1,1,539,91,0.024000," ","int((d*x+c)^4*cos(b*x+a),x)","\frac{\frac{d^{4} \left(\left(b x +a \right)^{4} \sin \left(b x +a \right)+4 \left(b x +a \right)^{3} \cos \left(b x +a \right)-12 \left(b x +a \right)^{2} \sin \left(b x +a \right)+24 \sin \left(b x +a \right)-24 \left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{4}}-\frac{4 a \,d^{4} \left(\left(b x +a \right)^{3} \sin \left(b x +a \right)+3 \left(b x +a \right)^{2} \cos \left(b x +a \right)-6 \cos \left(b x +a \right)-6 \left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{4}}+\frac{4 c \,d^{3} \left(\left(b x +a \right)^{3} \sin \left(b x +a \right)+3 \left(b x +a \right)^{2} \cos \left(b x +a \right)-6 \cos \left(b x +a \right)-6 \left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{3}}+\frac{6 a^{2} d^{4} \left(\left(b x +a \right)^{2} \sin \left(b x +a \right)-2 \sin \left(b x +a \right)+2 \left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{4}}-\frac{12 a c \,d^{3} \left(\left(b x +a \right)^{2} \sin \left(b x +a \right)-2 \sin \left(b x +a \right)+2 \left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{3}}+\frac{6 c^{2} d^{2} \left(\left(b x +a \right)^{2} \sin \left(b x +a \right)-2 \sin \left(b x +a \right)+2 \left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{2}}-\frac{4 a^{3} d^{4} \left(\cos \left(b x +a \right)+\left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{4}}+\frac{12 a^{2} c \,d^{3} \left(\cos \left(b x +a \right)+\left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{3}}-\frac{12 a \,c^{2} d^{2} \left(\cos \left(b x +a \right)+\left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{2}}+\frac{4 c^{3} d \left(\cos \left(b x +a \right)+\left(b x +a \right) \sin \left(b x +a \right)\right)}{b}+\frac{a^{4} d^{4} \sin \left(b x +a \right)}{b^{4}}-\frac{4 a^{3} c \,d^{3} \sin \left(b x +a \right)}{b^{3}}+\frac{6 a^{2} c^{2} d^{2} \sin \left(b x +a \right)}{b^{2}}-\frac{4 a \,c^{3} d \sin \left(b x +a \right)}{b}+c^{4} \sin \left(b x +a \right)}{b}"," ",0,"1/b*(1/b^4*d^4*((b*x+a)^4*sin(b*x+a)+4*(b*x+a)^3*cos(b*x+a)-12*(b*x+a)^2*sin(b*x+a)+24*sin(b*x+a)-24*(b*x+a)*cos(b*x+a))-4/b^4*a*d^4*((b*x+a)^3*sin(b*x+a)+3*(b*x+a)^2*cos(b*x+a)-6*cos(b*x+a)-6*(b*x+a)*sin(b*x+a))+4/b^3*c*d^3*((b*x+a)^3*sin(b*x+a)+3*(b*x+a)^2*cos(b*x+a)-6*cos(b*x+a)-6*(b*x+a)*sin(b*x+a))+6/b^4*a^2*d^4*((b*x+a)^2*sin(b*x+a)-2*sin(b*x+a)+2*(b*x+a)*cos(b*x+a))-12/b^3*a*c*d^3*((b*x+a)^2*sin(b*x+a)-2*sin(b*x+a)+2*(b*x+a)*cos(b*x+a))+6/b^2*c^2*d^2*((b*x+a)^2*sin(b*x+a)-2*sin(b*x+a)+2*(b*x+a)*cos(b*x+a))-4/b^4*a^3*d^4*(cos(b*x+a)+(b*x+a)*sin(b*x+a))+12/b^3*a^2*c*d^3*(cos(b*x+a)+(b*x+a)*sin(b*x+a))-12/b^2*a*c^2*d^2*(cos(b*x+a)+(b*x+a)*sin(b*x+a))+4/b*c^3*d*(cos(b*x+a)+(b*x+a)*sin(b*x+a))+1/b^4*a^4*d^4*sin(b*x+a)-4/b^3*a^3*c*d^3*sin(b*x+a)+6/b^2*a^2*c^2*d^2*sin(b*x+a)-4/b*a*c^3*d*sin(b*x+a)+c^4*sin(b*x+a))","B"
2,1,302,70,0.031000," ","int((d*x+c)^3*cos(b*x+a),x)","\frac{\frac{d^{3} \left(\left(b x +a \right)^{3} \sin \left(b x +a \right)+3 \left(b x +a \right)^{2} \cos \left(b x +a \right)-6 \cos \left(b x +a \right)-6 \left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{3}}-\frac{3 a \,d^{3} \left(\left(b x +a \right)^{2} \sin \left(b x +a \right)-2 \sin \left(b x +a \right)+2 \left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{3}}+\frac{3 c \,d^{2} \left(\left(b x +a \right)^{2} \sin \left(b x +a \right)-2 \sin \left(b x +a \right)+2 \left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(\cos \left(b x +a \right)+\left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(\cos \left(b x +a \right)+\left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{2}}+\frac{3 c^{2} d \left(\cos \left(b x +a \right)+\left(b x +a \right) \sin \left(b x +a \right)\right)}{b}-\frac{a^{3} d^{3} \sin \left(b x +a \right)}{b^{3}}+\frac{3 a^{2} c \,d^{2} \sin \left(b x +a \right)}{b^{2}}-\frac{3 a \,c^{2} d \sin \left(b x +a \right)}{b}+c^{3} \sin \left(b x +a \right)}{b}"," ",0,"1/b*(1/b^3*d^3*((b*x+a)^3*sin(b*x+a)+3*(b*x+a)^2*cos(b*x+a)-6*cos(b*x+a)-6*(b*x+a)*sin(b*x+a))-3/b^3*a*d^3*((b*x+a)^2*sin(b*x+a)-2*sin(b*x+a)+2*(b*x+a)*cos(b*x+a))+3/b^2*c*d^2*((b*x+a)^2*sin(b*x+a)-2*sin(b*x+a)+2*(b*x+a)*cos(b*x+a))+3/b^3*a^2*d^3*(cos(b*x+a)+(b*x+a)*sin(b*x+a))-6/b^2*a*c*d^2*(cos(b*x+a)+(b*x+a)*sin(b*x+a))+3/b*c^2*d*(cos(b*x+a)+(b*x+a)*sin(b*x+a))-1/b^3*a^3*d^3*sin(b*x+a)+3/b^2*a^2*c*d^2*sin(b*x+a)-3/b*a*c^2*d*sin(b*x+a)+c^3*sin(b*x+a))","B"
3,1,143,49,0.024000," ","int((d*x+c)^2*cos(b*x+a),x)","\frac{\frac{d^{2} \left(\left(b x +a \right)^{2} \sin \left(b x +a \right)-2 \sin \left(b x +a \right)+2 \left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{2}}-\frac{2 a \,d^{2} \left(\cos \left(b x +a \right)+\left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{2}}+\frac{2 c d \left(\cos \left(b x +a \right)+\left(b x +a \right) \sin \left(b x +a \right)\right)}{b}+\frac{a^{2} d^{2} \sin \left(b x +a \right)}{b^{2}}-\frac{2 a c d \sin \left(b x +a \right)}{b}+c^{2} \sin \left(b x +a \right)}{b}"," ",0,"1/b*(1/b^2*d^2*((b*x+a)^2*sin(b*x+a)-2*sin(b*x+a)+2*(b*x+a)*cos(b*x+a))-2/b^2*a*d^2*(cos(b*x+a)+(b*x+a)*sin(b*x+a))+2/b*c*d*(cos(b*x+a)+(b*x+a)*sin(b*x+a))+1/b^2*a^2*d^2*sin(b*x+a)-2/b*a*c*d*sin(b*x+a)+c^2*sin(b*x+a))","B"
4,1,51,27,0.022000," ","int((d*x+c)*cos(b*x+a),x)","\frac{\frac{d \left(\cos \left(b x +a \right)+\left(b x +a \right) \sin \left(b x +a \right)\right)}{b}-\frac{d a \sin \left(b x +a \right)}{b}+c \sin \left(b x +a \right)}{b}"," ",0,"1/b*(1/b*d*(cos(b*x+a)+(b*x+a)*sin(b*x+a))-1/b*d*a*sin(b*x+a)+c*sin(b*x+a))","A"
5,1,72,52,0.027000," ","int(cos(b*x+a)/(d*x+c),x)","\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}"," ",0,"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","A"
6,1,109,73,0.026000," ","int(cos(b*x+a)/(d*x+c)^2,x)","b \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)"," ",0,"b*(-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)","A"
7,1,143,96,0.023000," ","int(cos(b*x+a)/(d*x+c)^3,x)","b^{2} \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)"," ",0,"b^2*(-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)","A"
8,1,179,117,0.024000," ","int(cos(b*x+a)/(d*x+c)^4,x)","b^{3} \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)"," ",0,"b^3*(-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)","A"
9,1,1027,147,0.077000," ","int((d*x+c)^4*cos(b*x+a)^2,x)","\frac{\frac{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}\right)}{b^{4}}-\frac{4 a \,d^{4} \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)}{b^{4}}+\frac{4 c \,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}\right)}{b^{3}}+\frac{6 a^{2} d^{4} \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)}{b^{4}}-\frac{12 a c \,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)}{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)}{b^{3}}+\frac{6 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}\right)}{b^{2}}-\frac{4 a^{3} d^{4} \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)}{b^{4}}+\frac{12 a^{2} c \,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}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b^{3}}-\frac{12 a \,c^{2} 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}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b^{2}}+\frac{4 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}\right)}{b}+\frac{a^{4} d^{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^{4}}-\frac{4 a^{3} c \,d^{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^{3}}+\frac{6 a^{2} c^{2} d^{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^{2}}-\frac{4 a \,c^{3} d \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^{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}"," ",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)+(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/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)+3/4*(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)+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)+3/4*(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/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)+1/2*(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)-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)+1/2*(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)+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)+1/2*(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/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)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+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)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)-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)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+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)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+1/b^4*a^4*d^4*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-4/b^3*a^3*c*d^3*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+6/b^2*a^2*c^2*d^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-4/b*a*c^3*d*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+c^4*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))","B"
10,1,587,120,0.023000," ","int((d*x+c)^3*cos(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)}{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)}{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)}{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)}{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)}{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)}{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}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\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}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\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}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b}-\frac{a^{3} d^{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^{3}}+\frac{3 a^{2} c \,d^{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^{2}}-\frac{3 a \,c^{2} d \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^{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}"," ",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)+3/4*(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/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)+1/2*(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/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)+1/2*(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/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)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)-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)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+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)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)-1/b^3*a^3*d^3*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+3/b^2*a^2*c*d^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-3/b*a*c^2*d*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+c^3*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))","B"
11,1,289,85,0.025000," ","int((d*x+c)^2*cos(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)}{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)}{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}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\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}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b}+\frac{a^{2} d^{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^{2}}-\frac{2 a c d \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^{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}"," ",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)+1/2*(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/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)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+2/b*c*d*((b*x+a)*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)+1/b^2*a^2*d^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)-2/b*a*c*d*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+c^2*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))","B"
12,1,112,47,0.022000," ","int((d*x+c)*cos(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}}{4}-\frac{\left(\sin^{2}\left(b x +a \right)\right)}{4}\right)}{b}-\frac{d a \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 \left(\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\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)-1/4*(b*x+a)^2-1/4*sin(b*x+a)^2)-1/b*d*a*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)+c*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a))","B"
13,1,105,72,0.026000," ","int(cos(b*x+a)^2/(d*x+c),x)","\frac{\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)}{2 d}+\frac{\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)}{2 d}+\frac{\ln \left(\left(b x +a \right) d -d a +c b \right)}{2 d}"," ",0,"1/2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d+1/2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d+1/2*ln((b*x+a)*d-d*a+c*b)/d","A"
14,1,156,83,0.025000," ","int(cos(b*x+a)^2/(d*x+c)^2,x)","\frac{\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)}{4}-\frac{b^{2}}{2 \left(\left(b x +a \right) d -d a +c b \right) d}}{b}"," ",0,"1/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"
15,1,193,110,0.025000," ","int(cos(b*x+a)^2/(d*x+c)^3,x)","\frac{\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)}{4}-\frac{b^{3}}{4 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}}{b}"," ",0,"1/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"
16,1,1023,205,0.054000," ","int((d*x+c)^4*cos(b*x+a)^3,x)","\frac{\frac{d^{4} \left(\frac{\left(b x +a \right)^{4} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}+\frac{8 \left(b x +a \right)^{3} \cos \left(b x +a \right)}{3}-8 \left(b x +a \right)^{2} \sin \left(b x +a \right)+\frac{160 \sin \left(b x +a \right)}{9}-\frac{160 \left(b x +a \right) \cos \left(b x +a \right)}{9}+\frac{4 \left(b x +a \right)^{3} \left(\cos^{3}\left(b x +a \right)\right)}{9}-\frac{4 \left(b x +a \right)^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{9}-\frac{8 \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)}{27}+\frac{8 \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{81}\right)}{b^{4}}-\frac{4 a \,d^{4} \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}+2 \left(b x +a \right)^{2} \cos \left(b x +a \right)-\frac{40 \cos \left(b x +a \right)}{9}-4 \left(b x +a \right) \sin \left(b x +a \right)+\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}\right)}{b^{4}}+\frac{4 c \,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}+2 \left(b x +a \right)^{2} \cos \left(b x +a \right)-\frac{40 \cos \left(b x +a \right)}{9}-4 \left(b x +a \right) \sin \left(b x +a \right)+\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}\right)}{b^{3}}+\frac{6 a^{2} d^{4} \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)}{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{12 a c \,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)}{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 c^{2} 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)}{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^{2}}-\frac{4 a^{3} d^{4} \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)}{9}+\frac{2 \cos \left(b x +a \right)}{3}\right)}{b^{4}}+\frac{12 a^{2} c \,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)}{9}+\frac{2 \cos \left(b x +a \right)}{3}\right)}{b^{3}}-\frac{12 a \,c^{2} 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)}{9}+\frac{2 \cos \left(b x +a \right)}{3}\right)}{b^{2}}+\frac{4 c^{3} 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)}{9}+\frac{2 \cos \left(b x +a \right)}{3}\right)}{b}+\frac{a^{4} d^{4} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3 b^{4}}-\frac{4 a^{3} c \,d^{3} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3 b^{3}}+\frac{2 a^{2} c^{2} d^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{b^{2}}-\frac{4 a \,c^{3} d \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3 b}+\frac{c^{4} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(1/b^4*d^4*(1/3*(b*x+a)^4*(2+cos(b*x+a)^2)*sin(b*x+a)+8/3*(b*x+a)^3*cos(b*x+a)-8*(b*x+a)^2*sin(b*x+a)+160/9*sin(b*x+a)-160/9*(b*x+a)*cos(b*x+a)+4/9*(b*x+a)^3*cos(b*x+a)^3-4/9*(b*x+a)^2*(2+cos(b*x+a)^2)*sin(b*x+a)-8/27*(b*x+a)*cos(b*x+a)^3+8/81*(2+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*(b*x+a)^2*cos(b*x+a)-40/9*cos(b*x+a)-4*(b*x+a)*sin(b*x+a)+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/b^3*c*d^3*(1/3*(b*x+a)^3*(2+cos(b*x+a)^2)*sin(b*x+a)+2*(b*x+a)^2*cos(b*x+a)-40/9*cos(b*x+a)-4*(b*x+a)*sin(b*x+a)+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)+6/b^4*a^2*d^4*(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))-12/b^3*a*c*d^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^2*c^2*d^2*(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^4*a^3*d^4*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/9*cos(b*x+a)^3+2/3*cos(b*x+a))+12/b^3*a^2*c*d^3*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/9*cos(b*x+a)^3+2/3*cos(b*x+a))-12/b^2*a*c^2*d^2*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/9*cos(b*x+a)^3+2/3*cos(b*x+a))+4/b*c^3*d*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/9*cos(b*x+a)^3+2/3*cos(b*x+a))+1/3/b^4*a^4*d^4*(2+cos(b*x+a)^2)*sin(b*x+a)-4/3/b^3*a^3*c*d^3*(2+cos(b*x+a)^2)*sin(b*x+a)+2/b^2*a^2*c^2*d^2*(2+cos(b*x+a)^2)*sin(b*x+a)-4/3/b*a*c^3*d*(2+cos(b*x+a)^2)*sin(b*x+a)+1/3*c^4*(2+cos(b*x+a)^2)*sin(b*x+a))","B"
17,1,560,161,0.031000," ","int((d*x+c)^3*cos(b*x+a)^3,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}+2 \left(b x +a \right)^{2} \cos \left(b x +a \right)-\frac{40 \cos \left(b x +a \right)}{9}-4 \left(b x +a \right) \sin \left(b x +a \right)+\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}\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)}{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 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)}{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^{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)}{9}+\frac{2 \cos \left(b x +a \right)}{3}\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)}{9}+\frac{2 \cos \left(b x +a \right)}{3}\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)}{9}+\frac{2 \cos \left(b x +a \right)}{3}\right)}{b}-\frac{a^{3} d^{3} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3 b^{3}}+\frac{a^{2} c \,d^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{b^{2}}-\frac{a \,c^{2} d \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{b}+\frac{c^{3} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}}{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*(b*x+a)^2*cos(b*x+a)-40/9*cos(b*x+a)-4*(b*x+a)*sin(b*x+a)+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)-3/b^3*a*d^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^2*c*d^2*(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^2*d^3*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/9*cos(b*x+a)^3+2/3*cos(b*x+a))-6/b^2*a*c*d^2*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/9*cos(b*x+a)^3+2/3*cos(b*x+a))+3/b*c^2*d*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/9*cos(b*x+a)^3+2/3*cos(b*x+a))-1/3/b^3*a^3*d^3*(2+cos(b*x+a)^2)*sin(b*x+a)+1/b^2*a^2*c*d^2*(2+cos(b*x+a)^2)*sin(b*x+a)-1/b*a*c^2*d*(2+cos(b*x+a)^2)*sin(b*x+a)+1/3*c^3*(2+cos(b*x+a)^2)*sin(b*x+a))","B"
18,1,265,111,0.034000," ","int((d*x+c)^2*cos(b*x+a)^3,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)}{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^{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)}{9}+\frac{2 \cos \left(b x +a \right)}{3}\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)}{9}+\frac{2 \cos \left(b x +a \right)}{3}\right)}{b}+\frac{a^{2} d^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3 b^{2}}-\frac{2 a c d \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3 b}+\frac{c^{2} \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}}{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)-4/3*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))-2/b^2*a*d^2*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/9*cos(b*x+a)^3+2/3*cos(b*x+a))+2/b*c*d*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/9*cos(b*x+a)^3+2/3*cos(b*x+a))+1/3/b^2*a^2*d^2*(2+cos(b*x+a)^2)*sin(b*x+a)-2/3/b*a*c*d*(2+cos(b*x+a)^2)*sin(b*x+a)+1/3*c^2*(2+cos(b*x+a)^2)*sin(b*x+a))","B"
19,1,95,67,0.030000," ","int((d*x+c)*cos(b*x+a)^3,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)}{9}+\frac{2 \cos \left(b x +a \right)}{3}\right)}{b}-\frac{d a \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3 b}+\frac{c \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(1/b*d*(1/3*(b*x+a)*(2+cos(b*x+a)^2)*sin(b*x+a)+1/9*cos(b*x+a)^3+2/3*cos(b*x+a))-1/3/b*d*a*(2+cos(b*x+a)^2)*sin(b*x+a)+1/3*c*(2+cos(b*x+a)^2)*sin(b*x+a))","A"
20,1,166,113,0.032000," ","int(cos(b*x+a)^3/(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) \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}+\frac{3 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}}{b}"," ",0,"1/b*(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)+3/4*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))","A"
21,1,242,137,0.028000," ","int(cos(b*x+a)^3/(d*x+c)^2,x)","\frac{\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}+\frac{3 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}}{b}"," ",0,"1/b*(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)+3/4*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))","A"
22,1,311,172,0.034000," ","int(cos(b*x+a)^3/(d*x+c)^3,x)","\frac{\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}+\frac{3 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}}{b}"," ",0,"1/b*(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)+3/4*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))","A"
23,1,440,152,0.078000," ","int(x^3*cos(b*x+a)^4,x)","\frac{\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}-3 a \left(\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)+\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{8}-\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)}{32}-\frac{15 b x}{64}-\frac{15 a}{64}+\frac{3 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{8}-\frac{3 \cos \left(b x +a \right) \sin \left(b x +a \right)}{16}-\frac{\left(b x +a \right)^{3}}{4}\right)+3 a^{2} \left(\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)-\frac{3 \left(b x +a \right)^{2}}{16}+\frac{\left(\cos^{4}\left(b x +a \right)\right)}{16}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{16}\right)-a^{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)}{b^{4}}"," ",0,"1/b^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)^4-3*a*((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)+1/8*(b*x+a)*cos(b*x+a)^4-1/32*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)-15/64*b*x-15/64*a+3/8*(b*x+a)*cos(b*x+a)^2-3/16*cos(b*x+a)*sin(b*x+a)-1/4*(b*x+a)^3)+3*a^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)-3/16*(b*x+a)^2+1/16*cos(b*x+a)^4+3/16*cos(b*x+a)^2)-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))","B"
24,1,241,118,0.030000," ","int(x^2*cos(b*x+a)^4,x)","\frac{\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)+\frac{\left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{8}-\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)}{32}-\frac{15 b x}{64}-\frac{15 a}{64}+\frac{3 \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{8}-\frac{3 \cos \left(b x +a \right) \sin \left(b x +a \right)}{16}-\frac{\left(b x +a \right)^{3}}{4}-2 a \left(\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)-\frac{3 \left(b x +a \right)^{2}}{16}+\frac{\left(\cos^{4}\left(b x +a \right)\right)}{16}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{16}\right)+a^{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)}{b^{3}}"," ",0,"1/b^3*((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)+1/8*(b*x+a)*cos(b*x+a)^4-1/32*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)-15/64*b*x-15/64*a+3/8*(b*x+a)*cos(b*x+a)^2-3/16*cos(b*x+a)*sin(b*x+a)-1/4*(b*x+a)^3-2*a*((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)-3/16*(b*x+a)^2+1/16*cos(b*x+a)^4+3/16*cos(b*x+a)^2)+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))","B"
25,1,110,70,0.027000," ","int(x*cos(b*x+a)^4,x)","\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)-\frac{3 \left(b x +a \right)^{2}}{16}+\frac{\left(\cos^{4}\left(b x +a \right)\right)}{16}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{16}-a \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)}{b^{2}}"," ",0,"1/b^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)-3/16*(b*x+a)^2+1/16*cos(b*x+a)^4+3/16*cos(b*x+a)^2-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))","A"
26,1,52,49,0.028000," ","int(cos(b*x+a)^4/x,x)","-\frac{\Si \left(4 b x \right) \sin \left(4 a \right)}{8}+\frac{\Ci \left(4 b x \right) \cos \left(4 a \right)}{8}-\frac{\Si \left(2 b x \right) \sin \left(2 a \right)}{2}+\frac{\Ci \left(2 b x \right) \cos \left(2 a \right)}{2}+\frac{3 \ln \left(b x \right)}{8}"," ",0,"-1/8*Si(4*b*x)*sin(4*a)+1/8*Ci(4*b*x)*cos(4*a)-1/2*Si(2*b*x)*sin(2*a)+1/2*Ci(2*b*x)*cos(2*a)+3/8*ln(b*x)","A"
27,1,90,62,0.030000," ","int(cos(b*x+a)^4/x^2,x)","b \left(-\frac{\cos \left(4 b x +4 a \right)}{8 x b}-\frac{\Si \left(4 b x \right) \cos \left(4 a \right)}{2}-\frac{\Ci \left(4 b x \right) \sin \left(4 a \right)}{2}-\frac{\cos \left(2 b x +2 a \right)}{2 x b}-\Si \left(2 b x \right) \cos \left(2 a \right)-\Ci \left(2 b x \right) \sin \left(2 a \right)-\frac{3}{8 x b}\right)"," ",0,"b*(-1/8*cos(4*b*x+4*a)/x/b-1/2*Si(4*b*x)*cos(4*a)-1/2*Ci(4*b*x)*sin(4*a)-1/2*cos(2*b*x+2*a)/x/b-Si(2*b*x)*cos(2*a)-Ci(2*b*x)*sin(2*a)-3/8/x/b)","A"
28,1,124,88,0.032000," ","int(cos(b*x+a)^4/x^3,x)","b^{2} \left(-\frac{\cos \left(4 b x +4 a \right)}{16 x^{2} b^{2}}+\frac{\sin \left(4 b x +4 a \right)}{4 x b}+\Si \left(4 b x \right) \sin \left(4 a \right)-\Ci \left(4 b x \right) \cos \left(4 a \right)-\frac{\cos \left(2 b x +2 a \right)}{4 x^{2} b^{2}}+\frac{\sin \left(2 b x +2 a \right)}{2 x b}+\Si \left(2 b x \right) \sin \left(2 a \right)-\Ci \left(2 b x \right) \cos \left(2 a \right)-\frac{3}{16 x^{2} b^{2}}\right)"," ",0,"b^2*(-1/16*cos(4*b*x+4*a)/x^2/b^2+1/4*sin(4*b*x+4*a)/x/b+Si(4*b*x)*sin(4*a)-Ci(4*b*x)*cos(4*a)-1/4*cos(2*b*x+2*a)/x^2/b^2+1/2*sin(2*b*x+2*a)/x/b+Si(2*b*x)*sin(2*a)-Ci(2*b*x)*cos(2*a)-3/16/x^2/b^2)","A"
29,1,685,180,0.216000," ","int((d*x+c)^3*sec(b*x+a),x)","-\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{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{a^{3} d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\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{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^{2} c \polylog \left(3, 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) 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^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\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 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{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 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{2 i d^{3} a^{3} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",0,"6*I*d^3*polylog(4,I*exp(I*(b*x+a)))/b^4-6*I/b^2*d^2*c*polylog(2,I*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*d^3*polylog(4,-I*exp(I*(b*x+a)))/b^4+6/b^3*d^2*c*polylog(3,I*exp(I*(b*x+a)))+6/b^3*d^3*polylog(3,I*exp(I*(b*x+a)))*x-1/b^4*a^3*d^3*ln(1+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)))-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-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^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+2*I/b^4*d^3*a^3*arctan(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^2-3*I/b^2*c^2*d*polylog(2,I*exp(I*(b*x+a)))+3*I/b^2*c^2*d*polylog(2,-I*exp(I*(b*x+a)))","B"
30,1,392,120,0.140000," ","int((d*x+c)^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 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) x}{b}+\frac{2 c d \ln \left(1-i {\mathrm e}^{i \left(b x +a \right)}\right) a}{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 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 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{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 i d^{2} \polylog \left(2, i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 c d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{2 i d^{2} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}"," ",0,"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/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*I/b*c^2*arctan(exp(I*(b*x+a)))+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*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*I/b^2*d^2*polylog(2,-I*exp(I*(b*x+a)))*x-2*I/b^2*c*d*polylog(2,I*exp(I*(b*x+a)))-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*I/b^3*d^2*a^2*arctan(exp(I*(b*x+a)))+2*d^2*polylog(3,I*exp(I*(b*x+a)))/b^3-2/b^2*c*d*ln(1+I*exp(I*(b*x+a)))*a-2*I/b^2*d^2*polylog(2,I*exp(I*(b*x+a)))*x","B"
31,1,172,64,0.007000," ","int((d*x+c)*sec(b*x+a),x)","-\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*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"
32,0,0,16,0.092000," ","int(sec(b*x+a)/(d*x+c),x)","\int \frac{\sec \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)/(d*x+c),x)","F"
33,1,316,104,0.195000," ","int((d*x+c)^3*sec(b*x+a)^2,x)","-\frac{2 i d^{3} x^{3}}{b}+\frac{3 d \,c^{2} \ln \left({\mathrm e}^{2 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{6 d^{3} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 i d^{2} c \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right)}{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({\mathrm e}^{2 i \left(b x +a \right)}+1\right)}-\frac{12 i d^{2} c a x}{b^{2}}+\frac{6 d^{2} c \ln \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right) x}{b^{2}}+\frac{3 d^{3} \ln \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{2 i \left(b x +a \right)}\right) x}{b^{3}}+\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{6 i d^{2} c \,a^{2}}{b^{3}}-\frac{6 i d^{2} c \,x^{2}}{b}+\frac{6 i d^{3} a^{2} x}{b^{3}}+\frac{4 i d^{3} a^{3}}{b^{4}}"," ",0,"-2*I/b*d^3*x^3+3/b^2*d*c^2*ln(exp(2*I*(b*x+a))+1)-6/b^2*d*c^2*ln(exp(I*(b*x+a)))-6/b^4*d^3*a^2*ln(exp(I*(b*x+a)))+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)-12*I/b^2*d^2*c*a*x-3*I/b^3*d^2*c*polylog(2,-exp(2*I*(b*x+a)))+6/b^2*d^2*c*ln(exp(2*I*(b*x+a))+1)*x+3/b^2*d^3*ln(exp(2*I*(b*x+a))+1)*x^2-6*I/b^3*d^2*c*a^2+3/2*d^3*polylog(3,-exp(2*I*(b*x+a)))/b^4+12/b^3*d^2*c*a*ln(exp(I*(b*x+a)))-3*I/b^3*d^3*polylog(2,-exp(2*I*(b*x+a)))*x-6*I/b*d^2*c*x^2+6*I/b^3*d^3*a^2*x+4*I/b^4*d^3*a^3","B"
34,1,170,76,0.077000," ","int((d*x+c)^2*sec(b*x+a)^2,x)","\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 c \ln \left({\mathrm e}^{2 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} 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({\mathrm e}^{2 i \left(b x +a \right)}+1\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,"2*I*(d^2*x^2+2*c*d*x+c^2)/b/(exp(2*I*(b*x+a))+1)+2/b^2*d*c*ln(exp(2*I*(b*x+a))+1)-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/b^2*d^2*ln(exp(2*I*(b*x+a))+1)*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"
35,1,37,28,0.022000," ","int((d*x+c)*sec(b*x+a)^2,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/b*d*tan(b*x+a)*x+d*ln(cos(b*x+a))/b^2+1/b*c*tan(b*x+a)","A"
36,0,0,18,0.203000," ","int(sec(b*x+a)^2/(d*x+c),x)","\int \frac{\sec^{2}\left(b x +a \right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)^2/(d*x+c),x)","F"
37,1,1127,293,0.304000," ","int((d*x+c)^3*sec(b*x+a)^3,x)","-\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{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{a^{3} d^{3} \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{4}}+\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{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^{2} c \polylog \left(3, i {\mathrm e}^{i \left(b x +a \right)}\right)}{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^{3} \polylog \left(3, -i {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\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 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 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 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{i d^{3} a^{3} \arctan \left({\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{3 i d^{3} \polylog \left(2, 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}{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{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({\mathrm e}^{2 i \left(b x +a \right)}+1\right)^{2}}-\frac{6 i c \,d^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 i d^{3} a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}"," ",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/b^3*d^2*c*polylog(3,I*exp(I*(b*x+a)))+3/b^3*d^3*polylog(3,I*exp(I*(b*x+a)))*x-1/2/b^4*a^3*d^3*ln(1+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)))-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*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/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^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-6*I/b^3*c*d^2*arctan(exp(I*(b*x+a)))+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+3/2*I/b^2*c^2*d*polylog(2,-I*exp(I*(b*x+a)))-3/2*I/b^2*c^2*d*polylog(2,I*exp(I*(b*x+a)))+6*I/b^4*d^3*a*arctan(exp(I*(b*x+a)))+I/b^4*d^3*a^3*arctan(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^3*c*d^2*a^2*arctan(exp(I*(b*x+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^2*c^2*d*a*arctan(exp(I*(b*x+a)))-I/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)))","B"
38,1,584,174,0.170000," ","int((d*x+c)^2*sec(b*x+a)^3,x)","-\frac{i c^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{i d^{2} a^{2} \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 i c d a \arctan \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{2 i d^{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) a}{b^{2}}-\frac{c d \ln \left(1+i {\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{i c d \polylog \left(2, i {\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{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{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{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) x}{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 c d \,{\mathrm e}^{3 i \left(b x +a \right)}-2 i d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}-2 i c d \,{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)^{2}}+\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) x}{b}-\frac{d^{2} \polylog \left(3, -i {\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}}"," ",0,"-I/b*c^2*arctan(exp(I*(b*x+a)))-I/b^3*d^2*a^2*arctan(exp(I*(b*x+a)))-I/b^2*d^2*polylog(2,I*exp(I*(b*x+a)))*x+I/b^2*d^2*polylog(2,-I*exp(I*(b*x+a)))*x+1/b^2*c*d*ln(1-I*exp(I*(b*x+a)))*a-1/b^2*c*d*ln(1+I*exp(I*(b*x+a)))*a-I/b^2*c*d*polylog(2,I*exp(I*(b*x+a)))+I/b^2*c*d*polylog(2,-I*exp(I*(b*x+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^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+d^2*polylog(3,I*exp(I*(b*x+a)))/b^3-1/b*c*d*ln(1+I*exp(I*(b*x+a)))*x+2*I/b^2*c*d*a*arctan(exp(I*(b*x+a)))-2*I/b^3*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/(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*c*d*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)))","B"
39,1,267,98,0.115000," ","int((d*x+c)*sec(b*x+a)^3,x)","-\frac{i \left(d x b \,{\mathrm e}^{3 i \left(b x +a \right)}+c b \,{\mathrm e}^{3 i \left(b x +a \right)}-d x b \,{\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)}\right)}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}+1\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/(exp(2*I*(b*x+a))+1)^2*(d*x*b*exp(3*I*(b*x+a))+c*b*exp(3*I*(b*x+a))-d*x*b*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)))-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"
40,0,0,18,0.000000," ","int(sec(b*x+a)^2/(d*x+c),x)","\int \frac{\sec^{2}\left(b x +a \right)}{d x +c}\, dx"," ",0,"int(sec(b*x+a)^2/(d*x+c),x)","F"
41,1,232,148,0.035000," ","int((d*x+c)^(5/2)*cos(b*x+a),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)}{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)}{b}}{d}"," ",0,"2/d*(1/2*d/b*(d*x+c)^(5/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-5/2*d/b*(-1/2*d/b*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/2*d/b*(1/2*d/b*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4*d/b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
42,1,189,127,0.028000," ","int((d*x+c)^(3/2)*cos(b*x+a),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)}{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)}{b}}{d}"," ",0,"2/d*(1/2*d/b*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/2*d/b*(-1/2*d/b*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4*d/b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
43,1,144,108,0.029000," ","int((d*x+c)^(1/2)*cos(b*x+a),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)}{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)}{2 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(1/2*d/b*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4*d/b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
44,1,100,90,0.032000," ","int(cos(b*x+a)/(d*x+c)^(1/2),x)","\frac{\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)}{d \sqrt{\frac{b}{d}}}"," ",0,"1/d*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))","A"
45,1,140,109,0.032000," ","int(cos(b*x+a)/(d*x+c)^(3/2),x)","\frac{-\frac{2 \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{\sqrt{d x +c}}-\frac{2 b \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)}{d \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/d*b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
46,1,180,128,0.030000," ","int(cos(b*x+a)/(d*x+c)^(5/2),x)","\frac{-\frac{2 \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{3 \left(d x +c \right)^{\frac{3}{2}}}-\frac{4 b \left(-\frac{\sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{\sqrt{d x +c}}+\frac{b \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)}{d \sqrt{\frac{b}{d}}}\right)}{3 d}}{d}"," ",0,"2/d*(-1/3/(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-2/3/d*b*(-1/(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/d*b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
47,1,220,149,0.031000," ","int(cos(b*x+a)/(d*x+c)^(7/2),x)","\frac{-\frac{2 \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{5 \left(d x +c \right)^{\frac{5}{2}}}-\frac{4 b \left(-\frac{\sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{3 \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 b \left(-\frac{\cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{\sqrt{d x +c}}-\frac{b \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)}{d \sqrt{\frac{b}{d}}}\right)}{3 d}\right)}{5 d}}{d}"," ",0,"2/d*(-1/5/(d*x+c)^(5/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-2/5/d*b*(-1/3/(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+2/3/d*b*(-1/(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/d*b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
48,1,242,179,0.054000," ","int((d*x+c)^(5/2)*cos(b*x+a)^2,x)","\frac{\frac{\left(d x +c \right)^{\frac{7}{2}}}{7}+\frac{d \left(d x +c \right)^{\frac{5}{2}} \sin \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}} \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}\right)}{4 b}}{d}"," ",0,"2/d*(1/14*(d*x+c)^(7/2)+1/8*d/b*(d*x+c)^(5/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-5/8*d/b*(-1/4*d/b*(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/4*d/b*(1/4*d/b*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/8*d/b*Pi^(1/2)/(1/d*b)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
49,1,197,155,0.044000," ","int((d*x+c)^(3/2)*cos(b*x+a)^2,x)","\frac{\frac{\left(d x +c \right)^{\frac{5}{2}}}{5}+\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}}{d}"," ",0,"2/d*(1/10*(d*x+c)^(5/2)+1/8*d/b*(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-3/8*d/b*(-1/4*d/b*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/8*d/b*Pi^(1/2)/(1/d*b)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
50,1,150,118,0.044000," ","int((d*x+c)^(1/2)*cos(b*x+a)^2,x)","\frac{\frac{\left(d x +c \right)^{\frac{3}{2}}}{3}+\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}}}}{d}"," ",0,"2/d*(1/6*(d*x+c)^(3/2)+1/8*d/b*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/16*d/b*Pi^(1/2)/(1/d*b)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
51,1,108,96,0.057000," ","int(cos(b*x+a)^2/(d*x+c)^(1/2),x)","\frac{\sqrt{d x +c}+\frac{\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)}{2 \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(1/2*(d*x+c)^(1/2)+1/4*Pi^(1/2)/(1/d*b)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
52,1,146,105,0.048000," ","int(cos(b*x+a)^2/(d*x+c)^(3/2),x)","\frac{-\frac{1}{\sqrt{d x +c}}-\frac{\cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{\sqrt{d x +c}}-\frac{2 b \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)}{d \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/2/(d*x+c)^(1/2)-1/2/(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/d*b*Pi^(1/2)/(1/d*b)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
53,1,189,130,0.046000," ","int(cos(b*x+a)^2/(d*x+c)^(5/2),x)","\frac{-\frac{1}{3 \left(d x +c \right)^{\frac{3}{2}}}-\frac{\cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{3 \left(d x +c \right)^{\frac{3}{2}}}-\frac{4 b \left(-\frac{\sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{\sqrt{d x +c}}+\frac{2 b \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)}{d \sqrt{\frac{b}{d}}}\right)}{3 d}}{d}"," ",0,"2/d*(-1/6/(d*x+c)^(3/2)-1/6/(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-2/3/d*b*(-1/(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+2/d*b*Pi^(1/2)/(1/d*b)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
54,1,230,168,0.044000," ","int(cos(b*x+a)^2/(d*x+c)^(7/2),x)","\frac{-\frac{1}{5 \left(d x +c \right)^{\frac{5}{2}}}-\frac{\cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{5 \left(d x +c \right)^{\frac{5}{2}}}-\frac{4 b \left(-\frac{\sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{3 \left(d x +c \right)^{\frac{3}{2}}}+\frac{4 b \left(-\frac{\cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{\sqrt{d x +c}}-\frac{2 b \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)}{d \sqrt{\frac{b}{d}}}\right)}{3 d}\right)}{5 d}}{d}"," ",0,"2/d*(-1/10/(d*x+c)^(5/2)-1/10/(d*x+c)^(5/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-2/5/d*b*(-1/3/(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+4/3/d*b*(-1/(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-2/d*b*Pi^(1/2)/(1/d*b)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
55,1,273,195,0.056000," ","int(cos(b*x+a)^2/(d*x+c)^(9/2),x)","\frac{-\frac{1}{7 \left(d x +c \right)^{\frac{7}{2}}}-\frac{\cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{7 \left(d x +c \right)^{\frac{7}{2}}}-\frac{4 b \left(-\frac{\sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{5 \left(d x +c \right)^{\frac{5}{2}}}+\frac{4 b \left(-\frac{\cos \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{3 \left(d x +c \right)^{\frac{3}{2}}}-\frac{4 b \left(-\frac{\sin \left(\frac{2 \left(d x +c \right) b}{d}+\frac{2 d a -2 c b}{d}\right)}{\sqrt{d x +c}}+\frac{2 b \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)}{d \sqrt{\frac{b}{d}}}\right)}{3 d}\right)}{5 d}\right)}{7 d}}{d}"," ",0,"2/d*(-1/14/(d*x+c)^(7/2)-1/14/(d*x+c)^(7/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-2/7/d*b*(-1/5/(d*x+c)^(5/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+4/5/d*b*(-1/3/(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-4/3/d*b*(-1/(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+2/d*b*Pi^(1/2)/(1/d*b)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))))))","A"
56,1,474,314,0.057000," ","int((d*x+c)^(5/2)*cos(b*x+a)^3,x)","\frac{\frac{3 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{15 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*(3/8*d/b*(d*x+c)^(5/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-15/8*d/b*(-1/2*d/b*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/2*d/b*(1/2*d/b*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4*d/b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))))+1/24*d/b*(d*x+c)^(5/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-5/24*d/b*(-1/6*d/b*(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/2*d/b*(1/6*d/b*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/36*d/b*2^(1/2)*Pi^(1/2)*3^(1/2)/(1/d*b)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/d*b)^(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)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
57,1,386,268,0.053000," ","int((d*x+c)^(3/2)*cos(b*x+a)^3,x)","\frac{\frac{3 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{9 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*(3/8*d/b*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-9/8*d/b*(-1/2*d/b*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4*d/b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))+1/24*d/b*(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/8*d/b*(-1/6*d/b*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/36*d/b*2^(1/2)*Pi^(1/2)*3^(1/2)/(1/d*b)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/d*b)^(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)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
58,1,294,224,0.052000," ","int((d*x+c)^(1/2)*cos(b*x+a)^3,x)","\frac{\frac{3 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{3 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*(3/8*d/b*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/16*d/b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))+1/24*d/b*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/144*d/b*2^(1/2)*Pi^(1/2)*3^(1/2)/(1/d*b)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/d*b)^(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)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
59,1,212,185,0.061000," ","int(cos(b*x+a)^3/(d*x+c)^(1/2),x)","\frac{\frac{3 \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 \sqrt{\frac{b}{d}}}+\frac{\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)}{12 \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(3/8*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))+1/24*2^(1/2)*Pi^(1/2)*3^(1/2)/(1/d*b)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/d*b)^(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)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
60,1,286,205,0.052000," ","int(cos(b*x+a)^3/(d*x+c)^(3/2),x)","\frac{-\frac{3 \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 \sqrt{d x +c}}-\frac{3 b \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)}{2 d \sqrt{\frac{b}{d}}}-\frac{\cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{2 \sqrt{d x +c}}-\frac{b \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)}{2 d \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-3/4/(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/4/d*b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))-1/4/(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/4/d*b*2^(1/2)*Pi^(1/2)*3^(1/2)/(1/d*b)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/d*b)^(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)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
61,1,368,230,0.053000," ","int(cos(b*x+a)^3/(d*x+c)^(5/2),x)","\frac{-\frac{\cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 \left(d x +c \right)^{\frac{3}{2}}}-\frac{b \left(-\frac{\sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{\sqrt{d x +c}}+\frac{b \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)}{d \sqrt{\frac{b}{d}}}\right)}{d}-\frac{\cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 \left(d x +c \right)^{\frac{3}{2}}}-\frac{b \left(-\frac{\sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{\sqrt{d x +c}}+\frac{b \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)}{d \sqrt{\frac{b}{d}}}\right)}{d}}{d}"," ",0,"2/d*(-1/4/(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/2/d*b*(-1/(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/d*b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))-1/12/(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/2/d*b*(-1/(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/d*b*2^(1/2)*Pi^(1/2)*3^(1/2)/(1/d*b)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/d*b)^(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)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
62,1,450,276,0.048000," ","int(cos(b*x+a)^3/(d*x+c)^(7/2),x)","\frac{-\frac{3 \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{10 \left(d x +c \right)^{\frac{5}{2}}}-\frac{3 b \left(-\frac{\sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{3 \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 b \left(-\frac{\cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{\sqrt{d x +c}}-\frac{b \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)}{d \sqrt{\frac{b}{d}}}\right)}{3 d}\right)}{5 d}-\frac{\cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{10 \left(d x +c \right)^{\frac{5}{2}}}-\frac{3 b \left(-\frac{\sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{3 \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 b \left(-\frac{\cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{\sqrt{d x +c}}-\frac{b \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)}{d \sqrt{\frac{b}{d}}}\right)}{d}\right)}{5 d}}{d}"," ",0,"2/d*(-3/20/(d*x+c)^(5/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/10/d*b*(-1/3/(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+2/3/d*b*(-1/(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/d*b*2^(1/2)*Pi^(1/2)/(1/d*b)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d))))-1/20/(d*x+c)^(5/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-3/10/d*b*(-1/3/(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+2/d*b*(-1/(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/d*b*2^(1/2)*Pi^(1/2)*3^(1/2)/(1/d*b)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/d*b)^(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)/(1/d*b)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
63,1,34,33,0.035000," ","int(x^(3/2)*cos(x),x)","x^{\frac{3}{2}} \sin \left(x \right)-\frac{3 \FresnelC \left(\frac{\sqrt{2}\, \sqrt{x}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{4}+\frac{3 \sqrt{x}\, \cos \left(x \right)}{2}"," ",0,"x^(3/2)*sin(x)-3/4*FresnelC(2^(1/2)/Pi^(1/2)*x^(1/2))*2^(1/2)*Pi^(1/2)+3/2*x^(1/2)*cos(x)","A"
64,1,27,26,0.032000," ","int(x^(1/2)*cos(x),x)","-\frac{\mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{x}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}}{2}+\sin \left(x \right) \sqrt{x}"," ",0,"-1/2*FresnelS(2^(1/2)/Pi^(1/2)*x^(1/2))*2^(1/2)*Pi^(1/2)+sin(x)*x^(1/2)","A"
65,1,19,18,0.031000," ","int(cos(x)/x^(1/2),x)","\FresnelC \left(\frac{\sqrt{2}\, \sqrt{x}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}"," ",0,"FresnelC(2^(1/2)/Pi^(1/2)*x^(1/2))*2^(1/2)*Pi^(1/2)","A"
66,1,28,27,0.031000," ","int(cos(x)/x^(3/2),x)","-2 \,\mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{x}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}-\frac{2 \cos \left(x \right)}{\sqrt{x}}"," ",0,"-2*FresnelS(2^(1/2)/Pi^(1/2)*x^(1/2))*2^(1/2)*Pi^(1/2)-2*cos(x)/x^(1/2)","A"
67,0,0,153,0.091000," ","int((d*x+c)^(4/3)*cos(b*x+a),x)","\int \left(d x +c \right)^{\frac{4}{3}} \cos \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^(4/3)*cos(b*x+a),x)","F"
68,0,0,128,0.099000," ","int((d*x+c)^(2/3)*cos(b*x+a),x)","\int \left(d x +c \right)^{\frac{2}{3}} \cos \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^(2/3)*cos(b*x+a),x)","F"
69,0,0,128,0.092000," ","int((d*x+c)^(1/3)*cos(b*x+a),x)","\int \left(d x +c \right)^{\frac{1}{3}} \cos \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^(1/3)*cos(b*x+a),x)","F"
70,0,0,111,0.085000," ","int(cos(b*x+a)/(d*x+c)^(1/3),x)","\int \frac{\cos \left(b x +a \right)}{\left(d x +c \right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(b*x+a)/(d*x+c)^(1/3),x)","F"
71,0,0,111,0.085000," ","int(cos(b*x+a)/(d*x+c)^(2/3),x)","\int \frac{\cos \left(b x +a \right)}{\left(d x +c \right)^{\frac{2}{3}}}\, dx"," ",0,"int(cos(b*x+a)/(d*x+c)^(2/3),x)","F"
72,0,0,127,0.056000," ","int(cos(b*x+a)/(d*x+c)^(4/3),x)","\int \frac{\cos \left(b x +a \right)}{\left(d x +c \right)^{\frac{4}{3}}}\, dx"," ",0,"int(cos(b*x+a)/(d*x+c)^(4/3),x)","F"
73,0,0,127,0.070000," ","int(cos(b*x+a)/(d*x+c)^(5/3),x)","\int \frac{\cos \left(b x +a \right)}{\left(d x +c \right)^{\frac{5}{3}}}\, dx"," ",0,"int(cos(b*x+a)/(d*x+c)^(5/3),x)","F"
74,0,0,150,0.078000," ","int(cos(b*x+a)/(d*x+c)^(7/3),x)","\int \frac{\cos \left(b x +a \right)}{\left(d x +c \right)^{\frac{7}{3}}}\, dx"," ",0,"int(cos(b*x+a)/(d*x+c)^(7/3),x)","F"
75,0,0,12,0.326000," ","int(x*cos(b*x+a)^(1/2),x)","\int x \left(\sqrt{\cos}\left(b x +a \right)\right)\, dx"," ",0,"int(x*cos(b*x+a)^(1/2),x)","F"
76,1,133,42,0.001000," ","int(cos(b*x+a)^(1/2),x)","\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, b}"," ",0,"2*((2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))/(-2*sin(1/2*b*x+1/2*a)^4+sin(1/2*b*x+1/2*a)^2)^(1/2)/sin(1/2*b*x+1/2*a)/(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)/b","B"
77,0,0,14,0.055000," ","int(cos(b*x+a)^(1/2)/x,x)","\int \frac{\sqrt{\cos}\left(b x +a \right)}{x}\, dx"," ",0,"int(cos(b*x+a)^(1/2)/x,x)","F"
78,0,0,48,0.043000," ","int(x*cos(b*x+a)^(3/2),x)","\int x \left(\cos^{\frac{3}{2}}\left(b x +a \right)\right)\, dx"," ",0,"int(x*cos(b*x+a)^(3/2),x)","F"
79,1,179,62,0.183000," ","int(cos(b*x+a)^(3/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(4 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, b}"," ",0,"-2/3*((2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*(4*sin(1/2*b*x+1/2*a)^4*cos(1/2*b*x+1/2*a)+(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))-2*sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/(-2*sin(1/2*b*x+1/2*a)^4+sin(1/2*b*x+1/2*a)^2)^(1/2)/sin(1/2*b*x+1/2*a)/(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)/b","B"
80,0,0,14,0.042000," ","int(cos(b*x+a)^(3/2)/x,x)","\int \frac{\cos^{\frac{3}{2}}\left(b x +a \right)}{x}\, dx"," ",0,"int(cos(b*x+a)^(3/2)/x,x)","F"
81,0,0,34,0.211000," ","int(x*cos(b*x+a)^(3/2)-1/3*x/cos(b*x+a)^(1/2),x)","\int x \left(\cos^{\frac{3}{2}}\left(b x +a \right)\right)-\frac{x}{3 \sqrt{\cos \left(b x +a \right)}}\, dx"," ",0,"int(x*cos(b*x+a)^(3/2)-1/3*x/cos(b*x+a)^(1/2),x)","F"
82,0,0,45,0.059000," ","int(cos(x)^(3/2)/x^3,x)","\int \frac{\cos^{\frac{3}{2}}\left(x \right)}{x^{3}}\, dx"," ",0,"int(cos(x)^(3/2)/x^3,x)","F"
83,0,0,12,0.039000," ","int(x/cos(b*x+a)^(1/2),x)","\int \frac{x}{\sqrt{\cos \left(b x +a \right)}}\, dx"," ",0,"int(x/cos(b*x+a)^(1/2),x)","F"
84,1,18,42,0.000000," ","int(1/cos(b*x+a)^(1/2),x)","\frac{2 \,\mathrm{am}^{-1}\left(\frac{b x}{2}+\frac{a}{2}| \sqrt{2}\right)}{b}"," ",0,"2/b*InverseJacobiAM(1/2*b*x+1/2*a,2^(1/2))","C"
85,0,0,14,0.052000," ","int(1/x/cos(b*x+a)^(1/2),x)","\int \frac{1}{x \sqrt{\cos \left(b x +a \right)}}\, dx"," ",0,"int(1/x/cos(b*x+a)^(1/2),x)","F"
86,0,0,48,0.048000," ","int(x/cos(b*x+a)^(3/2),x)","\int \frac{x}{\cos \left(b x +a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/cos(b*x+a)^(3/2),x)","F"
87,1,101,62,0.000000," ","int(1/cos(b*x+a)^(3/2),x)","-\frac{2 \left(\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{\sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, b}"," ",0,"-2*((sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-2*sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/sin(1/2*b*x+1/2*a)/(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)/b","A"
88,0,0,14,0.042000," ","int(1/x/cos(b*x+a)^(3/2),x)","\int \frac{1}{x \cos \left(b x +a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x/cos(b*x+a)^(3/2),x)","F"
89,0,0,34,0.178000," ","int(x/cos(b*x+a)^(3/2)+x*cos(b*x+a)^(1/2),x)","\int \frac{x}{\cos \left(b x +a \right)^{\frac{3}{2}}}+x \left(\sqrt{\cos}\left(b x +a \right)\right)\, dx"," ",0,"int(x/cos(b*x+a)^(3/2)+x*cos(b*x+a)^(1/2),x)","F"
90,0,0,16,0.257000," ","int(x/cos(x)^(3/2)+x*cos(x)^(1/2),x)","\int \frac{x}{\cos \left(x \right)^{\frac{3}{2}}}+x \left(\sqrt{\cos}\left(x \right)\right)\, dx"," ",0,"int(x/cos(x)^(3/2)+x*cos(x)^(1/2),x)","F"
91,0,0,16,0.260000," ","int(x/cos(x)^(5/2)-1/3*x/cos(x)^(1/2),x)","\int \frac{x}{\cos \left(x \right)^{\frac{5}{2}}}-\frac{x}{3 \sqrt{\cos \left(x \right)}}\, dx"," ",0,"int(x/cos(x)^(5/2)-1/3*x/cos(x)^(1/2),x)","F"
92,0,0,31,0.365000," ","int(x/cos(x)^(7/2)+3/5*x*cos(x)^(1/2),x)","\int \frac{x}{\cos \left(x \right)^{\frac{7}{2}}}+\frac{3 x \left(\sqrt{\cos}\left(x \right)\right)}{5}\, dx"," ",0,"int(x/cos(x)^(7/2)+3/5*x*cos(x)^(1/2),x)","F"
93,0,0,43,0.262000," ","int(x^2/cos(x)^(3/2)+x^2*cos(x)^(1/2),x)","\int \frac{x^{2}}{\cos \left(x \right)^{\frac{3}{2}}}+x^{2} \left(\sqrt{\cos}\left(x \right)\right)\, dx"," ",0,"int(x^2/cos(x)^(3/2)+x^2*cos(x)^(1/2),x)","F"
94,0,0,16,0.183000," ","int(x/sec(x)^(3/2)-1/3*x*sec(x)^(1/2),x)","\int \frac{x}{\sec \left(x \right)^{\frac{3}{2}}}-\frac{x \left(\sqrt{\sec}\left(x \right)\right)}{3}\, dx"," ",0,"int(x/sec(x)^(3/2)-1/3*x*sec(x)^(1/2),x)","F"
95,0,0,16,0.182000," ","int(x/sec(x)^(5/2)-3/5*x/sec(x)^(1/2),x)","\int \frac{x}{\sec \left(x \right)^{\frac{5}{2}}}-\frac{3 x}{5 \sqrt{\sec \left(x \right)}}\, dx"," ",0,"int(x/sec(x)^(5/2)-3/5*x/sec(x)^(1/2),x)","F"
96,0,0,31,0.198000," ","int(x/sec(x)^(7/2)-5/21*x*sec(x)^(1/2),x)","\int \frac{x}{\sec \left(x \right)^{\frac{7}{2}}}-\frac{5 x \left(\sqrt{\sec}\left(x \right)\right)}{21}\, dx"," ",0,"int(x/sec(x)^(7/2)-5/21*x*sec(x)^(1/2),x)","F"
97,0,0,59,0.170000," ","int(x^2/sec(x)^(3/2)-1/3*x^2*sec(x)^(1/2),x)","\int \frac{x^{2}}{\sec \left(x \right)^{\frac{3}{2}}}-\frac{x^{2} \left(\sqrt{\sec}\left(x \right)\right)}{3}\, dx"," ",0,"int(x^2/sec(x)^(3/2)-1/3*x^2*sec(x)^(1/2),x)","F"
98,0,0,20,0.295000," ","int((d*x+c)^m*(b*cos(f*x+e))^n,x)","\int \left(d x +c \right)^{m} \left(b \cos \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((d*x+c)^m*(b*cos(f*x+e))^n,x)","F"
99,0,0,251,0.295000," ","int((d*x+c)^m*cos(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \left(\cos^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)^3,x)","F"
100,0,0,152,0.214000," ","int((d*x+c)^m*cos(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \left(\cos^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a)^2,x)","F"
101,0,0,119,0.104000," ","int((d*x+c)^m*cos(b*x+a),x)","\int \left(d x +c \right)^{m} \cos \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*cos(b*x+a),x)","F"
102,0,0,16,0.091000," ","int((d*x+c)^m*sec(b*x+a),x)","\int \left(d x +c \right)^{m} \sec \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*sec(b*x+a),x)","F"
103,0,0,18,0.086000," ","int((d*x+c)^m*sec(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \left(\sec^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*sec(b*x+a)^2,x)","F"
104,1,455,65,0.154000," ","int(x^(3+m)*cos(b*x+a),x)","\frac{2^{3+m} \left(b^{2}\right)^{-\frac{m}{2}} \sqrt{\pi}\, \left(\frac{3 \,2^{-4-m} x^{3+m} b^{3} \left(b^{2}\right)^{\frac{m}{2}} \left(\frac{8}{3}+\frac{2 m}{3}\right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(4+m \right)}-\frac{2^{-3-m} x^{1+m} b \left(b^{2}\right)^{\frac{m}{2}} \left(-m^{2}-7 m -12\right) \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right)}{\sqrt{\pi}\, \left(4+m \right)}+\frac{2^{-3-m} x^{2+m} b^{2} \left(b^{2}\right)^{\frac{m}{2}} \left(-m^{3}-8 m^{2}-19 m -12\right) \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{3}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(4+m \right)}-\frac{2^{-3-m} x^{2+m} b^{2} \left(b^{2}\right)^{\frac{m}{2}} \left(2+m \right) \left(1+m \right) \left(3+m \right) \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{1}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}}\right) \cos \left(a \right)}{b^{4}}-2^{3+m} b^{-4-m} \sqrt{\pi}\, \left(\frac{2^{-3-m} x^{2+m} b^{2+m} \left(m^{2}+7 m +10\right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(5+m \right)}-\frac{2^{-3-m} x^{2+m} b^{2+m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right)}{\sqrt{\pi}}-\frac{2^{-3-m} x^{2+m} b^{2+m} m \left(3+m \right) \left(2+m \right) \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{1}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}}+\frac{2^{-3-m} x^{2+m} b^{2+m} \left(3+m \right) \left(2+m \right) \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{3}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}}\right) \sin \left(a \right)"," ",0,"2^(3+m)/b^4*(b^2)^(-1/2*m)*Pi^(1/2)*(3*2^(-4-m)/Pi^(1/2)/(4+m)*x^(3+m)*b^3*(b^2)^(1/2*m)*(8/3+2/3*m)*sin(b*x)-2^(-3-m)/Pi^(1/2)/(4+m)*x^(1+m)*b*(b^2)^(1/2*m)*(-m^2-7*m-12)*(cos(b*x)*x*b-sin(b*x))+2^(-3-m)/Pi^(1/2)/(4+m)*x^(2+m)*b^2*(b^2)^(1/2*m)*(-m^3-8*m^2-19*m-12)*(b*x)^(-3/2-m)*LommelS1(m+3/2,3/2,b*x)*sin(b*x)-2^(-3-m)/Pi^(1/2)*x^(2+m)*b^2*(b^2)^(1/2*m)*(2+m)*(1+m)*(3+m)*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+1/2,1/2,b*x))*cos(a)-2^(3+m)*b^(-4-m)*Pi^(1/2)*(2^(-3-m)/Pi^(1/2)/(5+m)*x^(2+m)*b^(2+m)*(m^2+7*m+10)*sin(b*x)-2^(-3-m)/Pi^(1/2)*x^(2+m)*b^(2+m)*(cos(b*x)*x*b-sin(b*x))-2^(-3-m)/Pi^(1/2)*x^(2+m)*b^(2+m)*m*(3+m)*(2+m)*(b*x)^(-3/2-m)*LommelS1(m+1/2,3/2,b*x)*sin(b*x)+2^(-3-m)/Pi^(1/2)*x^(2+m)*b^(2+m)*(3+m)*(2+m)*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+3/2,1/2,b*x))*sin(a)","C"
105,1,354,67,0.115000," ","int(x^(2+m)*cos(b*x+a),x)","\frac{2^{2+m} \left(b^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \sqrt{\pi}\, \left(\frac{3 \,2^{-3-m} x^{2+m} \left(b^{2}\right)^{\frac{3}{2}+\frac{m}{2}} \left(2+\frac{2 m}{3}\right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(3+m \right) b}-\frac{2^{-2-m} x^{2+m} \left(b^{2}\right)^{\frac{3}{2}+\frac{m}{2}} \left(2+m \right) m \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{1}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, b}+\frac{2^{-2-m} x^{2+m} \left(b^{2}\right)^{\frac{3}{2}+\frac{m}{2}} \left(2+m \right) \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{3}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}\, b}\right) \cos \left(a \right)}{b^{2}}-2^{2+m} b^{-3-m} \sqrt{\pi}\, \left(-\frac{2^{-2-m} x^{1+m} b^{1+m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right)}{\sqrt{\pi}}+\frac{2^{-2-m} x^{2+m} b^{2+m} \left(m^{2}+5 m +4\right) \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{3}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(4+m \right)}+\frac{2^{-2-m} x^{2+m} b^{2+m} \left(2+m \right) \left(1+m \right) \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{1}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}}\right) \sin \left(a \right)"," ",0,"2^(2+m)/b^2*(b^2)^(-1/2-1/2*m)*Pi^(1/2)*(3*2^(-3-m)/Pi^(1/2)/(3+m)*x^(2+m)*(b^2)^(3/2+1/2*m)*(2+2/3*m)/b*sin(b*x)-2^(-2-m)/Pi^(1/2)*x^(2+m)*(b^2)^(3/2+1/2*m)/b*(2+m)*m*(b*x)^(-3/2-m)*LommelS1(m+1/2,3/2,b*x)*sin(b*x)+2^(-2-m)/Pi^(1/2)*x^(2+m)*(b^2)^(3/2+1/2*m)/b*(2+m)*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+3/2,1/2,b*x))*cos(a)-2^(2+m)*b^(-3-m)*Pi^(1/2)*(-2^(-2-m)/Pi^(1/2)*x^(1+m)*b^(1+m)*(cos(b*x)*x*b-sin(b*x))+2^(-2-m)/Pi^(1/2)/(4+m)*x^(2+m)*b^(2+m)*(m^2+5*m+4)*(b*x)^(-3/2-m)*LommelS1(m+3/2,3/2,b*x)*sin(b*x)+2^(-2-m)/Pi^(1/2)*x^(2+m)*b^(2+m)*(2+m)*(1+m)*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+1/2,1/2,b*x))*sin(a)","C"
106,1,291,65,0.109000," ","int(x^(1+m)*cos(b*x+a),x)","\frac{2^{1+m} \left(b^{2}\right)^{-\frac{m}{2}} \sqrt{\pi}\, \left(\frac{2^{-1-m} x^{1+m} b \left(b^{2}\right)^{\frac{m}{2}} \sin \left(b x \right)}{\sqrt{\pi}\, \left(2+m \right)}+\frac{3 \,2^{-2-m} x^{2+m} b^{2} \left(b^{2}\right)^{\frac{m}{2}} \left(\frac{2}{3}+\frac{2 m}{3}\right) \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{3}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(2+m \right)}+\frac{2^{-1-m} x^{2+m} b^{2} \left(b^{2}\right)^{\frac{m}{2}} \left(1+m \right) \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{1}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}}\right) \cos \left(a \right)}{b^{2}}-2^{1+m} b^{-2-m} \sqrt{\pi}\, \left(\frac{2^{-1-m} x^{2+m} b^{2+m} m \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{1}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}}-\frac{2^{-1-m} x^{2+m} b^{2+m} \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{3}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}}\right) \sin \left(a \right)"," ",0,"2^(1+m)/b^2*(b^2)^(-1/2*m)*Pi^(1/2)*(2^(-1-m)/Pi^(1/2)/(2+m)*x^(1+m)*b*(b^2)^(1/2*m)*sin(b*x)+3*2^(-2-m)/Pi^(1/2)/(2+m)*x^(2+m)*b^2*(b^2)^(1/2*m)*(2/3+2/3*m)*(b*x)^(-3/2-m)*LommelS1(m+3/2,3/2,b*x)*sin(b*x)+2^(-1-m)/Pi^(1/2)*x^(2+m)*b^2*(b^2)^(1/2*m)*(1+m)*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+1/2,1/2,b*x))*cos(a)-2^(1+m)*b^(-2-m)*Pi^(1/2)*(2^(-1-m)/Pi^(1/2)*x^(2+m)*b^(2+m)*m*(b*x)^(-3/2-m)*LommelS1(m+1/2,3/2,b*x)*sin(b*x)-2^(-1-m)/Pi^(1/2)*x^(2+m)*b^(2+m)*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+3/2,1/2,b*x))*sin(a)","C"
107,1,379,67,0.102000," ","int(x^m*cos(b*x+a),x)","2^{m} \left(b^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \sqrt{\pi}\, \left(\frac{3 \,2^{-1-m} \left(b^{2}\right)^{\frac{1}{2}+\frac{m}{2}} x^{m} \left(6+2 m \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(1+m \right) \left(9+3 m \right) b}+\frac{\left(b^{2}\right)^{\frac{1}{2}+\frac{m}{2}} x^{m} 2^{-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right)}{\sqrt{\pi}\, \left(1+m \right) b}+\frac{2^{-m} x^{2+m} \left(b^{2}\right)^{\frac{1}{2}+\frac{m}{2}} b m \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{1}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(1+m \right)}-\frac{2^{-m} x^{2+m} \left(b^{2}\right)^{\frac{1}{2}+\frac{m}{2}} b \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{3}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}\, \left(1+m \right)}\right) \cos \left(a \right)-2^{m} b^{-1-m} \sqrt{\pi}\, \left(\frac{x^{1+m} b^{1+m} 2^{-m} \sin \left(b x \right)}{\sqrt{\pi}\, \left(2+m \right)}-\frac{2^{-m} x^{2+m} b^{2+m} \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{3}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(2+m \right)}-\frac{3 \,2^{-1-m} x^{2+m} b^{2+m} \left(\frac{4}{3}+\frac{2 m}{3}\right) \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{1}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}\, \left(2+m \right)}\right) \sin \left(a \right)"," ",0,"2^m*(b^2)^(-1/2-1/2*m)*Pi^(1/2)*(3*2^(-1-m)/Pi^(1/2)/(1+m)*(b^2)^(1/2+1/2*m)*x^m*(6+2*m)/(9+3*m)/b*sin(b*x)+1/Pi^(1/2)/(1+m)*(b^2)^(1/2+1/2*m)*x^m*2^(-m)/b*(cos(b*x)*x*b-sin(b*x))+2^(-m)/Pi^(1/2)/(1+m)*x^(2+m)*(b^2)^(1/2+1/2*m)*b*m*(b*x)^(-3/2-m)*LommelS1(m+1/2,3/2,b*x)*sin(b*x)-2^(-m)/Pi^(1/2)/(1+m)*x^(2+m)*(b^2)^(1/2+1/2*m)*b*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+3/2,1/2,b*x))*cos(a)-2^m*b^(-1-m)*Pi^(1/2)*(1/Pi^(1/2)/(2+m)*x^(1+m)*b^(1+m)*2^(-m)*sin(b*x)-2^(-m)/Pi^(1/2)/(2+m)*x^(2+m)*b^(2+m)*(b*x)^(-3/2-m)*LommelS1(m+3/2,3/2,b*x)*sin(b*x)-3*2^(-1-m)/Pi^(1/2)/(2+m)*x^(2+m)*b^(2+m)*(4/3+2/3*m)*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+1/2,1/2,b*x))*sin(a)","C"
108,1,427,55,0.108000," ","int(x^(-1+m)*cos(b*x+a),x)","2^{-1+m} \left(b^{2}\right)^{-\frac{m}{2}} \sqrt{\pi}\, \left(\frac{3 x^{-1+m} 2^{-m} \left(b^{2}\right)^{\frac{m}{2}} \left(2 x^{2} b^{2}+2 m +4\right) \sin \left(b x \right)}{\sqrt{\pi}\, m \left(6+3 m \right) b}+\frac{2^{1-m} x^{-1+m} \left(b^{2}\right)^{\frac{m}{2}} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right)}{\sqrt{\pi}\, m b}-\frac{3 x^{2+m} 2^{1-m} \left(b^{2}\right)^{\frac{m}{2}} b^{2} \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{3}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, m \left(6+3 m \right)}-\frac{x^{2+m} 2^{1-m} \left(b^{2}\right)^{\frac{m}{2}} b^{2} \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{1}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}\, m}\right) \cos \left(a \right)-2^{-1+m} b^{-m} \sqrt{\pi}\, \left(\frac{2^{1-m} x^{m} b^{m} \sin \left(b x \right)}{\sqrt{\pi}\, \left(1+m \right)}-\frac{2^{1-m} x^{m} b^{m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right)}{\sqrt{\pi}\, \left(1+m \right) m}-\frac{x^{2+m} b^{2+m} 2^{1-m} \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{1}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(1+m \right)}+\frac{x^{2+m} b^{2+m} 2^{1-m} \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{3}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}\, \left(1+m \right) m}\right) \sin \left(a \right)"," ",0,"2^(-1+m)*(b^2)^(-1/2*m)*Pi^(1/2)*(3/Pi^(1/2)/m*x^(-1+m)*2^(-m)*(b^2)^(1/2*m)*(2*b^2*x^2+2*m+4)/(6+3*m)/b*sin(b*x)+2^(1-m)/Pi^(1/2)/m*x^(-1+m)*(b^2)^(1/2*m)/b*(cos(b*x)*x*b-sin(b*x))-3/Pi^(1/2)/m*x^(2+m)*2^(1-m)*(b^2)^(1/2*m)*b^2/(6+3*m)*(b*x)^(-3/2-m)*LommelS1(m+3/2,3/2,b*x)*sin(b*x)-1/Pi^(1/2)/m*x^(2+m)*2^(1-m)*(b^2)^(1/2*m)*b^2*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+1/2,1/2,b*x))*cos(a)-2^(-1+m)*b^(-m)*Pi^(1/2)*(2^(1-m)/Pi^(1/2)/(1+m)*x^m*b^m*sin(b*x)-2^(1-m)/Pi^(1/2)/(1+m)*x^m*b^m/m*(cos(b*x)*x*b-sin(b*x))-1/Pi^(1/2)/(1+m)*x^(2+m)*b^(2+m)*2^(1-m)*(b*x)^(-3/2-m)*LommelS1(m+1/2,3/2,b*x)*sin(b*x)+1/Pi^(1/2)/(1+m)*x^(2+m)*b^(2+m)*2^(1-m)/m*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+3/2,1/2,b*x))*sin(a)","C"
109,1,530,63,0.115000," ","int(x^(-2+m)*cos(b*x+a),x)","2^{-2+m} b^{2} \left(b^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} \sqrt{\pi}\, \left(\frac{3 \,2^{1-m} x^{-2+m} \left(b^{2}\right)^{-\frac{1}{2}+\frac{m}{2}} \left(2 x^{2} b^{2}+2 m +2\right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(-1+m \right) \left(3+3 m \right) b}-\frac{2^{2-m} x^{-2+m} \left(b^{2}\right)^{-\frac{1}{2}+\frac{m}{2}} \left(x^{2} b^{2}-m^{2}-m \right) \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right)}{\sqrt{\pi}\, \left(-1+m \right) b \left(1+m \right) m}-\frac{3 \,2^{2-m} x^{2+m} \left(b^{2}\right)^{-\frac{1}{2}+\frac{m}{2}} b^{3} \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{1}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(-1+m \right) \left(3+3 m \right)}+\frac{2^{2-m} x^{2+m} \left(b^{2}\right)^{-\frac{1}{2}+\frac{m}{2}} b^{3} \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{3}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}\, \left(-1+m \right) \left(1+m \right) m}\right) \cos \left(a \right)-2^{-2+m} b^{1-m} \sqrt{\pi}\, \left(\frac{2^{1-m} x^{-1+m} b^{-1+m} \left(-2 x^{2} b^{2}+2 m^{2}+2 m -4\right) \sin \left(b x \right)}{\sqrt{\pi}\, m \left(2+m \right) \left(-1+m \right)}-\frac{3 \,2^{2-m} x^{-1+m} b^{-1+m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right)}{\sqrt{\pi}\, m \left(-3+3 m \right)}+\frac{2^{2-m} x^{2+m} b^{2+m} \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{3}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, m \left(2+m \right) \left(-1+m \right)}+\frac{3 \,2^{2-m} x^{2+m} b^{2+m} \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{1}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}\, m \left(-3+3 m \right)}\right) \sin \left(a \right)"," ",0,"2^(-2+m)*b^2*(b^2)^(-1/2-1/2*m)*Pi^(1/2)*(3*2^(1-m)/Pi^(1/2)/(-1+m)*x^(-2+m)*(b^2)^(-1/2+1/2*m)*(2*b^2*x^2+2*m+2)/(3+3*m)/b*sin(b*x)-2^(2-m)/Pi^(1/2)/(-1+m)*x^(-2+m)*(b^2)^(-1/2+1/2*m)/b*(b^2*x^2-m^2-m)/(1+m)/m*(cos(b*x)*x*b-sin(b*x))-3*2^(2-m)/Pi^(1/2)/(-1+m)*x^(2+m)*(b^2)^(-1/2+1/2*m)*b^3/(3+3*m)*(b*x)^(-3/2-m)*LommelS1(m+1/2,3/2,b*x)*sin(b*x)+2^(2-m)/Pi^(1/2)/(-1+m)*x^(2+m)*(b^2)^(-1/2+1/2*m)*b^3/(1+m)/m*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+3/2,1/2,b*x))*cos(a)-2^(-2+m)*b^(1-m)*Pi^(1/2)*(2^(1-m)/Pi^(1/2)/m*x^(-1+m)*b^(-1+m)*(-2*b^2*x^2+2*m^2+2*m-4)/(2+m)/(-1+m)*sin(b*x)-3*2^(2-m)/Pi^(1/2)/m*x^(-1+m)*b^(-1+m)/(-3+3*m)*(cos(b*x)*x*b-sin(b*x))+2^(2-m)/Pi^(1/2)/m*x^(2+m)*b^(2+m)/(2+m)/(-1+m)*(b*x)^(-3/2-m)*LommelS1(m+3/2,3/2,b*x)*sin(b*x)+3*2^(2-m)/Pi^(1/2)/m*x^(2+m)*b^(2+m)/(-3+3*m)*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+1/2,1/2,b*x))*sin(a)","C"
110,1,600,65,0.113000," ","int(x^(-3+m)*cos(b*x+a),x)","2^{-3+m} b^{2} \left(b^{2}\right)^{-\frac{m}{2}} \sqrt{\pi}\, \left(\frac{2^{2-m} x^{-3+m} \left(b^{2}\right)^{\frac{m}{2}} \left(-2 x^{4} b^{4}+2 x^{2} b^{2} m^{2}+2 x^{2} b^{2} m -4 x^{2} b^{2}+2 m^{3}+2 m^{2}-4 m \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(-2+m \right) b^{3} m \left(2+m \right) \left(-1+m \right)}-\frac{2^{-m +3} x^{-3+m} \left(b^{2}\right)^{\frac{m}{2}} \left(x^{2} b^{2}-m^{2}+m \right) \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right)}{\sqrt{\pi}\, \left(-2+m \right) b^{3} m \left(-1+m \right)}+\frac{2^{-m +3} x^{2+m} b^{2} \left(b^{2}\right)^{\frac{m}{2}} \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{3}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(-2+m \right) m \left(2+m \right) \left(-1+m \right)}+\frac{2^{-m +3} x^{2+m} b^{2} \left(b^{2}\right)^{\frac{m}{2}} \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{1}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}\, \left(-2+m \right) m \left(-1+m \right)}\right) \cos \left(a \right)-2^{-3+m} b^{2-m} \sqrt{\pi}\, \left(\frac{2^{2-m} x^{-2+m} b^{-2+m} \left(-2 x^{2} b^{2}+2 m^{2}-2 m -4\right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(-1+m \right) \left(1+m \right) \left(-2+m \right)}+\frac{2^{-m +3} x^{-2+m} b^{-2+m} \left(x^{2} b^{2}-m^{2}-m \right) \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right)}{\sqrt{\pi}\, \left(-1+m \right) \left(1+m \right) \left(-2+m \right) m}+\frac{2^{-m +3} x^{2+m} b^{2+m} \left(b x \right)^{-\frac{3}{2}-m} \LommelS1 \left(m +\frac{1}{2}, \frac{3}{2}, b x \right) \sin \left(b x \right)}{\sqrt{\pi}\, \left(-1+m \right) \left(1+m \right) \left(-2+m \right)}-\frac{2^{-m +3} x^{2+m} b^{2+m} \left(b x \right)^{-\frac{5}{2}-m} \left(\cos \left(b x \right) x b -\sin \left(b x \right)\right) \LommelS1 \left(m +\frac{3}{2}, \frac{1}{2}, b x \right)}{\sqrt{\pi}\, \left(-1+m \right) \left(1+m \right) \left(-2+m \right) m}\right) \sin \left(a \right)"," ",0,"2^(-3+m)*b^2*(b^2)^(-1/2*m)*Pi^(1/2)*(2^(2-m)/Pi^(1/2)/(-2+m)*x^(-3+m)/b^3*(b^2)^(1/2*m)*(-2*b^4*x^4+2*b^2*m^2*x^2+2*b^2*m*x^2-4*b^2*x^2+2*m^3+2*m^2-4*m)/m/(2+m)/(-1+m)*sin(b*x)-2^(-m+3)/Pi^(1/2)/(-2+m)*x^(-3+m)/b^3*(b^2)^(1/2*m)*(b^2*x^2-m^2+m)/m/(-1+m)*(cos(b*x)*x*b-sin(b*x))+2^(-m+3)/Pi^(1/2)/(-2+m)*x^(2+m)*b^2*(b^2)^(1/2*m)/m/(2+m)/(-1+m)*(b*x)^(-3/2-m)*LommelS1(m+3/2,3/2,b*x)*sin(b*x)+2^(-m+3)/Pi^(1/2)/(-2+m)*x^(2+m)*b^2*(b^2)^(1/2*m)/m/(-1+m)*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+1/2,1/2,b*x))*cos(a)-2^(-3+m)*b^(2-m)*Pi^(1/2)*(2^(2-m)/Pi^(1/2)/(-1+m)*x^(-2+m)*b^(-2+m)*(-2*b^2*x^2+2*m^2-2*m-4)/(1+m)/(-2+m)*sin(b*x)+2^(-m+3)/Pi^(1/2)/(-1+m)*x^(-2+m)*b^(-2+m)*(b^2*x^2-m^2-m)/(1+m)/(-2+m)/m*(cos(b*x)*x*b-sin(b*x))+2^(-m+3)/Pi^(1/2)/(-1+m)*x^(2+m)*b^(2+m)/(1+m)/(-2+m)*(b*x)^(-3/2-m)*LommelS1(m+1/2,3/2,b*x)*sin(b*x)-2^(-m+3)/Pi^(1/2)/(-1+m)*x^(2+m)*b^(2+m)/(1+m)/(-2+m)/m*(b*x)^(-5/2-m)*(cos(b*x)*x*b-sin(b*x))*LommelS1(m+3/2,1/2,b*x))*sin(a)","C"
111,0,0,91,0.135000," ","int(x^(3+m)*cos(b*x+a)^2,x)","\int x^{3+m} \left(\cos^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(3+m)*cos(b*x+a)^2,x)","F"
112,0,0,93,0.147000," ","int(x^(2+m)*cos(b*x+a)^2,x)","\int x^{2+m} \left(\cos^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(2+m)*cos(b*x+a)^2,x)","F"
113,0,0,89,0.215000," ","int(x^(1+m)*cos(b*x+a)^2,x)","\int x^{1+m} \left(\cos^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(1+m)*cos(b*x+a)^2,x)","F"
114,0,0,93,0.162000," ","int(x^m*cos(b*x+a)^2,x)","\int x^{m} \left(\cos^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^m*cos(b*x+a)^2,x)","F"
115,0,0,77,0.202000," ","int(x^(-1+m)*cos(b*x+a)^2,x)","\int x^{-1+m} \left(\cos^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(-1+m)*cos(b*x+a)^2,x)","F"
116,0,0,91,0.136000," ","int(x^(-2+m)*cos(b*x+a)^2,x)","\int x^{-2+m} \left(\cos^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(-2+m)*cos(b*x+a)^2,x)","F"
117,0,0,87,0.151000," ","int(x^(-3+m)*cos(b*x+a)^2,x)","\int x^{-3+m} \left(\cos^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(-3+m)*cos(b*x+a)^2,x)","F"
118,1,476,87,0.047000," ","int((d*x+c)^3*(a+a*cos(f*x+e)),x)","\frac{\frac{a \,d^{3} \left(\left(f x +e \right)^{3} \sin \left(f x +e \right)+3 \left(f x +e \right)^{2} \cos \left(f x +e \right)-6 \cos \left(f x +e \right)-6 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{3}}+\frac{3 a c \,d^{2} \left(\left(f x +e \right)^{2} \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+2 \left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}-\frac{3 a \,d^{3} e \left(\left(f x +e \right)^{2} \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+2 \left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{3}}+\frac{3 a \,c^{2} d \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f}-\frac{6 a c \,d^{2} e \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}+\frac{3 a \,d^{3} e^{2} \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{3}}+a \,c^{3} \sin \left(f x +e \right)-\frac{3 a \,c^{2} d e \sin \left(f x +e \right)}{f}+\frac{3 a c \,d^{2} e^{2} \sin \left(f x +e \right)}{f^{2}}-\frac{a \,d^{3} e^{3} \sin \left(f x +e \right)}{f^{3}}+\frac{a \,d^{3} \left(f x +e \right)^{4}}{4 f^{3}}+\frac{a c \,d^{2} \left(f x +e \right)^{3}}{f^{2}}-\frac{a \,d^{3} e \left(f x +e \right)^{3}}{f^{3}}+\frac{3 a \,c^{2} d \left(f x +e \right)^{2}}{2 f}-\frac{3 a c \,d^{2} e \left(f x +e \right)^{2}}{f^{2}}+\frac{3 a \,d^{3} e^{2} \left(f x +e \right)^{2}}{2 f^{3}}+a \,c^{3} \left(f x +e \right)-\frac{3 a \,c^{2} d e \left(f x +e \right)}{f}+\frac{3 a c \,d^{2} e^{2} \left(f x +e \right)}{f^{2}}-\frac{a \,d^{3} e^{3} \left(f x +e \right)}{f^{3}}}{f}"," ",0,"1/f*(a/f^3*d^3*((f*x+e)^3*sin(f*x+e)+3*(f*x+e)^2*cos(f*x+e)-6*cos(f*x+e)-6*(f*x+e)*sin(f*x+e))+3*a/f^2*c*d^2*((f*x+e)^2*sin(f*x+e)-2*sin(f*x+e)+2*(f*x+e)*cos(f*x+e))-3*a/f^3*d^3*e*((f*x+e)^2*sin(f*x+e)-2*sin(f*x+e)+2*(f*x+e)*cos(f*x+e))+3*a/f*c^2*d*(cos(f*x+e)+(f*x+e)*sin(f*x+e))-6*a/f^2*c*d^2*e*(cos(f*x+e)+(f*x+e)*sin(f*x+e))+3*a/f^3*d^3*e^2*(cos(f*x+e)+(f*x+e)*sin(f*x+e))+a*c^3*sin(f*x+e)-3*a/f*c^2*d*e*sin(f*x+e)+3*a/f^2*c*d^2*e^2*sin(f*x+e)-a/f^3*d^3*e^3*sin(f*x+e)+1/4*a/f^3*d^3*(f*x+e)^4+a/f^2*c*d^2*(f*x+e)^3-a/f^3*d^3*e*(f*x+e)^3+3/2*a/f*c^2*d*(f*x+e)^2-3*a/f^2*c*d^2*e*(f*x+e)^2+3/2*a/f^3*d^3*e^2*(f*x+e)^2+a*c^3*(f*x+e)-3*a/f*c^2*d*e*(f*x+e)+3*a/f^2*c*d^2*e^2*(f*x+e)-a/f^3*d^3*e^3*(f*x+e))","B"
119,1,236,65,0.033000," ","int((d*x+c)^2*(a+a*cos(f*x+e)),x)","\frac{\frac{a \,d^{2} \left(\left(f x +e \right)^{2} \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+2 \left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}+\frac{2 a c d \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f}-\frac{2 a \,d^{2} e \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}+a \,c^{2} \sin \left(f x +e \right)-\frac{2 a c d e \sin \left(f x +e \right)}{f}+\frac{a \,d^{2} e^{2} \sin \left(f x +e \right)}{f^{2}}+\frac{a \,d^{2} \left(f x +e \right)^{3}}{3 f^{2}}+\frac{a c d \left(f x +e \right)^{2}}{f}-\frac{a \,d^{2} e \left(f x +e \right)^{2}}{f^{2}}+a \,c^{2} \left(f x +e \right)-\frac{2 a c d e \left(f x +e \right)}{f}+\frac{a \,d^{2} e^{2} \left(f x +e \right)}{f^{2}}}{f}"," ",0,"1/f*(a/f^2*d^2*((f*x+e)^2*sin(f*x+e)-2*sin(f*x+e)+2*(f*x+e)*cos(f*x+e))+2*a/f*c*d*(cos(f*x+e)+(f*x+e)*sin(f*x+e))-2*a/f^2*d^2*e*(cos(f*x+e)+(f*x+e)*sin(f*x+e))+a*c^2*sin(f*x+e)-2*a/f*c*d*e*sin(f*x+e)+a/f^2*d^2*e^2*sin(f*x+e)+1/3*a/f^2*d^2*(f*x+e)^3+a/f*c*d*(f*x+e)^2-a/f^2*d^2*e*(f*x+e)^2+a*c^2*(f*x+e)-2*a/f*c*d*e*(f*x+e)+a/f^2*d^2*e^2*(f*x+e))","B"
120,1,89,42,0.033000," ","int((d*x+c)*(a+a*cos(f*x+e)),x)","\frac{\frac{a d \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f}+a c \sin \left(f x +e \right)-\frac{a d e \sin \left(f x +e \right)}{f}+\frac{a d \left(f x +e \right)^{2}}{2 f}+a c \left(f x +e \right)-\frac{a d e \left(f x +e \right)}{f}}{f}"," ",0,"1/f*(a/f*d*(cos(f*x+e)+(f*x+e)*sin(f*x+e))+a*c*sin(f*x+e)-a/f*d*e*sin(f*x+e)+1/2*a/f*d*(f*x+e)^2+a*c*(f*x+e)-a/f*d*e*(f*x+e))","B"
121,1,95,66,0.036000," ","int((a+a*cos(f*x+e))/(d*x+c),x)","\frac{a \Si \left(f x +e +\frac{c f -d e}{d}\right) \sin \left(\frac{c f -d e}{d}\right)}{d}+\frac{a \Ci \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}+\frac{a \ln \left(\left(f x +e \right) d +c f -d e \right)}{d}"," ",0,"a*Si(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d+a*Ci(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d+a*ln((f*x+e)*d+c*f-d*e)/d","A"
122,1,143,90,0.039000," ","int((a+a*cos(f*x+e))/(d*x+c)^2,x)","\frac{f^{2} a \left(-\frac{\cos \left(f x +e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}-\frac{\frac{\Si \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}-\frac{\Ci \left(f x +e +\frac{c f -d e}{d}\right) \sin \left(\frac{c f -d e}{d}\right)}{d}}{d}\right)-\frac{f^{2} a}{\left(\left(f x +e \right) d +c f -d e \right) d}}{f}"," ",0,"1/f*(f^2*a*(-cos(f*x+e)/((f*x+e)*d+c*f-d*e)/d-(Si(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d-Ci(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d)/d)-f^2*a/((f*x+e)*d+c*f-d*e)/d)","A"
123,1,1129,223,0.052000," ","int((d*x+c)^3*(a+a*cos(f*x+e))^2,x)","\frac{-\frac{3 a^{2} c \,d^{2} e \left(f x +e \right)^{2}}{f^{2}}-\frac{12 a^{2} c \,d^{2} e \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}-\frac{6 a^{2} c \,d^{2} e \left(\left(f x +e \right) \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\sin^{2}\left(f x +e \right)\right)}{4}\right)}{f^{2}}+\frac{2 a^{2} d^{3} \left(\left(f x +e \right)^{3} \sin \left(f x +e \right)+3 \left(f x +e \right)^{2} \cos \left(f x +e \right)-6 \cos \left(f x +e \right)-6 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{3}}+\frac{a^{2} d^{3} \left(\left(f x +e \right)^{3} \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+\frac{3 \left(f x +e \right)^{2} \left(\cos^{2}\left(f x +e \right)\right)}{4}-\frac{3 \left(f x +e \right) \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{2}+\frac{3 \left(f x +e \right)^{2}}{8}+\frac{3 \left(\sin^{2}\left(f x +e \right)\right)}{8}-\frac{3 \left(f x +e \right)^{4}}{8}\right)}{f^{3}}+\frac{a^{2} d^{3} \left(f x +e \right)^{4}}{4 f^{3}}-\frac{3 a^{2} c^{2} d e \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}-\frac{6 a^{2} c^{2} d e \sin \left(f x +e \right)}{f}+\frac{3 a^{2} c \,d^{2} e^{2} \left(f x +e \right)}{f^{2}}-\frac{3 a^{2} c^{2} d e \left(f x +e \right)}{f}+2 a^{2} c^{3} \sin \left(f x +e \right)+a^{2} c^{3} \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+a^{2} c^{3} \left(f x +e \right)+\frac{3 a^{2} c \,d^{2} \left(\left(f x +e \right)^{2} \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+\frac{\left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)}{2}-\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{4}-\frac{f x}{4}-\frac{e}{4}-\frac{\left(f x +e \right)^{3}}{3}\right)}{f^{2}}+\frac{3 a^{2} c^{2} d \left(\left(f x +e \right) \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\sin^{2}\left(f x +e \right)\right)}{4}\right)}{f}+\frac{a^{2} c \,d^{2} \left(f x +e \right)^{3}}{f^{2}}+\frac{3 a^{2} d^{3} e^{2} \left(f x +e \right)^{2}}{2 f^{3}}+\frac{6 a^{2} c \,d^{2} \left(\left(f x +e \right)^{2} \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+2 \left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}+\frac{6 a^{2} c^{2} d \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f}-\frac{a^{2} d^{3} e^{3} \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f^{3}}-\frac{2 a^{2} d^{3} e^{3} \sin \left(f x +e \right)}{f^{3}}-\frac{6 a^{2} d^{3} e \left(\left(f x +e \right)^{2} \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+2 \left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{3}}-\frac{a^{2} d^{3} e^{3} \left(f x +e \right)}{f^{3}}+\frac{6 a^{2} d^{3} e^{2} \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{3}}+\frac{3 a^{2} c^{2} d \left(f x +e \right)^{2}}{2 f}-\frac{a^{2} d^{3} e \left(f x +e \right)^{3}}{f^{3}}+\frac{3 a^{2} d^{3} e^{2} \left(\left(f x +e \right) \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\sin^{2}\left(f x +e \right)\right)}{4}\right)}{f^{3}}-\frac{3 a^{2} d^{3} e \left(\left(f x +e \right)^{2} \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+\frac{\left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)}{2}-\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{4}-\frac{f x}{4}-\frac{e}{4}-\frac{\left(f x +e \right)^{3}}{3}\right)}{f^{3}}+\frac{6 a^{2} c \,d^{2} e^{2} \sin \left(f x +e \right)}{f^{2}}+\frac{3 a^{2} c \,d^{2} e^{2} \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f^{2}}}{f}"," ",0,"1/f*(-3*a^2/f^2*c*d^2*e*(f*x+e)^2-6*a^2/f^2*c*d^2*e*((f*x+e)*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2-1/4*sin(f*x+e)^2)-12*a^2/f^2*c*d^2*e*(cos(f*x+e)+(f*x+e)*sin(f*x+e))+2*a^2/f^3*d^3*((f*x+e)^3*sin(f*x+e)+3*(f*x+e)^2*cos(f*x+e)-6*cos(f*x+e)-6*(f*x+e)*sin(f*x+e))+1/4*a^2/f^3*d^3*(f*x+e)^4+a^2/f^3*d^3*((f*x+e)^3*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)+3/4*(f*x+e)^2*cos(f*x+e)^2-3/2*(f*x+e)*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)+3/8*(f*x+e)^2+3/8*sin(f*x+e)^2-3/8*(f*x+e)^4)-3*a^2/f*c^2*d*e*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)-6*a^2/f*c^2*d*e*sin(f*x+e)+3*a^2/f^2*c*d^2*e^2*(f*x+e)-3*a^2/f*c^2*d*e*(f*x+e)+2*a^2*c^3*sin(f*x+e)+a^2*c^3*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)+a^2*c^3*(f*x+e)+a^2/f^2*c*d^2*(f*x+e)^3+3/2*a^2/f^3*d^3*e^2*(f*x+e)^2+6*a^2/f^2*c*d^2*((f*x+e)^2*sin(f*x+e)-2*sin(f*x+e)+2*(f*x+e)*cos(f*x+e))+6*a^2/f*c^2*d*(cos(f*x+e)+(f*x+e)*sin(f*x+e))-a^2/f^3*d^3*e^3*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)-2*a^2/f^3*d^3*e^3*sin(f*x+e)+3*a^2/f^2*c*d^2*((f*x+e)^2*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)+1/2*(f*x+e)*cos(f*x+e)^2-1/4*cos(f*x+e)*sin(f*x+e)-1/4*f*x-1/4*e-1/3*(f*x+e)^3)+3*a^2/f*c^2*d*((f*x+e)*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2-1/4*sin(f*x+e)^2)-6*a^2/f^3*d^3*e*((f*x+e)^2*sin(f*x+e)-2*sin(f*x+e)+2*(f*x+e)*cos(f*x+e))+3*a^2/f^3*d^3*e^2*((f*x+e)*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2-1/4*sin(f*x+e)^2)-a^2/f^3*d^3*e^3*(f*x+e)-3*a^2/f^3*d^3*e*((f*x+e)^2*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)+1/2*(f*x+e)*cos(f*x+e)^2-1/4*cos(f*x+e)*sin(f*x+e)-1/4*f*x-1/4*e-1/3*(f*x+e)^3)+6*a^2/f^3*d^3*e^2*(cos(f*x+e)+(f*x+e)*sin(f*x+e))+3/2*a^2/f*c^2*d*(f*x+e)^2-a^2/f^3*d^3*e*(f*x+e)^3+6*a^2/f^2*c*d^2*e^2*sin(f*x+e)+3*a^2/f^2*c*d^2*e^2*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e))","B"
124,1,564,158,0.051000," ","int((d*x+c)^2*(a+a*cos(f*x+e))^2,x)","\frac{\frac{a^{2} d^{2} \left(\left(f x +e \right)^{2} \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+\frac{\left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)}{2}-\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{4}-\frac{f x}{4}-\frac{e}{4}-\frac{\left(f x +e \right)^{3}}{3}\right)}{f^{2}}+\frac{2 a^{2} c d \left(\left(f x +e \right) \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\sin^{2}\left(f x +e \right)\right)}{4}\right)}{f}-\frac{2 a^{2} d^{2} e \left(\left(f x +e \right) \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\sin^{2}\left(f x +e \right)\right)}{4}\right)}{f^{2}}+a^{2} c^{2} \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{2 a^{2} c d e \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}+\frac{a^{2} d^{2} e^{2} \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f^{2}}+\frac{2 a^{2} d^{2} \left(\left(f x +e \right)^{2} \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+2 \left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}+\frac{4 a^{2} c d \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f}-\frac{4 a^{2} d^{2} e \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}+2 a^{2} c^{2} \sin \left(f x +e \right)-\frac{4 a^{2} c d e \sin \left(f x +e \right)}{f}+\frac{2 a^{2} d^{2} e^{2} \sin \left(f x +e \right)}{f^{2}}+\frac{a^{2} d^{2} \left(f x +e \right)^{3}}{3 f^{2}}+\frac{a^{2} c d \left(f x +e \right)^{2}}{f}-\frac{a^{2} d^{2} e \left(f x +e \right)^{2}}{f^{2}}+a^{2} c^{2} \left(f x +e \right)-\frac{2 a^{2} c d e \left(f x +e \right)}{f}+\frac{a^{2} d^{2} e^{2} \left(f x +e \right)}{f^{2}}}{f}"," ",0,"1/f*(a^2/f^2*d^2*((f*x+e)^2*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)+1/2*(f*x+e)*cos(f*x+e)^2-1/4*cos(f*x+e)*sin(f*x+e)-1/4*f*x-1/4*e-1/3*(f*x+e)^3)+2*a^2/f*c*d*((f*x+e)*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2-1/4*sin(f*x+e)^2)-2*a^2/f^2*d^2*e*((f*x+e)*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2-1/4*sin(f*x+e)^2)+a^2*c^2*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)-2*a^2/f*c*d*e*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)+a^2/f^2*d^2*e^2*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)+2*a^2/f^2*d^2*((f*x+e)^2*sin(f*x+e)-2*sin(f*x+e)+2*(f*x+e)*cos(f*x+e))+4*a^2/f*c*d*(cos(f*x+e)+(f*x+e)*sin(f*x+e))-4*a^2/f^2*d^2*e*(cos(f*x+e)+(f*x+e)*sin(f*x+e))+2*a^2*c^2*sin(f*x+e)-4*a^2/f*c*d*e*sin(f*x+e)+2*a^2/f^2*d^2*e^2*sin(f*x+e)+1/3*a^2/f^2*d^2*(f*x+e)^3+a^2/f*c*d*(f*x+e)^2-a^2/f^2*d^2*e*(f*x+e)^2+a^2*c^2*(f*x+e)-2*a^2/f*c*d*e*(f*x+e)+a^2/f^2*d^2*e^2*(f*x+e))","B"
125,1,218,108,0.047000," ","int((d*x+c)*(a+a*cos(f*x+e))^2,x)","\frac{\frac{a^{2} d \left(\left(f x +e \right) \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{\left(f x +e \right)^{2}}{4}-\frac{\left(\sin^{2}\left(f x +e \right)\right)}{4}\right)}{f}+a^{2} c \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{a^{2} d e \left(\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}+\frac{2 a^{2} d \left(\cos \left(f x +e \right)+\left(f x +e \right) \sin \left(f x +e \right)\right)}{f}+2 a^{2} c \sin \left(f x +e \right)-\frac{2 a^{2} d e \sin \left(f x +e \right)}{f}+\frac{a^{2} d \left(f x +e \right)^{2}}{2 f}+a^{2} c \left(f x +e \right)-\frac{a^{2} d e \left(f x +e \right)}{f}}{f}"," ",0,"1/f*(a^2/f*d*((f*x+e)*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2-1/4*sin(f*x+e)^2)+a^2*c*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)-a^2/f*d*e*(1/2*cos(f*x+e)*sin(f*x+e)+1/2*f*x+1/2*e)+2*a^2/f*d*(cos(f*x+e)+(f*x+e)*sin(f*x+e))+2*a^2*c*sin(f*x+e)-2*a^2/f*d*e*sin(f*x+e)+1/2*a^2/f*d*(f*x+e)^2+a^2*c*(f*x+e)-a^2/f*d*e*(f*x+e))","B"
126,1,192,141,0.050000," ","int((a+a*cos(f*x+e))^2/(d*x+c),x)","\frac{a^{2} \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{2 d}+\frac{a^{2} \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{2 d}+\frac{3 a^{2} \ln \left(\left(f x +e \right) d +c f -d e \right)}{2 d}+\frac{2 a^{2} \Si \left(f x +e +\frac{c f -d e}{d}\right) \sin \left(\frac{c f -d e}{d}\right)}{d}+\frac{2 a^{2} \Ci \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}"," ",0,"1/2*a^2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d+1/2*a^2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d+3/2*a^2*ln((f*x+e)*d+c*f-d*e)/d+2*a^2*Si(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d+2*a^2*Ci(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d","A"
127,1,276,156,0.049000," ","int((a+a*cos(f*x+e))^2/(d*x+c)^2,x)","\frac{\frac{f^{2} a^{2} \left(-\frac{2 \cos \left(2 f x +2 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}-\frac{2 \left(\frac{2 \Si \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \cos \left(\frac{2 c f -2 d e}{d}\right)}{d}-\frac{2 \Ci \left(2 f x +2 e +\frac{2 c f -2 d e}{d}\right) \sin \left(\frac{2 c f -2 d e}{d}\right)}{d}\right)}{d}\right)}{4}-\frac{3 f^{2} a^{2}}{2 \left(\left(f x +e \right) d +c f -d e \right) d}+2 f^{2} a^{2} \left(-\frac{\cos \left(f x +e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}-\frac{\frac{\Si \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}-\frac{\Ci \left(f x +e +\frac{c f -d e}{d}\right) \sin \left(\frac{c f -d e}{d}\right)}{d}}{d}\right)}{f}"," ",0,"1/f*(1/4*f^2*a^2*(-2*cos(2*f*x+2*e)/((f*x+e)*d+c*f-d*e)/d-2*(2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d-2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d)/d)-3/2*f^2*a^2/((f*x+e)*d+c*f-d*e)/d+2*f^2*a^2*(-cos(f*x+e)/((f*x+e)*d+c*f-d*e)/d-(Si(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d-Ci(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d)/d))","A"
128,1,364,122,0.165000," ","int((d*x+c)^3/(a+a*cos(f*x+e)),x)","\frac{2 i \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{f a \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}+\frac{6 d \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{a \,f^{2}}-\frac{6 d \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{2}}-\frac{6 d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{4}}-\frac{12 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{3}}+\frac{12 d^{2} c \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{a \,f^{2}}+\frac{6 i d^{3} e^{2} x}{a \,f^{3}}+\frac{4 i d^{3} e^{3}}{a \,f^{4}}+\frac{6 d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{a \,f^{2}}-\frac{12 i d^{2} c e x}{a \,f^{2}}+\frac{12 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{4}}+\frac{12 d^{2} c e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}-\frac{2 i d^{3} x^{3}}{a f}-\frac{6 i d^{2} c \,e^{2}}{a \,f^{3}}-\frac{12 i d^{2} c \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}-\frac{6 i d^{2} c \,x^{2}}{a f}"," ",0,"2*I*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/f/a/(exp(I*(f*x+e))+1)+6/a/f^2*d*c^2*ln(exp(I*(f*x+e))+1)-6/a/f^2*d*c^2*ln(exp(I*(f*x+e)))-6/a/f^4*d^3*e^2*ln(exp(I*(f*x+e)))-12*I/a/f^3*d^3*polylog(2,-exp(I*(f*x+e)))*x+12/a/f^2*d^2*c*ln(exp(I*(f*x+e))+1)*x+6*I/a/f^3*d^3*e^2*x+4*I/a/f^4*d^3*e^3+6/a/f^2*d^3*ln(exp(I*(f*x+e))+1)*x^2-12*I/a/f^2*d^2*c*e*x+12*d^3*polylog(3,-exp(I*(f*x+e)))/a/f^4+12/a/f^3*d^2*c*e*ln(exp(I*(f*x+e)))-2*I/a/f*d^3*x^3-6*I/a/f^3*d^2*c*e^2-12*I/a/f^3*d^2*c*polylog(2,-exp(I*(f*x+e)))-6*I/a/f*d^2*c*x^2","B"
129,1,197,91,0.113000," ","int((d*x+c)^2/(a+a*cos(f*x+e)),x)","\frac{2 i \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{f a \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}+\frac{4 d c \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{a \,f^{2}}-\frac{4 d c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{2}}-\frac{2 i d^{2} x^{2}}{a f}-\frac{4 i d^{2} e x}{a \,f^{2}}-\frac{2 i d^{2} e^{2}}{a \,f^{3}}+\frac{4 d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{a \,f^{2}}-\frac{4 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}+\frac{4 d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}"," ",0,"2*I*(d^2*x^2+2*c*d*x+c^2)/f/a/(exp(I*(f*x+e))+1)+4/a/f^2*d*c*ln(exp(I*(f*x+e))+1)-4/a/f^2*d*c*ln(exp(I*(f*x+e)))-2*I/a/f*d^2*x^2-4*I/a/f^2*d^2*e*x-2*I/a/f^3*d^2*e^2+4/a/f^2*d^2*ln(exp(I*(f*x+e))+1)*x-4*I*d^2*polylog(2,-exp(I*(f*x+e)))/a/f^3+4/a/f^3*d^2*e*ln(exp(I*(f*x+e)))","B"
130,1,60,41,0.086000," ","int((d*x+c)/(a+a*cos(f*x+e)),x)","\frac{c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{d x \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{d \ln \left(1+\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a \,f^{2}}"," ",0,"1/a*c/f*tan(1/2*e+1/2*f*x)+1/a*d*x/f*tan(1/2*e+1/2*f*x)-1/a*d/f^2*ln(1+tan(1/2*e+1/2*f*x)^2)","A"
131,0,0,22,0.171000," ","int(1/(d*x+c)/(a+a*cos(f*x+e)),x)","\int \frac{1}{\left(d x +c \right) \left(a +a \cos \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)/(a+a*cos(f*x+e)),x)","F"
132,0,0,22,0.228000," ","int(1/(d*x+c)^2/(a+a*cos(f*x+e)),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +a \cos \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)^2/(a+a*cos(f*x+e)),x)","F"
133,1,678,231,0.459000," ","int((d*x+c)^3/(a+a*cos(f*x+e))^2,x)","-\frac{4 i d^{2} c e x}{a^{2} f^{2}}+\frac{4 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{4}}+\frac{4 d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{a^{2} f^{4}}-\frac{4 d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{4}}-\frac{4 i d^{2} c \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{3}}+\frac{2 d \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{a^{2} f^{2}}-\frac{2 d \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{2}}-\frac{2 d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{4}}-\frac{2 i d^{2} c \,x^{2}}{a^{2} f}-\frac{4 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right) x}{a^{2} f^{3}}-\frac{2 i d^{3} x^{3}}{3 a^{2} f}+\frac{2 d^{3} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x^{2}}{a^{2} f^{2}}+\frac{4 i d^{3} e^{3}}{3 a^{2} f^{4}}+\frac{4 d^{2} c e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{3}}+\frac{2 i d^{3} e^{2} x}{a^{2} f^{3}}-\frac{2 i d^{2} c \,e^{2}}{a^{2} f^{3}}+\frac{4 d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) c x}{a^{2} f^{2}}+\frac{2 i \left(3 i c^{2} d f \,{\mathrm e}^{i \left(f x +e \right)}+3 d^{3} f^{2} x^{3} {\mathrm e}^{i \left(f x +e \right)}+3 i d^{3} f \,x^{2} {\mathrm e}^{2 i \left(f x +e \right)}+6 i c \,d^{2} f x \,{\mathrm e}^{i \left(f x +e \right)}+9 c \,d^{2} f^{2} x^{2} {\mathrm e}^{i \left(f x +e \right)}+d^{3} f^{2} x^{3}+3 i d^{3} f \,x^{2} {\mathrm e}^{i \left(f x +e \right)}+3 i c^{2} d f \,{\mathrm e}^{2 i \left(f x +e \right)}+9 c^{2} d \,f^{2} x \,{\mathrm e}^{i \left(f x +e \right)}+3 c \,d^{2} f^{2} x^{2}+6 i c \,d^{2} f x \,{\mathrm e}^{2 i \left(f x +e \right)}+3 c^{3} f^{2} {\mathrm e}^{i \left(f x +e \right)}+3 c^{2} d \,f^{2} x +6 d^{3} x \,{\mathrm e}^{2 i \left(f x +e \right)}+c^{3} f^{2}+6 c \,d^{2} {\mathrm e}^{2 i \left(f x +e \right)}+12 d^{3} x \,{\mathrm e}^{i \left(f x +e \right)}+12 c \,d^{2} {\mathrm e}^{i \left(f x +e \right)}+6 d^{3} x +6 c \,d^{2}\right)}{3 f^{3} a^{2} \left({\mathrm e}^{i \left(f x +e \right)}+1\right)^{3}}"," ",0,"-4*I/a^2/f^2*d^2*c*e*x+4*d^3*polylog(3,-exp(I*(f*x+e)))/a^2/f^4+4/a^2/f^4*d^3*ln(exp(I*(f*x+e))+1)-4/a^2/f^4*d^3*ln(exp(I*(f*x+e)))-2*I/a^2/f*d^2*c*x^2+2/a^2/f^2*d*c^2*ln(exp(I*(f*x+e))+1)-2/a^2/f^2*d*c^2*ln(exp(I*(f*x+e)))-2/a^2/f^4*d^3*e^2*ln(exp(I*(f*x+e)))-4*I/a^2/f^3*d^2*c*polylog(2,-exp(I*(f*x+e)))-4*I/a^2/f^3*d^3*polylog(2,-exp(I*(f*x+e)))*x-2/3*I/a^2/f*d^3*x^3+2/a^2/f^2*d^3*ln(exp(I*(f*x+e))+1)*x^2+4/3*I/a^2/f^4*d^3*e^3+4/a^2/f^3*d^2*c*e*ln(exp(I*(f*x+e)))+2*I/a^2/f^3*d^3*e^2*x-2*I/a^2/f^3*d^2*c*e^2+4/a^2/f^2*d^2*ln(exp(I*(f*x+e))+1)*c*x+2/3*I*(3*I*c^2*d*f*exp(I*(f*x+e))+3*d^3*f^2*x^3*exp(I*(f*x+e))+3*I*d^3*f*x^2*exp(2*I*(f*x+e))+6*I*c*d^2*f*x*exp(I*(f*x+e))+9*c*d^2*f^2*x^2*exp(I*(f*x+e))+d^3*f^2*x^3+3*I*d^3*f*x^2*exp(I*(f*x+e))+3*I*c^2*d*f*exp(2*I*(f*x+e))+9*c^2*d*f^2*x*exp(I*(f*x+e))+3*c*d^2*f^2*x^2+6*I*c*d^2*f*x*exp(2*I*(f*x+e))+3*c^3*f^2*exp(I*(f*x+e))+3*c^2*d*f^2*x+6*d^3*x*exp(2*I*(f*x+e))+c^3*f^2+6*c*d^2*exp(2*I*(f*x+e))+12*d^3*x*exp(I*(f*x+e))+12*c*d^2*exp(I*(f*x+e))+6*d^3*x+6*c*d^2)/f^3/a^2/(exp(I*(f*x+e))+1)^3","B"
134,1,358,172,0.353000," ","int((d*x+c)^2/(a+a*cos(f*x+e))^2,x)","\frac{2 i \left(2 i d^{2} f x \,{\mathrm e}^{2 i \left(f x +e \right)}+3 d^{2} f^{2} x^{2} {\mathrm e}^{i \left(f x +e \right)}+2 i c d f \,{\mathrm e}^{2 i \left(f x +e \right)}+2 i d^{2} f x \,{\mathrm e}^{i \left(f x +e \right)}+6 c d \,f^{2} x \,{\mathrm e}^{i \left(f x +e \right)}+d^{2} f^{2} x^{2}+2 i c d f \,{\mathrm e}^{i \left(f x +e \right)}+3 c^{2} f^{2} {\mathrm e}^{i \left(f x +e \right)}+2 c d \,f^{2} x +c^{2} f^{2}+2 d^{2} {\mathrm e}^{2 i \left(f x +e \right)}+4 d^{2} {\mathrm e}^{i \left(f x +e \right)}+2 d^{2}\right)}{3 f^{3} a^{2} \left({\mathrm e}^{i \left(f x +e \right)}+1\right)^{3}}+\frac{4 d c \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right)}{3 a^{2} f^{2}}-\frac{4 d c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{3 a^{2} f^{2}}-\frac{2 i d^{2} x^{2}}{3 a^{2} f}-\frac{4 i d^{2} e x}{3 a^{2} f^{2}}-\frac{2 i d^{2} e^{2}}{3 a^{2} f^{3}}+\frac{4 d^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+1\right) x}{3 a^{2} f^{2}}-\frac{4 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(f x +e \right)}\right)}{3 a^{2} f^{3}}+\frac{4 d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{3 a^{2} f^{3}}"," ",0,"2/3*I*(2*I*d^2*f*x*exp(2*I*(f*x+e))+3*d^2*f^2*x^2*exp(I*(f*x+e))+2*I*c*d*f*exp(2*I*(f*x+e))+2*I*d^2*f*x*exp(I*(f*x+e))+6*c*d*f^2*x*exp(I*(f*x+e))+d^2*f^2*x^2+2*I*c*d*f*exp(I*(f*x+e))+3*c^2*f^2*exp(I*(f*x+e))+2*c*d*f^2*x+c^2*f^2+2*d^2*exp(2*I*(f*x+e))+4*d^2*exp(I*(f*x+e))+2*d^2)/f^3/a^2/(exp(I*(f*x+e))+1)^3+4/3/a^2*d/f^2*c*ln(exp(I*(f*x+e))+1)-4/3/a^2*d/f^2*c*ln(exp(I*(f*x+e)))-2/3*I/a^2*d^2/f*x^2-4/3*I/a^2*d^2/f^2*e*x-2/3*I/a^2*d^2/f^3*e^2+4/3/a^2*d^2/f^2*ln(exp(I*(f*x+e))+1)*x-4/3*I*d^2*polylog(2,-exp(I*(f*x+e)))/a^2/f^3+4/3/a^2*d^2/f^3*e*ln(exp(I*(f*x+e)))","B"
135,1,123,95,0.179000," ","int((d*x+c)/(a+a*cos(f*x+e))^2,x)","\frac{c \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{6 a^{2} f}+\frac{c \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 a^{2} f}-\frac{d \left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{6 a^{2} f^{2}}+\frac{x d \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{2 a^{2} f}+\frac{x d \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{6 a^{2} f}-\frac{d \ln \left(1+\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 a^{2} f^{2}}"," ",0,"1/6/a^2*c/f*tan(1/2*e+1/2*f*x)^3+1/2/a^2*c/f*tan(1/2*e+1/2*f*x)-1/6/a^2*d/f^2*tan(1/2*e+1/2*f*x)^2+1/2/a^2/f*x*d*tan(1/2*e+1/2*f*x)+1/6/a^2/f*x*d*tan(1/2*e+1/2*f*x)^3-1/3/a^2*d/f^2*ln(1+tan(1/2*e+1/2*f*x)^2)","A"
136,0,0,22,2.537000," ","int(1/(d*x+c)/(a+a*cos(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right) \left(a +a \cos \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)/(a+a*cos(f*x+e))^2,x)","F"
137,0,0,22,3.264000," ","int(1/(d*x+c)^2/(a+a*cos(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +a \cos \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)^2/(a+a*cos(f*x+e))^2,x)","F"
138,1,468,121,0.158000," ","int((d*x+c)^3/(a-a*cos(f*x+e)),x)","-\frac{6 i d^{2} c \,e^{2}}{a \,f^{3}}-\frac{6 d \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{2}}+\frac{6 d \,c^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{a \,f^{2}}-\frac{6 d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{4}}+\frac{6 d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{a \,f^{4}}-\frac{12 i d^{2} c e x}{a \,f^{2}}-\frac{2 i \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}\right)}{f a \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}+\frac{6 i d^{3} e^{2} x}{a \,f^{3}}-\frac{6 i d^{2} c \,x^{2}}{a f}+\frac{6 d^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{a \,f^{2}}-\frac{6 d^{3} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e^{2}}{a \,f^{4}}-\frac{12 i d^{2} c \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}+\frac{12 d^{3} \polylog \left(3, {\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{4}}+\frac{12 d^{2} c e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}-\frac{12 d^{2} c e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{a \,f^{3}}+\frac{12 d^{2} c \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{2}}+\frac{12 d^{2} c \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e}{a \,f^{3}}-\frac{12 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{3}}-\frac{2 i d^{3} x^{3}}{a f}+\frac{4 i d^{3} e^{3}}{a \,f^{4}}"," ",0,"-12*I/a*d^3/f^3*polylog(2,exp(I*(f*x+e)))*x-6/a/f^2*d*c^2*ln(exp(I*(f*x+e)))+6/a*d/f^2*c^2*ln(exp(I*(f*x+e))-1)-6/a/f^4*d^3*e^2*ln(exp(I*(f*x+e)))+6/a*d^3/f^4*e^2*ln(exp(I*(f*x+e))-1)-6*I/a/f^3*d^2*c*e^2-12*I/a/f^2*d^2*c*e*x-12*I/a*d^2/f^3*c*polylog(2,exp(I*(f*x+e)))-2*I*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/f/a/(exp(I*(f*x+e))-1)+6/a*d^3/f^2*ln(1-exp(I*(f*x+e)))*x^2-6/a*d^3/f^4*ln(1-exp(I*(f*x+e)))*e^2+6*I/a/f^3*d^3*e^2*x+12*d^3*polylog(3,exp(I*(f*x+e)))/a/f^4+12/a/f^3*d^2*c*e*ln(exp(I*(f*x+e)))-12/a*d^2/f^3*c*e*ln(exp(I*(f*x+e))-1)+12/a*d^2/f^2*c*ln(1-exp(I*(f*x+e)))*x+12/a*d^2/f^3*c*ln(1-exp(I*(f*x+e)))*e-6*I/a/f*d^2*c*x^2-2*I/a/f*d^3*x^3+4*I/a/f^4*d^3*e^3","B"
139,1,247,92,0.119000," ","int((d*x+c)^2/(a-a*cos(f*x+e)),x)","-\frac{2 i \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{f a \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}-\frac{4 d c \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{2}}+\frac{4 d c \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{a \,f^{2}}-\frac{2 i d^{2} x^{2}}{a f}-\frac{4 i d^{2} e x}{a \,f^{2}}-\frac{2 i d^{2} e^{2}}{a \,f^{3}}+\frac{4 d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{2}}+\frac{4 d^{2} \ln \left(1-{\mathrm e}^{i \left(f x +e \right)}\right) e}{a \,f^{3}}-\frac{4 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}+\frac{4 d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}-\frac{4 d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}-1\right)}{a \,f^{3}}"," ",0,"-2*I*(d^2*x^2+2*c*d*x+c^2)/f/a/(exp(I*(f*x+e))-1)-4/a/f^2*d*c*ln(exp(I*(f*x+e)))+4/a*d/f^2*c*ln(exp(I*(f*x+e))-1)-2*I/a/f*d^2*x^2-4*I/a/f^2*d^2*e*x-2*I/a/f^3*d^2*e^2+4/a*d^2/f^2*ln(1-exp(I*(f*x+e)))*x+4/a*d^2/f^3*ln(1-exp(I*(f*x+e)))*e-4*I*d^2*polylog(2,exp(I*(f*x+e)))/a/f^3+4/a/f^3*d^2*e*ln(exp(I*(f*x+e)))-4/a*d^2/f^3*e*ln(exp(I*(f*x+e))-1)","B"
140,1,85,42,0.089000," ","int((d*x+c)/(a-a*cos(f*x+e)),x)","-\frac{c}{a f \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}-\frac{d x}{a f \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}-\frac{d \ln \left(1+\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a \,f^{2}}+\frac{2 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a \,f^{2}}"," ",0,"-1/a*c/f/tan(1/2*e+1/2*f*x)-1/a*d*x/f/tan(1/2*e+1/2*f*x)-1/a*d/f^2*ln(1+tan(1/2*e+1/2*f*x)^2)+2/a*d/f^2*ln(tan(1/2*e+1/2*f*x))","A"
141,0,0,23,0.154000," ","int(1/(d*x+c)/(a-a*cos(f*x+e)),x)","\int \frac{1}{\left(d x +c \right) \left(a -a \cos \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)/(a-a*cos(f*x+e)),x)","F"
142,0,0,23,0.209000," ","int(1/(d*x+c)^2/(a-a*cos(f*x+e)),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a -a \cos \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)^2/(a-a*cos(f*x+e)),x)","F"
143,1,132,94,0.097000," ","int(x^3*(a+a*cos(d*x+c))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{a \left({\mathrm e}^{i \left(d x +c \right)}+1\right)^{2} {\mathrm e}^{-i \left(d x +c \right)}}\, \left(d^{3} x^{3} {\mathrm e}^{i \left(d x +c \right)}+6 i d^{2} x^{2} {\mathrm e}^{i \left(d x +c \right)}-d^{3} x^{3}+6 i d^{2} x^{2}-24 d x \,{\mathrm e}^{i \left(d x +c \right)}-48 i {\mathrm e}^{i \left(d x +c \right)}+24 d x -48 i\right)}{\left({\mathrm e}^{i \left(d x +c \right)}+1\right) d^{4}}"," ",0,"-I*2^(1/2)*(a*(exp(I*(d*x+c))+1)^2*exp(-I*(d*x+c)))^(1/2)/(exp(I*(d*x+c))+1)*(d^3*x^3*exp(I*(d*x+c))+6*I*d^2*x^2*exp(I*(d*x+c))-d^3*x^3+6*I*d^2*x^2-24*d*x*exp(I*(d*x+c))-48*I*exp(I*(d*x+c))+24*d*x-48*I)/d^4","C"
144,1,105,74,0.064000," ","int(x^2*(a+a*cos(d*x+c))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{a \left({\mathrm e}^{i \left(d x +c \right)}+1\right)^{2} {\mathrm e}^{-i \left(d x +c \right)}}\, \left(d^{2} x^{2} {\mathrm e}^{i \left(d x +c \right)}+4 i d x \,{\mathrm e}^{i \left(d x +c \right)}-d^{2} x^{2}+4 i d x -8 \,{\mathrm e}^{i \left(d x +c \right)}+8\right)}{\left({\mathrm e}^{i \left(d x +c \right)}+1\right) d^{3}}"," ",0,"-I*2^(1/2)*(a*(exp(I*(d*x+c))+1)^2*exp(-I*(d*x+c)))^(1/2)/(exp(I*(d*x+c))+1)*(d^2*x^2*exp(I*(d*x+c))+4*I*d*x*exp(I*(d*x+c))-d^2*x^2+4*I*d*x-8*exp(I*(d*x+c))+8)/d^3","C"
145,1,80,45,0.061000," ","int(x*(a+a*cos(d*x+c))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{a \left({\mathrm e}^{i \left(d x +c \right)}+1\right)^{2} {\mathrm e}^{-i \left(d x +c \right)}}\, \left(d x \,{\mathrm e}^{i \left(d x +c \right)}+2 i {\mathrm e}^{i \left(d x +c \right)}-d x +2 i\right)}{\left({\mathrm e}^{i \left(d x +c \right)}+1\right) d^{2}}"," ",0,"-I*2^(1/2)*(a*(exp(I*(d*x+c))+1)^2*exp(-I*(d*x+c)))^(1/2)/(exp(I*(d*x+c))+1)*(d*x*exp(I*(d*x+c))+2*I*exp(I*(d*x+c))-d*x+2*I)/d^2","C"
146,1,43,24,0.073000," ","int((a+a*cos(d*x+c))^(1/2),x)","\frac{2 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}}{\sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"2*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
147,0,0,64,0.098000," ","int((a+a*cos(d*x+c))^(1/2)/x,x)","\int \frac{\sqrt{a +a \cos \left(d x +c \right)}}{x}\, dx"," ",0,"int((a+a*cos(d*x+c))^(1/2)/x,x)","F"
148,0,0,84,0.062000," ","int((a+a*cos(d*x+c))^(1/2)/x^2,x)","\int \frac{\sqrt{a +a \cos \left(d x +c \right)}}{x^{2}}\, dx"," ",0,"int((a+a*cos(d*x+c))^(1/2)/x^2,x)","F"
149,0,0,115,0.067000," ","int((a+a*cos(d*x+c))^(1/2)/x^3,x)","\int \frac{\sqrt{a +a \cos \left(d x +c \right)}}{x^{3}}\, dx"," ",0,"int((a+a*cos(d*x+c))^(1/2)/x^3,x)","F"
150,1,87,56,0.096000," ","int(x^3*(a+a*cos(x))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{a \left({\mathrm e}^{i x}+1\right)^{2} {\mathrm e}^{-i x}}\, \left(6 i x^{2} {\mathrm e}^{i x}+x^{3} {\mathrm e}^{i x}+6 i x^{2}-x^{3}-48 i {\mathrm e}^{i x}-24 x \,{\mathrm e}^{i x}-48 i+24 x \right)}{{\mathrm e}^{i x}+1}"," ",0,"-I*2^(1/2)*(a*(exp(I*x)+1)^2*exp(-I*x))^(1/2)/(exp(I*x)+1)*(6*I*x^2*exp(I*x)+x^3*exp(I*x)+6*I*x^2-x^3-48*I*exp(I*x)-24*x*exp(I*x)-48*I+24*x)","C"
151,1,70,43,0.067000," ","int(x^2*(a+a*cos(x))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{a \left({\mathrm e}^{i x}+1\right)^{2} {\mathrm e}^{-i x}}\, \left(4 i x \,{\mathrm e}^{i x}+x^{2} {\mathrm e}^{i x}+4 i x -x^{2}-8 \,{\mathrm e}^{i x}+8\right)}{{\mathrm e}^{i x}+1}"," ",0,"-I*2^(1/2)*(a*(exp(I*x)+1)^2*exp(-I*x))^(1/2)/(exp(I*x)+1)*(4*I*x*exp(I*x)+x^2*exp(I*x)+4*I*x-x^2-8*exp(I*x)+8)","C"
152,1,55,26,0.067000," ","int(x*(a+a*cos(x))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{a \left({\mathrm e}^{i x}+1\right)^{2} {\mathrm e}^{-i x}}\, \left(2 i {\mathrm e}^{i x}+x \,{\mathrm e}^{i x}+2 i-x \right)}{{\mathrm e}^{i x}+1}"," ",0,"-I*2^(1/2)*(a*(exp(I*x)+1)^2*exp(-I*x))^(1/2)/(exp(I*x)+1)*(2*I*exp(I*x)+x*exp(I*x)+2*I-x)","C"
153,1,25,13,0.070000," ","int((a+a*cos(x))^(1/2),x)","\frac{2 a \cos \left(\frac{x}{2}\right) \sin \left(\frac{x}{2}\right) \sqrt{2}}{\sqrt{a \left(\cos^{2}\left(\frac{x}{2}\right)\right)}}"," ",0,"2*a*cos(1/2*x)*sin(1/2*x)*2^(1/2)/(a*cos(1/2*x)^2)^(1/2)","A"
154,0,0,17,0.091000," ","int((a+a*cos(x))^(1/2)/x,x)","\int \frac{\sqrt{a +a \cos \left(x \right)}}{x}\, dx"," ",0,"int((a+a*cos(x))^(1/2)/x,x)","F"
155,0,0,32,0.066000," ","int((a+a*cos(x))^(1/2)/x^2,x)","\int \frac{\sqrt{a +a \cos \left(x \right)}}{x^{2}}\, dx"," ",0,"int((a+a*cos(x))^(1/2)/x^2,x)","F"
156,0,0,49,0.067000," ","int((a+a*cos(x))^(1/2)/x^3,x)","\int \frac{\sqrt{a +a \cos \left(x \right)}}{x^{3}}\, dx"," ",0,"int((a+a*cos(x))^(1/2)/x^3,x)","F"
157,1,86,60,0.070000," ","int(x^3*(a-a*cos(x))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{-a \left({\mathrm e}^{i x}-1\right)^{2} {\mathrm e}^{-i x}}\, \left(6 i x^{2} {\mathrm e}^{i x}+x^{3} {\mathrm e}^{i x}-6 i x^{2}+x^{3}-48 i {\mathrm e}^{i x}-24 x \,{\mathrm e}^{i x}+48 i-24 x \right)}{{\mathrm e}^{i x}-1}"," ",0,"-I*2^(1/2)*(-a*(exp(I*x)-1)^2*exp(-I*x))^(1/2)/(exp(I*x)-1)*(6*I*x^2*exp(I*x)+x^3*exp(I*x)-6*I*x^2+x^3-48*I*exp(I*x)-24*x*exp(I*x)+48*I-24*x)","C"
158,1,69,46,0.061000," ","int(x^2*(a-a*cos(x))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{-a \left({\mathrm e}^{i x}-1\right)^{2} {\mathrm e}^{-i x}}\, \left(4 i x \,{\mathrm e}^{i x}+x^{2} {\mathrm e}^{i x}-4 i x +x^{2}-8 \,{\mathrm e}^{i x}-8\right)}{{\mathrm e}^{i x}-1}"," ",0,"-I*2^(1/2)*(-a*(exp(I*x)-1)^2*exp(-I*x))^(1/2)/(exp(I*x)-1)*(4*I*x*exp(I*x)+x^2*exp(I*x)-4*I*x+x^2-8*exp(I*x)-8)","C"
159,1,54,28,0.055000," ","int(x*(a-a*cos(x))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{-a \left({\mathrm e}^{i x}-1\right)^{2} {\mathrm e}^{-i x}}\, \left(2 i {\mathrm e}^{i x}+x \,{\mathrm e}^{i x}-2 i+x \right)}{{\mathrm e}^{i x}-1}"," ",0,"-I*2^(1/2)*(-a*(exp(I*x)-1)^2*exp(-I*x))^(1/2)/(exp(I*x)-1)*(2*I*exp(I*x)+x*exp(I*x)-2*I+x)","C"
160,1,25,14,0.125000," ","int((a-a*cos(x))^(1/2),x)","-\frac{2 \sin \left(\frac{x}{2}\right) a \cos \left(\frac{x}{2}\right) \sqrt{2}}{\sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}}"," ",0,"-2*sin(1/2*x)*a*cos(1/2*x)*2^(1/2)/(a*sin(1/2*x)^2)^(1/2)","A"
161,0,0,18,0.083000," ","int((a-a*cos(x))^(1/2)/x,x)","\int \frac{\sqrt{a -a \cos \left(x \right)}}{x}\, dx"," ",0,"int((a-a*cos(x))^(1/2)/x,x)","F"
162,0,0,34,0.057000," ","int((a-a*cos(x))^(1/2)/x^2,x)","\int \frac{\sqrt{a -a \cos \left(x \right)}}{x^{2}}\, dx"," ",0,"int((a-a*cos(x))^(1/2)/x^2,x)","F"
163,0,0,52,0.068000," ","int((a-a*cos(x))^(1/2)/x^3,x)","\int \frac{\sqrt{a -a \cos \left(x \right)}}{x^{3}}\, dx"," ",0,"int((a-a*cos(x))^(1/2)/x^3,x)","F"
164,0,0,139,0.057000," ","int(x^3*(a+a*cos(x))^(3/2),x)","\int x^{3} \left(a +a \cos \left(x \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(x^3*(a+a*cos(x))^(3/2),x)","F"
165,0,0,107,0.055000," ","int(x^2*(a+a*cos(x))^(3/2),x)","\int x^{2} \left(a +a \cos \left(x \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(x^2*(a+a*cos(x))^(3/2),x)","F"
166,0,0,65,0.058000," ","int(x*(a+a*cos(x))^(3/2),x)","\int x \left(a +a \cos \left(x \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(x*(a+a*cos(x))^(3/2),x)","F"
167,0,0,39,0.058000," ","int((a+a*cos(x))^(3/2)/x,x)","\int \frac{\left(a +a \cos \left(x \right)\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int((a+a*cos(x))^(3/2)/x,x)","F"
168,0,0,59,0.053000," ","int((a+a*cos(x))^(3/2)/x^2,x)","\int \frac{\left(a +a \cos \left(x \right)\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int((a+a*cos(x))^(3/2)/x^2,x)","F"
169,0,0,81,0.054000," ","int((a+a*cos(x))^(3/2)/x^3,x)","\int \frac{\left(a +a \cos \left(x \right)\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"int((a+a*cos(x))^(3/2)/x^3,x)","F"
170,0,0,293,0.060000," ","int(x^3/(a+a*cos(d*x+c))^(1/2),x)","\int \frac{x^{3}}{\sqrt{a +a \cos \left(d x +c \right)}}\, dx"," ",0,"int(x^3/(a+a*cos(d*x+c))^(1/2),x)","F"
171,0,0,205,0.061000," ","int(x^2/(a+a*cos(d*x+c))^(1/2),x)","\int \frac{x^{2}}{\sqrt{a +a \cos \left(d x +c \right)}}\, dx"," ",0,"int(x^2/(a+a*cos(d*x+c))^(1/2),x)","F"
172,0,0,121,0.054000," ","int(x/(a+a*cos(d*x+c))^(1/2),x)","\int \frac{x}{\sqrt{a +a \cos \left(d x +c \right)}}\, dx"," ",0,"int(x/(a+a*cos(d*x+c))^(1/2),x)","F"
173,1,54,37,0.125000," ","int(1/(a+a*cos(d*x+c))^(1/2),x)","\frac{\sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \mathrm{am}^{-1}\left(\frac{d x}{2}+\frac{c}{2}| 1\right)}{d \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \mathrm{csgn}\left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}"," ",0,"1/d*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/csgn(cos(1/2*d*x+1/2*c))*cos(1/2*d*x+1/2*c)*InverseJacobiAM(1/2*d*x+1/2*c,1)","C"
174,0,0,18,0.055000," ","int(1/x/(a+a*cos(d*x+c))^(1/2),x)","\int \frac{1}{x \sqrt{a +a \cos \left(d x +c \right)}}\, dx"," ",0,"int(1/x/(a+a*cos(d*x+c))^(1/2),x)","F"
175,0,0,175,0.053000," ","int(x^3/(a-a*cos(x))^(1/2),x)","\int \frac{x^{3}}{\sqrt{a -a \cos \left(x \right)}}\, dx"," ",0,"int(x^3/(a-a*cos(x))^(1/2),x)","F"
176,0,0,121,0.056000," ","int(x^2/(a-a*cos(x))^(1/2),x)","\int \frac{x^{2}}{\sqrt{a -a \cos \left(x \right)}}\, dx"," ",0,"int(x^2/(a-a*cos(x))^(1/2),x)","F"
177,0,0,71,0.056000," ","int(x/(a-a*cos(x))^(1/2),x)","\int \frac{x}{\sqrt{a -a \cos \left(x \right)}}\, dx"," ",0,"int(x/(a-a*cos(x))^(1/2),x)","F"
178,1,25,28,0.183000," ","int(1/(a-a*cos(x))^(1/2),x)","-\frac{\sin \left(\frac{x}{2}\right) \arctanh \left(\cos \left(\frac{x}{2}\right)\right) \sqrt{2}}{\sqrt{a \left(\sin^{2}\left(\frac{x}{2}\right)\right)}}"," ",0,"-sin(1/2*x)*arctanh(cos(1/2*x))*2^(1/2)/(a*sin(1/2*x)^2)^(1/2)","A"
179,0,0,15,0.059000," ","int(1/x/(a-a*cos(x))^(1/2),x)","\int \frac{1}{x \sqrt{a -a \cos \left(x \right)}}\, dx"," ",0,"int(1/x/(a-a*cos(x))^(1/2),x)","F"
180,0,0,319,0.058000," ","int(x^3/(a+a*cos(x))^(3/2),x)","\int \frac{x^{3}}{\left(a +a \cos \left(x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3/(a+a*cos(x))^(3/2),x)","F"
181,0,0,196,0.056000," ","int(x^2/(a+a*cos(x))^(3/2),x)","\int \frac{x^{2}}{\left(a +a \cos \left(x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2/(a+a*cos(x))^(3/2),x)","F"
182,0,0,113,0.061000," ","int(x/(a+a*cos(x))^(3/2),x)","\int \frac{x}{\left(a +a \cos \left(x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/(a+a*cos(x))^(3/2),x)","F"
183,0,0,14,0.056000," ","int(1/x/(a+a*cos(x))^(3/2),x)","\int \frac{1}{x \left(a +a \cos \left(x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x/(a+a*cos(x))^(3/2),x)","F"
184,0,0,18,0.089000," ","int((a+a*cos(d*x+c))^(1/3)/x,x)","\int \frac{\left(a +a \cos \left(d x +c \right)\right)^{\frac{1}{3}}}{x}\, dx"," ",0,"int((a+a*cos(d*x+c))^(1/3)/x,x)","F"
185,0,0,331,0.065000," ","int(x^3/(a+b*cos(x)),x)","\int \frac{x^{3}}{a +b \cos \left(x \right)}\, dx"," ",0,"int(x^3/(a+b*cos(x)),x)","F"
186,0,0,289,0.158000," ","int(x^2/(a+b*cos(d*x+c)),x)","\int \frac{x^{2}}{a +b \cos \left(d x +c \right)}\, dx"," ",0,"int(x^2/(a+b*cos(d*x+c)),x)","F"
187,1,414,188,0.090000," ","int(x/(a+b*cos(d*x+c)),x)","-\frac{i \ln \left(\frac{-b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right) x}{d \sqrt{a^{2}-b^{2}}}+\frac{i \ln \left(\frac{b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}+a}{a +\sqrt{a^{2}-b^{2}}}\right) x}{d \sqrt{a^{2}-b^{2}}}-\frac{i \ln \left(\frac{-b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right) c}{d^{2} \sqrt{a^{2}-b^{2}}}+\frac{i \ln \left(\frac{b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}+a}{a +\sqrt{a^{2}-b^{2}}}\right) c}{d^{2} \sqrt{a^{2}-b^{2}}}-\frac{\dilog \left(\frac{-b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right)}{d^{2} \sqrt{a^{2}-b^{2}}}+\frac{\dilog \left(\frac{b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}+a}{a +\sqrt{a^{2}-b^{2}}}\right)}{d^{2} \sqrt{a^{2}-b^{2}}}+\frac{2 i c \arctan \left(\frac{2 b \,{\mathrm e}^{i \left(d x +c \right)}+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \sqrt{-a^{2}+b^{2}}}"," ",0,"-I/d/(a^2-b^2)^(1/2)*ln((-b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*x+I/d/(a^2-b^2)^(1/2)*ln((b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)+a)/(a+(a^2-b^2)^(1/2)))*x-I/d^2/(a^2-b^2)^(1/2)*ln((-b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*c+I/d^2/(a^2-b^2)^(1/2)*ln((b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)+a)/(a+(a^2-b^2)^(1/2)))*c-1/d^2/(a^2-b^2)^(1/2)*dilog((-b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))+1/d^2/(a^2-b^2)^(1/2)*dilog((b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)+a)/(a+(a^2-b^2)^(1/2)))+2*I/d^2*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*exp(I*(d*x+c))+2*a)/(-a^2+b^2)^(1/2))","B"
188,0,0,14,0.048000," ","int(1/x/(a+b*cos(x)),x)","\int \frac{1}{x \left(a +b \cos \left(x \right)\right)}\, dx"," ",0,"int(1/x/(a+b*cos(x)),x)","F"
189,1,674,270,0.696000," ","int((f*x+e)/(a+b*cos(d*x+c))^2,x)","\frac{2 i \left(f x +e \right) \left(a \,{\mathrm e}^{i \left(d x +c \right)}+b \right)}{d \left(-a^{2}+b^{2}\right) \left(b \,{\mathrm e}^{2 i \left(d x +c \right)}+2 a \,{\mathrm e}^{i \left(d x +c \right)}+b \right)}-\frac{2 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{f \ln \left(b \,{\mathrm e}^{2 i \left(d x +c \right)}+2 a \,{\mathrm e}^{i \left(d x +c \right)}+b \right)}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{2 i a e \arctan \left(\frac{2 b \,{\mathrm e}^{i \left(d x +c \right)}+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \left(-a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{i a f \ln \left(\frac{-b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right) x}{d \left(-a^{2}+b^{2}\right) \sqrt{a^{2}-b^{2}}}+\frac{i a f \ln \left(\frac{-b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right) c}{d^{2} \left(-a^{2}+b^{2}\right) \sqrt{a^{2}-b^{2}}}-\frac{i a f \ln \left(\frac{b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}+a}{a +\sqrt{a^{2}-b^{2}}}\right) x}{d \left(-a^{2}+b^{2}\right) \sqrt{a^{2}-b^{2}}}-\frac{i a f \ln \left(\frac{b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}+a}{a +\sqrt{a^{2}-b^{2}}}\right) c}{d^{2} \left(-a^{2}+b^{2}\right) \sqrt{a^{2}-b^{2}}}+\frac{a f \dilog \left(\frac{-b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right) \sqrt{a^{2}-b^{2}}}-\frac{a f \dilog \left(\frac{b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}+a}{a +\sqrt{a^{2}-b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right) \sqrt{a^{2}-b^{2}}}-\frac{2 i a f c \arctan \left(\frac{2 b \,{\mathrm e}^{i \left(d x +c \right)}+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right)^{\frac{3}{2}}}"," ",0,"2*I*(f*x+e)*(a*exp(I*(d*x+c))+b)/d/(-a^2+b^2)/(b*exp(2*I*(d*x+c))+2*a*exp(I*(d*x+c))+b)-2/d^2/(-a^2+b^2)*f*ln(exp(I*(d*x+c)))+1/d^2/(-a^2+b^2)*f*ln(b*exp(2*I*(d*x+c))+2*a*exp(I*(d*x+c))+b)+2*I/d/(-a^2+b^2)^(3/2)*a*e*arctan(1/2*(2*b*exp(I*(d*x+c))+2*a)/(-a^2+b^2)^(1/2))+I/d/(-a^2+b^2)*a*f/(a^2-b^2)^(1/2)*ln((-b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*x+I/d^2/(-a^2+b^2)*a*f/(a^2-b^2)^(1/2)*ln((-b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*c-I/d/(-a^2+b^2)*a*f/(a^2-b^2)^(1/2)*ln((b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)+a)/(a+(a^2-b^2)^(1/2)))*x-I/d^2/(-a^2+b^2)*a*f/(a^2-b^2)^(1/2)*ln((b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)+a)/(a+(a^2-b^2)^(1/2)))*c+1/d^2/(-a^2+b^2)*a*f/(a^2-b^2)^(1/2)*dilog((-b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))-1/d^2/(-a^2+b^2)*a*f/(a^2-b^2)^(1/2)*dilog((b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)+a)/(a+(a^2-b^2)^(1/2)))-2*I/d^2/(-a^2+b^2)^(3/2)*a*f*c*arctan(1/2*(2*b*exp(I*(d*x+c))+2*a)/(-a^2+b^2)^(1/2))","B"