x)","F"
347,1,308,66,0.115000," ","int(x*cos(b*x+a)/sin(b*x+a)^(1/2),x)","-\frac{i \left(b x +2 i\right) \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right) \sqrt{2}\, {\mathrm e}^{-i \left(b x +a \right)}}{b^{2} \sqrt{-i \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right) {\mathrm e}^{-i \left(b x +a \right)}}}-\frac{2 \left(\frac{2 i \left(i-i {\mathrm e}^{2 i \left(b x +a \right)}\right)}{\sqrt{{\mathrm e}^{i \left(b x +a \right)} \left(i-i {\mathrm e}^{2 i \left(b x +a \right)}\right)}}-\frac{\sqrt{{\mathrm e}^{i \left(b x +a \right)}+1}\, \sqrt{-2 \,{\mathrm e}^{i \left(b x +a \right)}+2}\, \sqrt{-{\mathrm e}^{i \left(b x +a \right)}}\, \left(-2 \EllipticE \left(\sqrt{{\mathrm e}^{i \left(b x +a \right)}+1}, \frac{\sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{{\mathrm e}^{i \left(b x +a \right)}+1}, \frac{\sqrt{2}}{2}\right)\right)}{\sqrt{-i {\mathrm e}^{3 i \left(b x +a \right)}+i {\mathrm e}^{i \left(b x +a \right)}}}\right) \sqrt{2}\, \sqrt{-i \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right) {\mathrm e}^{i \left(b x +a \right)}}\, {\mathrm e}^{-i \left(b x +a \right)}}{b^{2} \sqrt{-i \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right) {\mathrm e}^{-i \left(b x +a \right)}}}"," ",0,"-I*(b*x+2*I)*(exp(I*(b*x+a))^2-1)/b^2*2^(1/2)/(-I*(exp(I*(b*x+a))^2-1)/exp(I*(b*x+a)))^(1/2)/exp(I*(b*x+a))-2/b^2*(2*I*(I-I*exp(I*(b*x+a))^2)/(exp(I*(b*x+a))*(I-I*exp(I*(b*x+a))^2))^(1/2)-(exp(I*(b*x+a))+1)^(1/2)*(-2*exp(I*(b*x+a))+2)^(1/2)*(-exp(I*(b*x+a)))^(1/2)/(-I*exp(I*(b*x+a))^3+I*exp(I*(b*x+a)))^(1/2)*(-2*EllipticE((exp(I*(b*x+a))+1)^(1/2),1/2*2^(1/2))+EllipticF((exp(I*(b*x+a))+1)^(1/2),1/2*2^(1/2))))*2^(1/2)/(-I*(exp(I*(b*x+a))^2-1)/exp(I*(b*x+a)))^(1/2)*(-I*(exp(I*(b*x+a))^2-1)*exp(I*(b*x+a)))^(1/2)/exp(I*(b*x+a))","C"
348,0,0,66,0.040000," ","int(x*cos(b*x+a)/sin(b*x+a)^(3/2),x)","\int \frac{x \cos \left(b x +a \right)}{\sin \left(b x +a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*cos(b*x+a)/sin(b*x+a)^(3/2),x)","F"
349,0,0,85,0.042000," ","int(x*cos(b*x+a)/sin(b*x+a)^(5/2),x)","\int \frac{x \cos \left(b x +a \right)}{\sin \left(b x +a \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*cos(b*x+a)/sin(b*x+a)^(5/2),x)","F"
350,0,0,85,0.043000," ","int(x*cos(b*x+a)/sin(b*x+a)^(7/2),x)","\int \frac{x \cos \left(b x +a \right)}{\sin \left(b x +a \right)^{\frac{7}{2}}}\, dx"," ",0,"int(x*cos(b*x+a)/sin(b*x+a)^(7/2),x)","F"
351,0,0,104,0.043000," ","int(x*cos(b*x+a)/sin(b*x+a)^(9/2),x)","\int \frac{x \cos \left(b x +a \right)}{\sin \left(b x +a \right)^{\frac{9}{2}}}\, dx"," ",0,"int(x*cos(b*x+a)/sin(b*x+a)^(9/2),x)","F"
352,0,0,120,0.076000," ","int(x*cos(b*x+a)*csc(b*x+a)^(9/2),x)","\int x \cos \left(b x +a \right) \left(\csc^{\frac{9}{2}}\left(b x +a \right)\right)\, dx"," ",0,"int(x*cos(b*x+a)*csc(b*x+a)^(9/2),x)","F"
353,0,0,101,0.060000," ","int(x*cos(b*x+a)*csc(b*x+a)^(7/2),x)","\int x \cos \left(b x +a \right) \left(\csc^{\frac{7}{2}}\left(b x +a \right)\right)\, dx"," ",0,"int(x*cos(b*x+a)*csc(b*x+a)^(7/2),x)","F"
354,0,0,101,0.064000," ","int(x*cos(b*x+a)*csc(b*x+a)^(5/2),x)","\int x \cos \left(b x +a \right) \left(\csc^{\frac{5}{2}}\left(b x +a \right)\right)\, dx"," ",0,"int(x*cos(b*x+a)*csc(b*x+a)^(5/2),x)","F"
355,0,0,82,0.061000," ","int(x*cos(b*x+a)*csc(b*x+a)^(3/2),x)","\int x \cos \left(b x +a \right) \left(\csc^{\frac{3}{2}}\left(b x +a \right)\right)\, dx"," ",0,"int(x*cos(b*x+a)*csc(b*x+a)^(3/2),x)","F"
356,1,308,82,0.125000," ","int(x*cos(b*x+a)*csc(b*x+a)^(1/2),x)","-\frac{i \left(b x +2 i\right) \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right) \sqrt{2}\, \sqrt{\frac{i {\mathrm e}^{i \left(b x +a \right)}}{{\mathrm e}^{2 i \left(b x +a \right)}-1}}\, {\mathrm e}^{-i \left(b x +a \right)}}{b^{2}}-\frac{2 \left(-\frac{2 i \left(-i+i {\mathrm e}^{2 i \left(b x +a \right)}\right)}{\sqrt{{\mathrm e}^{i \left(b x +a \right)} \left(-i+i {\mathrm e}^{2 i \left(b x +a \right)}\right)}}-\frac{\sqrt{{\mathrm e}^{i \left(b x +a \right)}+1}\, \sqrt{-2 \,{\mathrm e}^{i \left(b x +a \right)}+2}\, \sqrt{-{\mathrm e}^{i \left(b x +a \right)}}\, \left(-2 \EllipticE \left(\sqrt{{\mathrm e}^{i \left(b x +a \right)}+1}, \frac{\sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{{\mathrm e}^{i \left(b x +a \right)}+1}, \frac{\sqrt{2}}{2}\right)\right)}{\sqrt{i {\mathrm e}^{3 i \left(b x +a \right)}-i {\mathrm e}^{i \left(b x +a \right)}}}\right) \sqrt{2}\, \sqrt{\frac{i {\mathrm e}^{i \left(b x +a \right)}}{{\mathrm e}^{2 i \left(b x +a \right)}-1}}\, \sqrt{i \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right) {\mathrm e}^{i \left(b x +a \right)}}\, {\mathrm e}^{-i \left(b x +a \right)}}{b^{2}}"," ",0,"-I*(b*x+2*I)*(exp(I*(b*x+a))^2-1)/b^2*2^(1/2)*(I*exp(I*(b*x+a))/(exp(I*(b*x+a))^2-1))^(1/2)/exp(I*(b*x+a))-2/b^2*(-2*I*(-I+I*exp(I*(b*x+a))^2)/(exp(I*(b*x+a))*(-I+I*exp(I*(b*x+a))^2))^(1/2)-(exp(I*(b*x+a))+1)^(1/2)*(-2*exp(I*(b*x+a))+2)^(1/2)*(-exp(I*(b*x+a)))^(1/2)/(I*exp(I*(b*x+a))^3-I*exp(I*(b*x+a)))^(1/2)*(-2*EllipticE((exp(I*(b*x+a))+1)^(1/2),1/2*2^(1/2))+EllipticF((exp(I*(b*x+a))+1)^(1/2),1/2*2^(1/2))))*2^(1/2)*(I*exp(I*(b*x+a))/(exp(I*(b*x+a))^2-1))^(1/2)*(I*(exp(I*(b*x+a))^2-1)*exp(I*(b*x+a)))^(1/2)/exp(I*(b*x+a))","C"
357,0,0,101,0.053000," ","int(x*cos(b*x+a)/csc(b*x+a)^(1/2),x)","\int \frac{x \cos \left(b x +a \right)}{\sqrt{\csc \left(b x +a \right)}}\, dx"," ",0,"int(x*cos(b*x+a)/csc(b*x+a)^(1/2),x)","F"
358,0,0,101,0.052000," ","int(x*cos(b*x+a)/csc(b*x+a)^(3/2),x)","\int \frac{x \cos \left(b x +a \right)}{\csc \left(b x +a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*cos(b*x+a)/csc(b*x+a)^(3/2),x)","F"
359,0,0,120,0.053000," ","int(x*cos(b*x+a)/csc(b*x+a)^(5/2),x)","\int \frac{x \cos \left(b x +a \right)}{\csc \left(b x +a \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*cos(b*x+a)/csc(b*x+a)^(5/2),x)","F"
360,1,26,25,0.055000," ","int(x*csc(x)*sin(3*x),x)","4 x \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{3 x^{2}}{2}-\left(\sin^{2}\left(x \right)\right)"," ",0,"4*x*(1/2*cos(x)*sin(x)+1/2*x)-3/2*x^2-sin(x)^2","A"
361,1,260,123,0.078000," ","int((d*x+c)^4*csc(x)*sin(3*x),x)","4 d^{4} \left(x^{4} \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)+x^{3} \left(\cos^{2}\left(x \right)\right)-3 x^{2} \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{3 x \left(\cos^{2}\left(x \right)\right)}{2}+\frac{3 \cos \left(x \right) \sin \left(x \right)}{4}+\frac{3 x}{4}+x^{3}-\frac{2 x^{5}}{5}\right)+16 d^{3} c \left(x^{3} \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)+\frac{3 x^{2} \left(\cos^{2}\left(x \right)\right)}{4}-\frac{3 x \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)}{2}+\frac{3 x^{2}}{8}+\frac{3 \left(\sin^{2}\left(x \right)\right)}{8}-\frac{3 x^{4}}{8}\right)+24 c^{2} d^{2} \left(x^{2} \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)+\frac{x \left(\cos^{2}\left(x \right)\right)}{2}-\frac{\cos \left(x \right) \sin \left(x \right)}{4}-\frac{x}{4}-\frac{x^{3}}{3}\right)-\frac{d^{4} x^{5}}{5}+16 c^{3} d \left(x \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{x^{2}}{4}-\frac{\left(\sin^{2}\left(x \right)\right)}{4}\right)-c \,d^{3} x^{4}+4 c^{4} \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-2 c^{2} d^{2} x^{3}-2 c^{3} d \,x^{2}-c^{4} x"," ",0,"4*d^4*(x^4*(1/2*cos(x)*sin(x)+1/2*x)+x^3*cos(x)^2-3*x^2*(1/2*cos(x)*sin(x)+1/2*x)-3/2*x*cos(x)^2+3/4*cos(x)*sin(x)+3/4*x+x^3-2/5*x^5)+16*d^3*c*(x^3*(1/2*cos(x)*sin(x)+1/2*x)+3/4*x^2*cos(x)^2-3/2*x*(1/2*cos(x)*sin(x)+1/2*x)+3/8*x^2+3/8*sin(x)^2-3/8*x^4)+24*c^2*d^2*(x^2*(1/2*cos(x)*sin(x)+1/2*x)+1/2*x*cos(x)^2-1/4*cos(x)*sin(x)-1/4*x-1/3*x^3)-1/5*d^4*x^5+16*c^3*d*(x*(1/2*cos(x)*sin(x)+1/2*x)-1/4*x^2-1/4*sin(x)^2)-c*d^3*x^4+4*c^4*(1/2*cos(x)*sin(x)+1/2*x)-2*c^2*d^2*x^3-2*c^3*d*x^2-c^4*x","B"
362,1,179,101,0.058000," ","int((d*x+c)^3*csc(x)*sin(3*x),x)","4 d^{3} \left(x^{3} \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)+\frac{3 x^{2} \left(\cos^{2}\left(x \right)\right)}{4}-\frac{3 x \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)}{2}+\frac{3 x^{2}}{8}+\frac{3 \left(\sin^{2}\left(x \right)\right)}{8}-\frac{3 x^{4}}{8}\right)+12 c \,d^{2} \left(x^{2} \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)+\frac{x \left(\cos^{2}\left(x \right)\right)}{2}-\frac{\cos \left(x \right) \sin \left(x \right)}{4}-\frac{x}{4}-\frac{x^{3}}{3}\right)+12 c^{2} d \left(x \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{x^{2}}{4}-\frac{\left(\sin^{2}\left(x \right)\right)}{4}\right)-\frac{d^{3} x^{4}}{4}+4 c^{3} \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-c \,d^{2} x^{3}-\frac{3 c^{2} d \,x^{2}}{2}-c^{3} x"," ",0,"4*d^3*(x^3*(1/2*cos(x)*sin(x)+1/2*x)+3/4*x^2*cos(x)^2-3/2*x*(1/2*cos(x)*sin(x)+1/2*x)+3/8*x^2+3/8*sin(x)^2-3/8*x^4)+12*c*d^2*(x^2*(1/2*cos(x)*sin(x)+1/2*x)+1/2*x*cos(x)^2-1/4*cos(x)*sin(x)-1/4*x-1/3*x^3)+12*c^2*d*(x*(1/2*cos(x)*sin(x)+1/2*x)-1/4*x^2-1/4*sin(x)^2)-1/4*d^3*x^4+4*c^3*(1/2*cos(x)*sin(x)+1/2*x)-c*d^2*x^3-3/2*c^2*d*x^2-c^3*x","A"
363,1,107,65,0.056000," ","int((d*x+c)^2*csc(x)*sin(3*x),x)","4 d^{2} \left(x^{2} \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)+\frac{x \left(\cos^{2}\left(x \right)\right)}{2}-\frac{\cos \left(x \right) \sin \left(x \right)}{4}-\frac{x}{4}-\frac{x^{3}}{3}\right)+8 c d \left(x \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{x^{2}}{4}-\frac{\left(\sin^{2}\left(x \right)\right)}{4}\right)+4 c^{2} \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{d^{2} x^{3}}{3}-c d \,x^{2}-c^{2} x"," ",0,"4*d^2*(x^2*(1/2*cos(x)*sin(x)+1/2*x)+1/2*x*cos(x)^2-1/4*cos(x)*sin(x)-1/4*x-1/3*x^3)+8*c*d*(x*(1/2*cos(x)*sin(x)+1/2*x)-1/4*x^2-1/4*sin(x)^2)+4*c^2*(1/2*cos(x)*sin(x)+1/2*x)-1/3*d^2*x^3-c*d*x^2-c^2*x","A"
364,1,52,35,0.056000," ","int((d*x+c)*csc(x)*sin(3*x),x)","4 d \left(x \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{x^{2}}{4}-\frac{\left(\sin^{2}\left(x \right)\right)}{4}\right)+4 c \left(\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{d \,x^{2}}{2}-c x"," ",0,"4*d*(x*(1/2*cos(x)*sin(x)+1/2*x)-1/4*x^2-1/4*sin(x)^2)+4*c*(1/2*cos(x)*sin(x)+1/2*x)-1/2*d*x^2-c*x","A"
365,1,58,57,0.056000," ","int(csc(x)*sin(3*x)/(d*x+c),x)","\frac{2 \Ci \left(\frac{2 c}{d}+2 x \right) \cos \left(\frac{2 c}{d}\right)}{d}+\frac{\ln \left(d x +c \right)}{d}+\frac{2 \Si \left(\frac{2 c}{d}+2 x \right) \sin \left(\frac{2 c}{d}\right)}{d}"," ",0,"2*Ci(2*c/d+2*x)*cos(2*c/d)/d+ln(d*x+c)/d+2*Si(2*c/d+2*x)*sin(2*c/d)/d","A"
366,1,82,78,0.054000," ","int(csc(x)*sin(3*x)/(d*x+c)^2,x)","-\frac{2 \cos \left(2 x \right)}{\left(d x +c \right) d}-\frac{2 \left(\frac{2 \Si \left(\frac{2 c}{d}+2 x \right) \cos \left(\frac{2 c}{d}\right)}{d}-\frac{2 \Ci \left(\frac{2 c}{d}+2 x \right) \sin \left(\frac{2 c}{d}\right)}{d}\right)}{d}-\frac{1}{d \left(d x +c \right)}"," ",0,"-2*cos(2*x)/(d*x+c)/d-2*(2*Si(2*c/d+2*x)*cos(2*c/d)/d-2*Ci(2*c/d+2*x)*sin(2*c/d)/d)/d-1/d/(d*x+c)","A"
367,1,104,95,0.058000," ","int(csc(x)*sin(3*x)/(d*x+c)^3,x)","-\frac{\cos \left(2 x \right)}{\left(d x +c \right)^{2} d}-\frac{-\frac{2 \sin \left(2 x \right)}{\left(d x +c \right) d}+\frac{\frac{4 \Si \left(\frac{2 c}{d}+2 x \right) \sin \left(\frac{2 c}{d}\right)}{d}+\frac{4 \Ci \left(\frac{2 c}{d}+2 x \right) \cos \left(\frac{2 c}{d}\right)}{d}}{d}}{d}-\frac{1}{2 d \left(d x +c \right)^{2}}"," ",0,"-cos(2*x)/(d*x+c)^2/d-(-2*sin(2*x)/(d*x+c)/d+2*(2*Si(2*c/d+2*x)*sin(2*c/d)/d+2*Ci(2*c/d+2*x)*cos(2*c/d)/d)/d)/d-1/2/d/(d*x+c)^2","A"
368,1,1000,190,0.056000," ","int((d*x+c)^4*csc(b*x+a)*sin(3*b*x+3*a),x)","-c^{4} x -\frac{d^{4} x^{5}}{5}+\frac{4 c^{4} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{b}-2 c^{3} d \,x^{2}-2 c^{2} d^{2} x^{3}-c \,d^{3} x^{4}+\frac{4 d^{4} \left(\left(b x +a \right)^{4} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\left(b x +a \right)^{3} \left(\cos^{2}\left(b x +a \right)\right)-3 \left(b x +a \right)^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{3 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}+\frac{3 \cos \left(b x +a \right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{4}+\frac{3 a}{4}+\left(b x +a \right)^{3}-\frac{2 \left(b x +a \right)^{5}}{5}-4 a \left(\left(b x +a \right)^{3} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{3 \left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{4}-\frac{3 \left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{2}+\frac{3 \left(b x +a \right)^{2}}{8}+\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{8}-\frac{3 \left(b x +a \right)^{4}}{8}\right)+6 a^{2} \left(\left(b x +a \right)^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}-\frac{b x}{4}-\frac{a}{4}-\frac{\left(b x +a \right)^{3}}{3}\right)-4 a^{3} \left(\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)+a^{4} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{5}}+\frac{16 c^{3} d \left(\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}-a \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{2}}+\frac{24 c^{2} d^{2} \left(\left(b x +a \right)^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}-\frac{b x}{4}-\frac{a}{4}-\frac{\left(b x +a \right)^{3}}{3}-2 a \left(\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)+a^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{3}}+\frac{16 d^{3} c \left(\left(b x +a \right)^{3} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{3 \left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{4}-\frac{3 \left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{2}+\frac{3 \left(b x +a \right)^{2}}{8}+\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{8}-\frac{3 \left(b x +a \right)^{4}}{8}-3 a \left(\left(b x +a \right)^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}-\frac{b x}{4}-\frac{a}{4}-\frac{\left(b x +a \right)^{3}}{3}\right)+3 a^{2} \left(\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)-a^{3} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{4}}"," ",0,"-c^4*x-1/5*d^4*x^5+4*c^4/b*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-2*c^3*d*x^2-2*c^2*d^2*x^3-c*d^3*x^4+4*d^4/b^5*((b*x+a)^4*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+(b*x+a)^3*cos(b*x+a)^2-3*(b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-3/2*(b*x+a)*cos(b*x+a)^2+3/4*cos(b*x+a)*sin(b*x+a)+3/4*b*x+3/4*a+(b*x+a)^3-2/5*(b*x+a)^5-4*a*((b*x+a)^3*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/4*(b*x+a)^2*cos(b*x+a)^2-3/2*(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/8*(b*x+a)^2+3/8*sin(b*x+a)^2-3/8*(b*x+a)^4)+6*a^2*((b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+1/2*(b*x+a)*cos(b*x+a)^2-1/4*cos(b*x+a)*sin(b*x+a)-1/4*b*x-1/4*a-1/3*(b*x+a)^3)-4*a^3*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+a^4*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))+16*c^3*d/b^2*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2-a*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))+24*c^2*d^2/b^3*((b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+1/2*(b*x+a)*cos(b*x+a)^2-1/4*cos(b*x+a)*sin(b*x+a)-1/4*b*x-1/4*a-1/3*(b*x+a)^3-2*a*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+a^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))+16*d^3*c/b^4*((b*x+a)^3*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/4*(b*x+a)^2*cos(b*x+a)^2-3/2*(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/8*(b*x+a)^2+3/8*sin(b*x+a)^2-3/8*(b*x+a)^4-3*a*((b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+1/2*(b*x+a)*cos(b*x+a)^2-1/4*cos(b*x+a)*sin(b*x+a)-1/4*b*x-1/4*a-1/3*(b*x+a)^3)+3*a^2*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)-a^3*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))","B"
369,1,580,157,0.036000," ","int((d*x+c)^3*csc(b*x+a)*sin(3*b*x+3*a),x)","-c^{3} x -\frac{d^{3} x^{4}}{4}+\frac{4 c^{3} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{b}-\frac{3 c^{2} d \,x^{2}}{2}-c \,d^{2} x^{3}+\frac{4 d^{3} \left(\left(b x +a \right)^{3} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{3 \left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{4}-\frac{3 \left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{2}+\frac{3 \left(b x +a \right)^{2}}{8}+\frac{3 \left(\sin^{2}\left(b x +a \right)\right)}{8}-\frac{3 \left(b x +a \right)^{4}}{8}-3 a \left(\left(b x +a \right)^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}-\frac{b x}{4}-\frac{a}{4}-\frac{\left(b x +a \right)^{3}}{3}\right)+3 a^{2} \left(\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)-a^{3} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{4}}+\frac{12 c^{2} d \left(\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}-a \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{2}}+\frac{12 c \,d^{2} \left(\left(b x +a \right)^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}-\frac{b x}{4}-\frac{a}{4}-\frac{\left(b x +a \right)^{3}}{3}-2 a \left(\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)+a^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{3}}"," ",0,"-c^3*x-1/4*d^3*x^4+4*c^3/b*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-3/2*c^2*d*x^2-c*d^2*x^3+4*d^3/b^4*((b*x+a)^3*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/4*(b*x+a)^2*cos(b*x+a)^2-3/2*(b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/8*(b*x+a)^2+3/8*sin(b*x+a)^2-3/8*(b*x+a)^4-3*a*((b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+1/2*(b*x+a)*cos(b*x+a)^2-1/4*cos(b*x+a)*sin(b*x+a)-1/4*b*x-1/4*a-1/3*(b*x+a)^3)+3*a^2*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)-a^3*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))+12*c^2*d/b^2*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2-a*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))+12*c*d^2/b^3*((b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+1/2*(b*x+a)*cos(b*x+a)^2-1/4*cos(b*x+a)*sin(b*x+a)-1/4*b*x-1/4*a-1/3*(b*x+a)^3-2*a*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+a^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))","B"
370,1,294,104,0.033000," ","int((d*x+c)^2*csc(b*x+a)*sin(3*b*x+3*a),x)","-c^{2} x -\frac{d^{2} x^{3}}{3}+\frac{4 c^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{b}-c d \,x^{2}+\frac{4 d^{2} \left(\left(b x +a \right)^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)+\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{2}-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{4}-\frac{b x}{4}-\frac{a}{4}-\frac{\left(b x +a \right)^{3}}{3}-2 a \left(\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)+a^{2} \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{3}}+\frac{8 c d \left(\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}-a \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{2}}"," ",0,"-c^2*x-1/3*d^2*x^3+4*c^2/b*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-c*d*x^2+4*d^2/b^3*((b*x+a)^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+1/2*(b*x+a)*cos(b*x+a)^2-1/4*cos(b*x+a)*sin(b*x+a)-1/4*b*x-1/4*a-1/3*(b*x+a)^3-2*a*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+a^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))+8*c*d/b^2*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2-a*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))","B"
371,1,119,60,0.032000," ","int((d*x+c)*csc(b*x+a)*sin(3*b*x+3*a),x)","-c x -\frac{d \,x^{2}}{2}+\frac{4 c \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)}{b}+\frac{4 d \left(\left(b x +a \right) \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}-a \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)\right)}{b^{2}}"," ",0,"-c*x-1/2*d*x^2+4*c/b*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+4*d/b^2*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2-a*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))","A"
372,1,116,71,0.040000," ","int(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c),x)","-\frac{\ln \left(d x +c \right)}{d}+\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{2 \ln \left(\left(b x +a \right) d -d a +c b \right)}{d}"," ",0,"-ln(d*x+c)/d+2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d+2*ln((b*x+a)*d-d*a+c*b)/d","A"
373,1,169,102,0.043000," ","int(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^2,x)","\frac{1}{d \left(d x +c \right)}+\frac{b^{2} \left(-\frac{2 \cos \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{2 \left(\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}-\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}\right)}{d}\right)-\frac{2 b^{2}}{\left(\left(b x +a \right) d -d a +c b \right) d}}{b}"," ",0,"1/d/(d*x+c)+4/b*(1/4*b^2*(-2*cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d-2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d)/d)-1/2*b^2/((b*x+a)*d-d*a+c*b)/d)","A"
374,1,207,132,0.041000," ","int(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^3,x)","\frac{1}{2 d \left(d x +c \right)^{2}}+\frac{b^{3} \left(-\frac{\cos \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\frac{-\frac{2 \sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{4 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}+\frac{4 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}}{d}}{d}\right)-\frac{b^{3}}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}}{b}"," ",0,"1/2/d/(d*x+c)^2+4/b*(1/4*b^3*(-cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d-(-2*sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d+2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d)/d)/d)-1/4*b^3/((b*x+a)*d-d*a+c*b)^2/d)","A"
375,1,243,193,0.040000," ","int(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^4,x)","\frac{1}{3 d \left(d x +c \right)^{3}}+\frac{b^{4} \left(-\frac{2 \cos \left(2 b x +2 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}-\frac{2 \left(-\frac{\sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{2 \cos \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{2 \left(\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}-\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}\right)}{d}}{d}\right)}{3 d}\right)-\frac{2 b^{4}}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}}{b}"," ",0,"1/3/d/(d*x+c)^3+4/b*(1/4*b^4*(-2/3*cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^3/d-2/3*(-sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d+(-2*cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d-2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d)/d)/d)/d)-1/6*b^4/((b*x+a)*d-d*a+c*b)^3/d)","A"
376,1,849,237,0.121000," ","int((d*x+c)^3*csc(b*x+a)^2*sin(3*b*x+3*a),x)","-\frac{18 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{18 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}+\frac{18 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{18 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{18 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{18 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{18 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{18 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{2 \left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}+3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x +6 i b^{2} c \,d^{2} x +b^{3} c^{3}+3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b -6 i d^{3}\right) {\mathrm e}^{i \left(b x +a \right)}}{b^{4}}+\frac{2 \left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}-3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x -6 i b^{2} c \,d^{2} x +b^{3} c^{3}-3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b +6 i d^{3}\right) {\mathrm e}^{-i \left(b x +a \right)}}{b^{4}}-\frac{6 c^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{9 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}+\frac{9 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}-\frac{18 c \,d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{18 c^{2} d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{9 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{9 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{9 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{9 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{9 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}+\frac{9 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{9 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{9 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{9 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{9 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{3}}{b^{4}}+\frac{6 d^{3} a^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"-18*I*d^3*polylog(4,-exp(I*(b*x+a)))/b^4+18*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x-18*I/b^2*c*d^2*polylog(2,exp(I*(b*x+a)))*x+18*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4-18/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+18/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))+18/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x-18/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x+2*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3+3*I*b^2*d^3*x^2-6*b*d^3*x+6*I*b^2*c*d^2*x-6*c*d^2*b+3*I*b^2*c^2*d-6*I*d^3)/b^4*exp(I*(b*x+a))+2*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3-3*I*b^2*d^3*x^2-6*b*d^3*x-6*I*b^2*c*d^2*x-6*c*d^2*b-3*I*b^2*c^2*d+6*I*d^3)/b^4*exp(-I*(b*x+a))-6/b*c^3*arctanh(exp(I*(b*x+a)))+6/b^4*d^3*a^3*arctanh(exp(I*(b*x+a)))-9/b^2*c^2*d*ln(exp(I*(b*x+a))+1)*a+9/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))+1)-3/b^4*d^3*ln(exp(I*(b*x+a))+1)*a^3-18/b^3*c*d^2*a^2*arctanh(exp(I*(b*x+a)))+18/b^2*c^2*d*a*arctanh(exp(I*(b*x+a)))-9/b*c^2*d*ln(exp(I*(b*x+a))+1)*x+9/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+9/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-9/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+9/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2-9/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2+3/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3-3/b*d^3*ln(exp(I*(b*x+a))+1)*x^3-9*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2+9*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2-9*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))+9*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))","B"
377,1,481,160,0.204000," ","int((d*x+c)^2*csc(b*x+a)^2*sin(3*b*x+3*a),x)","\frac{2 \left(d^{2} x^{2} b^{2}+2 b^{2} c d x +2 i b \,d^{2} x +b^{2} c^{2}+2 i b c d -2 d^{2}\right) {\mathrm e}^{i \left(b x +a \right)}}{b^{3}}+\frac{2 \left(d^{2} x^{2} b^{2}+2 b^{2} c d x -2 i b \,d^{2} x +b^{2} c^{2}-2 i b c d -2 d^{2}\right) {\mathrm e}^{-i \left(b x +a \right)}}{b^{3}}+\frac{12 c d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{6 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 c^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{6 d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{3 d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{b^{3}}+\frac{6 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{3 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}-\frac{6 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{6 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{6 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{6 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}-\frac{6 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"2*(d^2*x^2*b^2+2*b^2*c*d*x+b^2*c^2+2*I*b*d^2*x-2*d^2+2*I*b*c*d)/b^3*exp(I*(b*x+a))+2*(d^2*x^2*b^2+2*b^2*c*d*x+b^2*c^2-2*I*b*d^2*x-2*d^2-2*I*b*c*d)/b^3*exp(-I*(b*x+a))+12/b^2*c*d*a*arctanh(exp(I*(b*x+a)))-6*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))-6*I/b^2*polylog(2,exp(I*(b*x+a)))*d^2*x-6/b*c^2*arctanh(exp(I*(b*x+a)))-6/b^3*d^2*a^2*arctanh(exp(I*(b*x+a)))-3/b*d^2*ln(exp(I*(b*x+a))+1)*x^2+3/b^3*d^2*ln(exp(I*(b*x+a))+1)*a^2+6*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))+3/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-3/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2+6*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x+6/b*c*d*ln(1-exp(I*(b*x+a)))*x+6/b^2*c*d*ln(1-exp(I*(b*x+a)))*a-6/b*c*d*ln(exp(I*(b*x+a))+1)*x-6/b^2*c*d*ln(exp(I*(b*x+a))+1)*a-6*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+6*d^2*polylog(3,exp(I*(b*x+a)))/b^3","B"
378,1,204,87,0.068000," ","int((d*x+c)*csc(b*x+a)^2*sin(3*b*x+3*a),x)","\frac{3 c \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b}+\frac{3 d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{3 d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{3 d a \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b^{2}}+\frac{3 i d \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{3 i d \dilog \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}+\frac{4 c \cos \left(b x +a \right)}{b}+\frac{4 d \cos \left(b x +a \right) x}{b}-\frac{4 d \sin \left(b x +a \right)}{b^{2}}"," ",0,"3/b*c*ln(csc(b*x+a)-cot(b*x+a))+3/b*d*ln(1-exp(I*(b*x+a)))*x-3/b*d*ln(exp(I*(b*x+a))+1)*x-3/b^2*d*a*ln(csc(b*x+a)-cot(b*x+a))+3*I*d/b^2*dilog(exp(I*(b*x+a))+1)-3*I*d/b^2*dilog(1-exp(I*(b*x+a)))+3/b^2*d*ln(1-exp(I*(b*x+a)))*a-3/b^2*d*ln(exp(I*(b*x+a))+1)*a+4/b*c*cos(b*x+a)+4/b*d*cos(b*x+a)*x-4*d*sin(b*x+a)/b^2","B"
379,0,0,71,0.280000," ","int(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c),x)","\int \frac{\left(\csc^{2}\left(b x +a \right)\right) \sin \left(3 b x +3 a \right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c),x)","F"
380,0,0,91,0.471000," ","int(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^2,x)","\int \frac{\left(\csc^{2}\left(b x +a \right)\right) \sin \left(3 b x +3 a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^2,x)","F"
381,0,0,114,0.753000," ","int(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^3,x)","\int \frac{\left(\csc^{2}\left(b x +a \right)\right) \sin \left(3 b x +3 a \right)}{\left(d x +c \right)^{3}}\, dx"," ",0,"int(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^3,x)","F"
382,1,956,282,0.128000," ","int((d*x+c)^4*sec(b*x+a)*sin(3*b*x+3*a),x)","\frac{3 c^{2} d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 d^{4} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{3}}+\frac{d^{4} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{4}}{b}+\frac{2 i d^{4} a^{4} x}{b^{4}}-\frac{4 i c^{3} d \,a^{2}}{b^{2}}+\frac{8 i c^{2} d^{2} a^{3}}{b^{3}}-\frac{6 i c \,d^{3} a^{4}}{b^{4}}+\frac{8 c^{3} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{8 c \,d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{12 c^{2} d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i c \,d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{6 i c^{2} d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{c^{4} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{3 d^{4} \polylog \left(5, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{5}}+i c^{4} x -\frac{\left(2 d^{4} x^{4} b^{4}+8 b^{4} c \,d^{3} x^{3}+4 i b^{3} d^{4} x^{3}+12 b^{4} c^{2} d^{2} x^{2}+12 i b^{3} c \,d^{3} x^{2}+8 b^{4} c^{3} d x +12 i b^{3} c^{2} d^{2} x +2 b^{4} c^{4}+4 i b^{3} c^{3} d -6 b^{2} d^{4} x^{2}-12 b^{2} c \,d^{3} x -6 i b \,d^{4} x -6 c^{2} d^{2} b^{2}-6 i b c \,d^{3}+3 d^{4}\right) {\mathrm e}^{2 i \left(b x +a \right)}}{4 b^{5}}-\frac{\left(2 d^{4} x^{4} b^{4}+8 b^{4} c \,d^{3} x^{3}-4 i b^{3} d^{4} x^{3}+12 b^{4} c^{2} d^{2} x^{2}-12 i b^{3} c \,d^{3} x^{2}+8 b^{4} c^{3} d x -12 i b^{3} c^{2} d^{2} x +2 b^{4} c^{4}-4 i b^{3} c^{3} d -6 b^{2} d^{4} x^{2}-12 b^{2} c \,d^{3} x +6 i b \,d^{4} x -6 c^{2} d^{2} b^{2}+6 i b c \,d^{3}+3 d^{4}\right) {\mathrm e}^{-2 i \left(b x +a \right)}}{4 b^{5}}-\frac{2 c^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{i d^{4} x^{5}}{5}+\frac{4 c^{3} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{6 c^{2} d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}+\frac{4 c \,d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}+\frac{6 c \,d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 i d^{4} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{4}}-\frac{2 i d^{4} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b^{2}}+\frac{3 i c \,d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{4}}-\frac{2 i c^{3} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 d^{4} a^{4} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{5}}+\frac{8 i d^{4} a^{5}}{5 b^{5}}-i c \,d^{3} x^{4}-2 i c^{2} d^{2} x^{3}-2 i c^{3} d \,x^{2}-\frac{8 i c \,d^{3} a^{3} x}{b^{3}}+\frac{12 i c^{2} d^{2} a^{2} x}{b^{2}}-\frac{8 i c^{3} d a x}{b}"," ",0,"-3/2*d^4*polylog(5,-exp(2*I*(b*x+a)))/b^5-2/b^5*d^4*a^4*ln(exp(I*(b*x+a)))+8/5*I/b^5*d^4*a^5-I*c*d^3*x^4-2*I*c^2*d^2*x^3-2*I*c^3*d*x^2+3/b^3*c^2*d^2*polylog(3,-exp(2*I*(b*x+a)))+3/b^3*d^4*polylog(3,-exp(2*I*(b*x+a)))*x^2+4/b*c*d^3*ln(1+exp(2*I*(b*x+a)))*x^3+I*c^4*x+1/b*c^4*ln(1+exp(2*I*(b*x+a)))-1/4*(2*d^4*x^4*b^4+4*I*b^3*d^4*x^3+8*b^4*c*d^3*x^3+12*I*b^3*c*d^3*x^2+12*b^4*c^2*d^2*x^2+12*I*b^3*c^2*d^2*x+8*b^4*c^3*d*x+4*I*b^3*c^3*d+2*b^4*c^4-6*b^2*d^4*x^2-6*I*b*d^4*x-12*b^2*c*d^3*x-6*I*b*c*d^3-6*c^2*d^2*b^2+3*d^4)/b^5*exp(2*I*(b*x+a))-1/4*(2*d^4*x^4*b^4-4*I*b^3*d^4*x^3+8*b^4*c*d^3*x^3-12*I*b^3*c*d^3*x^2+12*b^4*c^2*d^2*x^2-12*I*b^3*c^2*d^2*x+8*b^4*c^3*d*x-4*I*b^3*c^3*d+2*b^4*c^4-6*b^2*d^4*x^2+6*I*b*d^4*x-12*b^2*c*d^3*x+6*I*b*c*d^3-6*c^2*d^2*b^2+3*d^4)/b^5*exp(-2*I*(b*x+a))-2/b*c^4*ln(exp(I*(b*x+a)))-1/5*I*d^4*x^5+1/b*d^4*ln(1+exp(2*I*(b*x+a)))*x^4+2*I/b^4*d^4*a^4*x-4*I/b^2*c^3*d*a^2+8*I/b^3*c^2*d^2*a^3-6*I/b^4*c*d^3*a^4+8/b^2*c^3*d*a*ln(exp(I*(b*x+a)))+8/b^4*c*d^3*a^3*ln(exp(I*(b*x+a)))-12/b^3*c^2*d^2*a^2*ln(exp(I*(b*x+a)))-8*I/b^3*c*d^3*a^3*x+12*I/b^2*c^2*d^2*a^2*x-8*I/b*c^3*d*a*x+3*I/b^4*c*d^3*polylog(4,-exp(2*I*(b*x+a)))+3*I/b^4*d^4*polylog(4,-exp(2*I*(b*x+a)))*x-2*I/b^2*d^4*polylog(2,-exp(2*I*(b*x+a)))*x^3-2*I/b^2*c^3*d*polylog(2,-exp(2*I*(b*x+a)))+4/b*c^3*d*ln(1+exp(2*I*(b*x+a)))*x+6/b^3*c*d^3*polylog(3,-exp(2*I*(b*x+a)))*x+6/b*c^2*d^2*ln(1+exp(2*I*(b*x+a)))*x^2-6*I/b^2*c^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x-6*I/b^2*c*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2","B"
383,1,639,219,0.115000," ","int((d*x+c)^3*sec(b*x+a)*sin(3*b*x+3*a),x)","\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{2 b^{3}}+\frac{d^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{3}}{b}+\frac{6 i c \,d^{2} a^{2} x}{b^{2}}-\frac{6 i c^{2} d a x}{b}+\frac{2 d^{3} a^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i a^{4} d^{3}}{2 b^{4}}-i c \,d^{2} x^{3}-\frac{3 i c^{2} d \,x^{2}}{2}+\frac{3 c \,d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{3 i d^{3} \polylog \left(4, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{4 b^{4}}+\frac{c^{3} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{3 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+i c^{3} x -\frac{i d^{3} x^{4}}{4}-\frac{2 c^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{\left(4 d^{3} x^{3} b^{3}+12 b^{3} c \,d^{2} x^{2}+6 i b^{2} d^{3} x^{2}+12 b^{3} c^{2} d x +12 i b^{2} c \,d^{2} x +4 b^{3} c^{3}+6 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b -3 i d^{3}\right) {\mathrm e}^{2 i \left(b x +a \right)}}{8 b^{4}}-\frac{\left(4 d^{3} x^{3} b^{3}+12 b^{3} c \,d^{2} x^{2}-6 i b^{2} d^{3} x^{2}+12 b^{3} c^{2} d x -12 i b^{2} c \,d^{2} x +4 b^{3} c^{3}-6 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b +3 i d^{3}\right) {\mathrm e}^{-2 i \left(b x +a \right)}}{8 b^{4}}-\frac{6 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i c^{2} d \,a^{2}}{b^{2}}-\frac{2 i a^{3} d^{3} x}{b^{3}}+\frac{4 i c \,d^{2} a^{3}}{b^{3}}+\frac{6 c^{2} d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}-\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{3 c^{2} d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}+\frac{3 c \,d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}"," ",0,"6*I/b^2*c*d^2*a^2*x-6*I/b*c^2*d*a*x+3/4*I*d^3*polylog(4,-exp(2*I*(b*x+a)))/b^4+I*c^3*x+1/b*c^3*ln(1+exp(2*I*(b*x+a)))+2/b^4*d^3*a^3*ln(exp(I*(b*x+a)))-3/2*I/b^4*a^4*d^3-I*c*d^2*x^3-3/2*I*c^2*d*x^2-1/8*(4*d^3*x^3*b^3+6*I*b^2*d^3*x^2+12*b^3*c*d^2*x^2+12*I*b^2*c*d^2*x+12*b^3*c^2*d*x+6*I*b^2*c^2*d+4*b^3*c^3-6*b*d^3*x-3*I*d^3-6*c*d^2*b)/b^4*exp(2*I*(b*x+a))-1/8*(4*d^3*x^3*b^3-6*I*b^2*d^3*x^2+12*b^3*c*d^2*x^2-12*I*b^2*c*d^2*x+12*b^3*c^2*d*x-6*I*b^2*c^2*d+4*b^3*c^3-6*b*d^3*x+3*I*d^3-6*c*d^2*b)/b^4*exp(-2*I*(b*x+a))+3/2/b^3*c*d^2*polylog(3,-exp(2*I*(b*x+a)))+3/2/b^3*d^3*polylog(3,-exp(2*I*(b*x+a)))*x-1/4*I*d^3*x^4-2/b*c^3*ln(exp(I*(b*x+a)))-3/2*I/b^2*d^3*polylog(2,-exp(2*I*(b*x+a)))*x^2-3/2*I/b^2*c^2*d*polylog(2,-exp(2*I*(b*x+a)))-6/b^3*c*d^2*a^2*ln(exp(I*(b*x+a)))-3*I/b^2*c^2*d*a^2-2*I/b^3*a^3*d^3*x+4*I/b^3*c*d^2*a^3+6/b^2*c^2*d*a*ln(exp(I*(b*x+a)))+1/b*d^3*ln(1+exp(2*I*(b*x+a)))*x^3-3*I/b^2*polylog(2,-exp(2*I*(b*x+a)))*c*d^2*x+3/b*c^2*d*ln(1+exp(2*I*(b*x+a)))*x+3/b*c*d^2*ln(1+exp(2*I*(b*x+a)))*x^2","B"
384,1,377,161,0.133000," ","int((d*x+c)^2*sec(b*x+a)*sin(3*b*x+3*a),x)","-\frac{i d^{2} x^{3}}{3}+\frac{2 i d^{2} a^{2} x}{b^{2}}+i c^{2} x -\frac{\left(2 d^{2} x^{2} b^{2}+4 b^{2} c d x +2 i b \,d^{2} x +2 b^{2} c^{2}+2 i b c d -d^{2}\right) {\mathrm e}^{2 i \left(b x +a \right)}}{4 b^{3}}-\frac{\left(2 d^{2} x^{2} b^{2}+4 b^{2} c d x -2 i b \,d^{2} x +2 b^{2} c^{2}-2 i b c d -d^{2}\right) {\mathrm e}^{-2 i \left(b x +a \right)}}{4 b^{3}}+\frac{c^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{2 c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{2 d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{2}}+\frac{4 i d^{2} a^{3}}{3 b^{3}}-i c d \,x^{2}+\frac{d^{2} \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x^{2}}{b}-\frac{i c d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b^{2}}+\frac{d^{2} \polylog \left(3, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{4 c d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 c d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{2 i c d \,a^{2}}{b^{2}}-\frac{4 i c d a x}{b}"," ",0,"-1/3*I*d^2*x^3-I/b^2*d^2*polylog(2,-exp(2*I*(b*x+a)))*x+2*I/b^2*d^2*a^2*x-1/4*(2*d^2*x^2*b^2+2*I*b*d^2*x+4*b^2*c*d*x+2*I*b*c*d+2*b^2*c^2-d^2)/b^3*exp(2*I*(b*x+a))-1/4*(2*d^2*x^2*b^2-2*I*b*d^2*x+4*b^2*c*d*x-2*I*b*c*d+2*b^2*c^2-d^2)/b^3*exp(-2*I*(b*x+a))+1/b*c^2*ln(1+exp(2*I*(b*x+a)))-2/b*c^2*ln(exp(I*(b*x+a)))-2/b^3*d^2*a^2*ln(exp(I*(b*x+a)))-I/b^2*c*d*polylog(2,-exp(2*I*(b*x+a)))+I*c^2*x+4/3*I/b^3*d^2*a^3+1/b*d^2*ln(1+exp(2*I*(b*x+a)))*x^2-I*c*d*x^2+1/2*d^2*polylog(3,-exp(2*I*(b*x+a)))/b^3+4/b^2*c*d*a*ln(exp(I*(b*x+a)))+2/b*c*d*ln(1+exp(2*I*(b*x+a)))*x-2*I/b^2*c*d*a^2-4*I/b*c*d*a*x","B"
385,1,177,97,0.310000," ","int((d*x+c)*sec(b*x+a)*sin(3*b*x+3*a),x)","-\frac{i d \,x^{2}}{2}+i c x -\frac{\left(2 b d x +2 c b +i d \right) {\mathrm e}^{2 i \left(b x +a \right)}}{4 b^{2}}-\frac{\left(2 b d x +2 c b -i d \right) {\mathrm e}^{-2 i \left(b x +a \right)}}{4 b^{2}}+\frac{c \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}{b}-\frac{2 c \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{2 i d a x}{b}-\frac{i d \,a^{2}}{b^{2}}+\frac{d \ln \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b}-\frac{i d \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{2 d a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"-1/2*I*d*x^2+I*c*x-1/4*(2*b*d*x+I*d+2*c*b)/b^2*exp(2*I*(b*x+a))-1/4*(2*b*d*x-I*d+2*c*b)/b^2*exp(-2*I*(b*x+a))+1/b*c*ln(1+exp(2*I*(b*x+a)))-2/b*c*ln(exp(I*(b*x+a)))-2*I/b*d*a*x-I/b^2*d*a^2+1/b*d*ln(1+exp(2*I*(b*x+a)))*x-1/2*I*d*polylog(2,-exp(2*I*(b*x+a)))/b^2+2/b^2*d*a*ln(exp(I*(b*x+a)))","A"
386,0,0,79,0.305000," ","int(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c),x)","\int \frac{\sec \left(b x +a \right) \sin \left(3 b x +3 a \right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c),x)","F"
387,0,0,102,0.493000," ","int(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^2,x)","\int \frac{\sec \left(b x +a \right) \sin \left(3 b x +3 a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^2,x)","F"
388,0,0,128,0.643000," ","int(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^3,x)","\int \frac{\sec \left(b x +a \right) \sin \left(3 b x +3 a \right)}{\left(d x +c \right)^{3}}\, dx"," ",0,"int(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^3,x)","F"
389,1,677,213,0.180000," ","int((d*x+c)^3*sec(b*x+a)^2*sin(3*b*x+3*a),x)","-\frac{2 \left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}+3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x +6 i b^{2} c \,d^{2} x +b^{3} c^{3}+3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b -6 i d^{3}\right) {\mathrm e}^{i \left(b x +a \right)}}{b^{4}}-\frac{2 \left(d^{3} x^{3} b^{3}+3 b^{3} c \,d^{2} x^{2}-3 i b^{2} d^{3} x^{2}+3 b^{3} c^{2} d x -6 i b^{2} c \,d^{2} x +b^{3} c^{3}-3 i b^{2} c^{2} d -6 b \,d^{3} x -6 c \,d^{2} b +6 i d^{3}\right) {\mathrm e}^{-i \left(b x +a \right)}}{b^{4}}-\frac{2 \,{\mathrm e}^{i \left(b x +a \right)} \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{b \left(1+{\mathrm e}^{2 i \left(b x +a \right)}\right)}-\frac{3 d^{3} a^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{6 d^{2} c \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{6 d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 i d^{3} x \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{3} x \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d \,c^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 i c \,d^{2} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 d^{3} a^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{12 i d^{2} c a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{6 d^{2} c \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{3 d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}+\frac{6 i c \,d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{3} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"-2*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3+3*I*b^2*d^3*x^2-6*b*d^3*x+6*I*b^2*c*d^2*x-6*c*d^2*b+3*I*b^2*c^2*d-6*I*d^3)/b^4*exp(I*(b*x+a))-2*(d^3*x^3*b^3+3*b^3*c*d^2*x^2+3*b^3*c^2*d*x+b^3*c^3-3*I*b^2*d^3*x^2-6*b*d^3*x-6*I*b^2*c*d^2*x-6*c*d^2*b-3*I*b^2*c^2*d+6*I*d^3)/b^4*exp(-I*(b*x+a))-2*exp(I*(b*x+a))*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/b/(1+exp(2*I*(b*x+a)))-3/b^4*d^3*a^2*ln(1-I*exp(I*(b*x+a)))-6/b^3*d^2*c*ln(1+I*exp(I*(b*x+a)))*a-6/b^2*d^2*c*ln(1+I*exp(I*(b*x+a)))*x-6*d^3*polylog(3,-I*exp(I*(b*x+a)))/b^4-6*I/b^2*d*c^2*arctan(exp(I*(b*x+a)))+12*I/b^3*d^2*c*a*arctan(exp(I*(b*x+a)))-6*I/b^3*d^2*c*polylog(2,I*exp(I*(b*x+a)))+6*I/b^3*d^3*polylog(2,-I*exp(I*(b*x+a)))*x+3/b^4*d^3*a^2*ln(1+I*exp(I*(b*x+a)))+3/b^2*d^3*ln(1-I*exp(I*(b*x+a)))*x^2-6*I/b^4*d^3*a^2*arctan(exp(I*(b*x+a)))+6*d^3*polylog(3,I*exp(I*(b*x+a)))/b^4+6/b^3*d^2*c*ln(1-I*exp(I*(b*x+a)))*a+6/b^2*d^2*c*ln(1-I*exp(I*(b*x+a)))*x-3/b^2*d^3*ln(1+I*exp(I*(b*x+a)))*x^2+6*I/b^3*d^2*c*polylog(2,-I*exp(I*(b*x+a)))-6*I/b^3*d^3*polylog(2,I*exp(I*(b*x+a)))*x","B"
390,1,328,136,0.073000," ","int((d*x+c)^2*sec(b*x+a)^2*sin(3*b*x+3*a),x)","-\frac{4 c^{2} \cos \left(b x +a \right)}{b}-\frac{c^{2}}{b \cos \left(b x +a \right)}-\frac{4 d^{2} \cos \left(b x +a \right) x^{2}}{b}+\frac{8 d^{2} \sin \left(b x +a \right) x}{b^{2}}+\frac{8 d^{2} \cos \left(b x +a \right)}{b^{3}}-\frac{d^{2} x^{2}}{b \cos \left(b x +a \right)}-\frac{2 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 d^{2} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{2 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{2 i d^{2} \dilog \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i d^{2} \dilog \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 a \,d^{2} \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b^{3}}-\frac{8 c d \cos \left(b x +a \right) x}{b}+\frac{8 c d \sin \left(b x +a \right)}{b^{2}}-\frac{2 c d x}{b \cos \left(b x +a \right)}+\frac{2 c d \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b^{2}}"," ",0,"-4*c^2/b*cos(b*x+a)-1/b/cos(b*x+a)*c^2-4*d^2/b*cos(b*x+a)*x^2+8*d^2/b^2*sin(b*x+a)*x+8*d^2*cos(b*x+a)/b^3-1/b*d^2/cos(b*x+a)*x^2-2/b^2*d^2*ln(1+I*exp(I*(b*x+a)))*x-2/b^3*d^2*ln(1+I*exp(I*(b*x+a)))*a+2/b^2*d^2*ln(1-I*exp(I*(b*x+a)))*x+2/b^3*d^2*ln(1-I*exp(I*(b*x+a)))*a-2*I*d^2/b^3*dilog(1-I*exp(I*(b*x+a)))+2*I*d^2/b^3*dilog(1+I*exp(I*(b*x+a)))-2/b^3*a*d^2*ln(sec(b*x+a)+tan(b*x+a))-8*c*d/b*cos(b*x+a)*x+8*c*d/b^2*sin(b*x+a)-2/b*c*d/cos(b*x+a)*x+2/b^2*c*d*ln(sec(b*x+a)+tan(b*x+a))","B"
391,1,87,57,0.041000," ","int((d*x+c)*sec(b*x+a)^2*sin(3*b*x+3*a),x)","-\frac{4 c \cos \left(b x +a \right)}{b}-\frac{c}{b \cos \left(b x +a \right)}-\frac{4 d \cos \left(b x +a \right) x}{b}+\frac{4 d \sin \left(b x +a \right)}{b^{2}}-\frac{d x}{b \cos \left(b x +a \right)}+\frac{d \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b^{2}}"," ",0,"-4/b*c*cos(b*x+a)-1/b*c/cos(b*x+a)-4/b*d*cos(b*x+a)*x+4*d*sin(b*x+a)/b^2-1/b*d/cos(b*x+a)*x+1/b^2*d*ln(sec(b*x+a)+tan(b*x+a))","A"
392,0,0,77,0.338000," ","int(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c),x)","\int \frac{\left(\sec^{2}\left(b x +a \right)\right) \sin \left(3 b x +3 a \right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c),x)","F"
393,0,0,97,0.442000," ","int(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^2,x)","\int \frac{\left(\sec^{2}\left(b x +a \right)\right) \sin \left(3 b x +3 a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^2,x)","F"
394,0,0,120,0.769000," ","int(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^3,x)","\int \frac{\left(\sec^{2}\left(b x +a \right)\right) \sin \left(3 b x +3 a \right)}{\left(d x +c \right)^{3}}\, dx"," ",0,"int(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^3,x)","F"
395,1,66,46,0.059000," ","int(x*cos(2*x)*sec(x),x)","x \ln \left(1+i {\mathrm e}^{i x}\right)-x \ln \left(1-i {\mathrm e}^{i x}\right)-i \dilog \left(1+i {\mathrm e}^{i x}\right)+i \dilog \left(1-i {\mathrm e}^{i x}\right)+2 \cos \left(x \right)+2 x \sin \left(x \right)"," ",0,"x*ln(1+I*exp(I*x))-x*ln(1-I*exp(I*x))-I*dilog(1+I*exp(I*x))+I*dilog(1-I*exp(I*x))+2*cos(x)+2*x*sin(x)","A"
396,1,15,14,0.056000," ","int(x*cos(2*x)*sec(x)^2,x)","x^{2}-\ln \left(\cos \left(x \right)\right)-x \tan \left(x \right)"," ",0,"x^2-ln(cos(x))-x*tan(x)","A"
397,1,102,48,0.209000," ","int(x*cos(2*x)*sec(x)^3,x)","\frac{i \left(x \,{\mathrm e}^{3 i x}-x \,{\mathrm e}^{i x}-i {\mathrm e}^{3 i x}-i {\mathrm e}^{i x}\right)}{\left({\mathrm e}^{2 i x}+1\right)^{2}}-\frac{3 x \ln \left(1+i {\mathrm e}^{i x}\right)}{2}+\frac{3 x \ln \left(1-i {\mathrm e}^{i x}\right)}{2}+\frac{3 i \dilog \left(1+i {\mathrm e}^{i x}\right)}{2}-\frac{3 i \dilog \left(1-i {\mathrm e}^{i x}\right)}{2}"," ",0,"I/(exp(2*I*x)+1)^2*(x*exp(3*I*x)-x*exp(I*x)-I*exp(3*I*x)-I*exp(I*x))-3/2*x*ln(1+I*exp(I*x))+3/2*x*ln(1-I*exp(I*x))+3/2*I*dilog(1+I*exp(I*x))-3/2*I*dilog(1-I*exp(I*x))","B"