1,1,551,92,0.023000," ","int((d*x+c)^4*sin(b*x+a),x)","\frac{\frac{d^{4} \left(-\left(b x +a \right)^{4} \cos \left(b x +a \right)+4 \left(b x +a \right)^{3} \sin \left(b x +a \right)+12 \left(b x +a \right)^{2} \cos \left(b x +a \right)-24 \cos \left(b x +a \right)-24 \left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{4}}-\frac{4 a \,d^{4} \left(-\left(b x +a \right)^{3} \cos \left(b x +a \right)+3 \left(b x +a \right)^{2} \sin \left(b x +a \right)-6 \sin \left(b x +a \right)+6 \left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{4}}+\frac{4 c \,d^{3} \left(-\left(b x +a \right)^{3} \cos \left(b x +a \right)+3 \left(b x +a \right)^{2} \sin \left(b x +a \right)-6 \sin \left(b x +a \right)+6 \left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{3}}+\frac{6 a^{2} d^{4} \left(-\left(b x +a \right)^{2} \cos \left(b x +a \right)+2 \cos \left(b x +a \right)+2 \left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{4}}-\frac{12 a c \,d^{3} \left(-\left(b x +a \right)^{2} \cos \left(b x +a \right)+2 \cos \left(b x +a \right)+2 \left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{3}}+\frac{6 c^{2} d^{2} \left(-\left(b x +a \right)^{2} \cos \left(b x +a \right)+2 \cos \left(b x +a \right)+2 \left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{2}}-\frac{4 a^{3} d^{4} \left(\sin \left(b x +a \right)-\left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{4}}+\frac{12 a^{2} c \,d^{3} \left(\sin \left(b x +a \right)-\left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{3}}-\frac{12 a \,c^{2} d^{2} \left(\sin \left(b x +a \right)-\left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{2}}+\frac{4 c^{3} d \left(\sin \left(b x +a \right)-\left(b x +a \right) \cos \left(b x +a \right)\right)}{b}-\frac{a^{4} d^{4} \cos \left(b x +a \right)}{b^{4}}+\frac{4 a^{3} c \,d^{3} \cos \left(b x +a \right)}{b^{3}}-\frac{6 a^{2} c^{2} d^{2} \cos \left(b x +a \right)}{b^{2}}+\frac{4 a \,c^{3} d \cos \left(b x +a \right)}{b}-c^{4} \cos \left(b x +a \right)}{b}"," ",0,"1/b*(1/b^4*d^4*(-(b*x+a)^4*cos(b*x+a)+4*(b*x+a)^3*sin(b*x+a)+12*(b*x+a)^2*cos(b*x+a)-24*cos(b*x+a)-24*(b*x+a)*sin(b*x+a))-4/b^4*a*d^4*(-(b*x+a)^3*cos(b*x+a)+3*(b*x+a)^2*sin(b*x+a)-6*sin(b*x+a)+6*(b*x+a)*cos(b*x+a))+4/b^3*c*d^3*(-(b*x+a)^3*cos(b*x+a)+3*(b*x+a)^2*sin(b*x+a)-6*sin(b*x+a)+6*(b*x+a)*cos(b*x+a))+6/b^4*a^2*d^4*(-(b*x+a)^2*cos(b*x+a)+2*cos(b*x+a)+2*(b*x+a)*sin(b*x+a))-12/b^3*a*c*d^3*(-(b*x+a)^2*cos(b*x+a)+2*cos(b*x+a)+2*(b*x+a)*sin(b*x+a))+6/b^2*c^2*d^2*(-(b*x+a)^2*cos(b*x+a)+2*cos(b*x+a)+2*(b*x+a)*sin(b*x+a))-4/b^4*a^3*d^4*(sin(b*x+a)-(b*x+a)*cos(b*x+a))+12/b^3*a^2*c*d^3*(sin(b*x+a)-(b*x+a)*cos(b*x+a))-12/b^2*a*c^2*d^2*(sin(b*x+a)-(b*x+a)*cos(b*x+a))+4/b*c^3*d*(sin(b*x+a)-(b*x+a)*cos(b*x+a))-1/b^4*a^4*d^4*cos(b*x+a)+4/b^3*a^3*c*d^3*cos(b*x+a)-6/b^2*a^2*c^2*d^2*cos(b*x+a)+4/b*a*c^3*d*cos(b*x+a)-c^4*cos(b*x+a))","B"
2,1,308,71,0.019000," ","int((d*x+c)^3*sin(b*x+a),x)","\frac{\frac{d^{3} \left(-\left(b x +a \right)^{3} \cos \left(b x +a \right)+3 \left(b x +a \right)^{2} \sin \left(b x +a \right)-6 \sin \left(b x +a \right)+6 \left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{3}}-\frac{3 a \,d^{3} \left(-\left(b x +a \right)^{2} \cos \left(b x +a \right)+2 \cos \left(b x +a \right)+2 \left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{3}}+\frac{3 c \,d^{2} \left(-\left(b x +a \right)^{2} \cos \left(b x +a \right)+2 \cos \left(b x +a \right)+2 \left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(\sin \left(b x +a \right)-\left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(\sin \left(b x +a \right)-\left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{2}}+\frac{3 c^{2} d \left(\sin \left(b x +a \right)-\left(b x +a \right) \cos \left(b x +a \right)\right)}{b}+\frac{a^{3} d^{3} \cos \left(b x +a \right)}{b^{3}}-\frac{3 a^{2} c \,d^{2} \cos \left(b x +a \right)}{b^{2}}+\frac{3 a \,c^{2} d \cos \left(b x +a \right)}{b}-c^{3} \cos \left(b x +a \right)}{b}"," ",0,"1/b*(1/b^3*d^3*(-(b*x+a)^3*cos(b*x+a)+3*(b*x+a)^2*sin(b*x+a)-6*sin(b*x+a)+6*(b*x+a)*cos(b*x+a))-3/b^3*a*d^3*(-(b*x+a)^2*cos(b*x+a)+2*cos(b*x+a)+2*(b*x+a)*sin(b*x+a))+3/b^2*c*d^2*(-(b*x+a)^2*cos(b*x+a)+2*cos(b*x+a)+2*(b*x+a)*sin(b*x+a))+3/b^3*a^2*d^3*(sin(b*x+a)-(b*x+a)*cos(b*x+a))-6/b^2*a*c*d^2*(sin(b*x+a)-(b*x+a)*cos(b*x+a))+3/b*c^2*d*(sin(b*x+a)-(b*x+a)*cos(b*x+a))+1/b^3*a^3*d^3*cos(b*x+a)-3/b^2*a^2*c*d^2*cos(b*x+a)+3/b*a*c^2*d*cos(b*x+a)-c^3*cos(b*x+a))","B"
3,1,148,50,0.019000," ","int((d*x+c)^2*sin(b*x+a),x)","\frac{\frac{d^{2} \left(-\left(b x +a \right)^{2} \cos \left(b x +a \right)+2 \cos \left(b x +a \right)+2 \left(b x +a \right) \sin \left(b x +a \right)\right)}{b^{2}}-\frac{2 a \,d^{2} \left(\sin \left(b x +a \right)-\left(b x +a \right) \cos \left(b x +a \right)\right)}{b^{2}}+\frac{2 c d \left(\sin \left(b x +a \right)-\left(b x +a \right) \cos \left(b x +a \right)\right)}{b}-\frac{a^{2} d^{2} \cos \left(b x +a \right)}{b^{2}}+\frac{2 a c d \cos \left(b x +a \right)}{b}-c^{2} \cos \left(b x +a \right)}{b}"," ",0,"1/b*(1/b^2*d^2*(-(b*x+a)^2*cos(b*x+a)+2*cos(b*x+a)+2*(b*x+a)*sin(b*x+a))-2/b^2*a*d^2*(sin(b*x+a)-(b*x+a)*cos(b*x+a))+2/b*c*d*(sin(b*x+a)-(b*x+a)*cos(b*x+a))-1/b^2*a^2*d^2*cos(b*x+a)+2/b*a*c*d*cos(b*x+a)-c^2*cos(b*x+a))","B"
4,1,52,28,0.018000," ","int((d*x+c)*sin(b*x+a),x)","\frac{\frac{d \left(\sin \left(b x +a \right)-\left(b x +a \right) \cos \left(b x +a \right)\right)}{b}+\frac{d a \cos \left(b x +a \right)}{b}-c \cos \left(b x +a \right)}{b}"," ",0,"1/b*(1/b*d*(sin(b*x+a)-(b*x+a)*cos(b*x+a))+1/b*d*a*cos(b*x+a)-c*cos(b*x+a))","A"
5,1,73,51,0.023000," ","int(sin(b*x+a)/(d*x+c),x)","\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}"," ",0,"Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d","A"
6,1,107,72,0.020000," ","int(sin(b*x+a)/(d*x+c)^2,x)","b \left(-\frac{\sin \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}+\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}}{d}\right)"," ",0,"b*(-sin(b*x+a)/((b*x+a)*d-d*a+c*b)/d+(Si(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)/d)","A"
7,1,145,96,0.020000," ","int(sin(b*x+a)/(d*x+c)^3,x)","b^{2} \left(-\frac{\sin \left(b x +a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{\cos \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}}{d}}{2 d}\right)"," ",0,"b^2*(-1/2*sin(b*x+a)/((b*x+a)*d-d*a+c*b)^2/d+1/2*(-cos(b*x+a)/((b*x+a)*d-d*a+c*b)/d-(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d)/d)/d)","A"
8,1,1030,147,0.093000," ","int((d*x+c)^4*sin(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"
9,1,587,120,0.019000," ","int((d*x+c)^3*sin(b*x+a)^2,x)","\frac{\frac{d^{3} \left(\left(b x +a \right)^{3} \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{3 \left(b x +a \right)^{2} \left(\cos^{2}\left(b x +a \right)\right)}{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"
10,1,289,85,0.019000," ","int((d*x+c)^2*sin(b*x+a)^2,x)","\frac{\frac{d^{2} \left(\left(b x +a \right)^{2} \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right)}{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"
11,1,112,47,0.018000," ","int((d*x+c)*sin(b*x+a)^2,x)","\frac{\frac{d \left(\left(b x +a \right) \left(-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}\right)-\frac{\left(b x +a \right)^{2}}{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"
12,1,105,72,0.023000," ","int(sin(b*x+a)^2/(d*x+c),x)","\frac{\ln \left(\left(b x +a \right) d -d a +c b \right)}{2 d}-\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}"," ",0,"1/2*ln((b*x+a)*d-d*a+c*b)/d-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","A"
13,1,156,81,0.021000," ","int(sin(b*x+a)^2/(d*x+c)^2,x)","\frac{-\frac{b^{2}}{2 \left(\left(b x +a \right) d -d a +c b \right) d}-\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}}{b}"," ",0,"1/b*(-1/2*b^2/((b*x+a)*d-d*a+c*b)/d-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))","A"
14,1,193,111,0.020000," ","int(sin(b*x+a)^2/(d*x+c)^3,x)","\frac{-\frac{b^{3}}{4 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}-\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}}{b}"," ",0,"1/b*(-1/4*b^3/((b*x+a)*d-d*a+c*b)^2/d-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))","A"
15,1,229,150,0.021000," ","int(sin(b*x+a)^2/(d*x+c)^4,x)","\frac{-\frac{b^{4}}{6 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}-\frac{b^{4} \left(-\frac{2 \cos \left(2 b x +2 a \right)}{3 \left(\left(b x +a \right) d -d a +c b \right)^{3} d}-\frac{2 \left(-\frac{\sin \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{2 \cos \left(2 b x +2 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{2 \left(\frac{2 \Si \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \cos \left(\frac{-2 d a +2 c b}{d}\right)}{d}-\frac{2 \Ci \left(2 b x +2 a +\frac{-2 d a +2 c b}{d}\right) \sin \left(\frac{-2 d a +2 c b}{d}\right)}{d}\right)}{d}}{d}\right)}{3 d}\right)}{4}}{b}"," ",0,"1/b*(-1/6*b^4/((b*x+a)*d-d*a+c*b)^3/d-1/4*b^4*(-2/3*cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^3/d-2/3*(-sin(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)^2/d+(-2*cos(2*b*x+2*a)/((b*x+a)*d-d*a+c*b)/d-2*(2*Si(2*b*x+2*a+2*(-a*d+b*c)/d)*cos(2*(-a*d+b*c)/d)/d-2*Ci(2*b*x+2*a+2*(-a*d+b*c)/d)*sin(2*(-a*d+b*c)/d)/d)/d)/d)/d))","A"
16,1,1023,205,0.058000," ","int((d*x+c)^4*sin(b*x+a)^3,x)","\frac{\frac{d^{4} \left(-\frac{\left(b x +a \right)^{4} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{8 \left(b x +a \right)^{3} \sin \left(b x +a \right)}{3}+8 \left(b x +a \right)^{2} \cos \left(b x +a \right)-\frac{160 \cos \left(b x +a \right)}{9}-\frac{160 \left(b x +a \right) \sin \left(b x +a \right)}{9}+\frac{4 \left(b x +a \right)^{3} \left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{4 \left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{8 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{27}-\frac{8 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{81}\right)}{b^{4}}-\frac{4 a \,d^{4} \left(-\frac{\left(b x +a \right)^{3} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+2 \left(b x +a \right)^{2} \sin \left(b x +a \right)-\frac{40 \sin \left(b x +a \right)}{9}+4 \left(b x +a \right) \cos \left(b x +a \right)+\frac{\left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{27}\right)}{b^{4}}+\frac{4 c \,d^{3} \left(-\frac{\left(b x +a \right)^{3} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+2 \left(b x +a \right)^{2} \sin \left(b x +a \right)-\frac{40 \sin \left(b x +a \right)}{9}+4 \left(b x +a \right) \cos \left(b x +a \right)+\frac{\left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{27}\right)}{b^{3}}+\frac{6 a^{2} d^{4} \left(-\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{4 \cos \left(b x +a \right)}{3}+\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{27}\right)}{b^{4}}-\frac{12 a c \,d^{3} \left(-\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{4 \cos \left(b x +a \right)}{3}+\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{27}\right)}{b^{3}}+\frac{6 c^{2} d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{4 \cos \left(b x +a \right)}{3}+\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{27}\right)}{b^{2}}-\frac{4 a^{3} d^{4} \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \sin \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+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \sin \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+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \sin \left(b x +a \right)}{3}\right)}{b^{2}}+\frac{4 c^{3} d \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \sin \left(b x +a \right)}{3}\right)}{b}-\frac{a^{4} d^{4} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3 b^{4}}+\frac{4 a^{3} c \,d^{3} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3 b^{3}}-\frac{2 a^{2} c^{2} d^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{b^{2}}+\frac{4 a \,c^{3} d \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3 b}-\frac{c^{4} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(1/b^4*d^4*(-1/3*(b*x+a)^4*(2+sin(b*x+a)^2)*cos(b*x+a)+8/3*(b*x+a)^3*sin(b*x+a)+8*(b*x+a)^2*cos(b*x+a)-160/9*cos(b*x+a)-160/9*(b*x+a)*sin(b*x+a)+4/9*(b*x+a)^3*sin(b*x+a)^3+4/9*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)-8/27*(b*x+a)*sin(b*x+a)^3-8/81*(2+sin(b*x+a)^2)*cos(b*x+a))-4/b^4*a*d^4*(-1/3*(b*x+a)^3*(2+sin(b*x+a)^2)*cos(b*x+a)+2*(b*x+a)^2*sin(b*x+a)-40/9*sin(b*x+a)+4*(b*x+a)*cos(b*x+a)+1/3*(b*x+a)^2*sin(b*x+a)^3+2/9*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)-2/27*sin(b*x+a)^3)+4/b^3*c*d^3*(-1/3*(b*x+a)^3*(2+sin(b*x+a)^2)*cos(b*x+a)+2*(b*x+a)^2*sin(b*x+a)-40/9*sin(b*x+a)+4*(b*x+a)*cos(b*x+a)+1/3*(b*x+a)^2*sin(b*x+a)^3+2/9*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)-2/27*sin(b*x+a)^3)+6/b^4*a^2*d^4*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/3*cos(b*x+a)+4/3*(b*x+a)*sin(b*x+a)+2/9*(b*x+a)*sin(b*x+a)^3+2/27*(2+sin(b*x+a)^2)*cos(b*x+a))-12/b^3*a*c*d^3*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/3*cos(b*x+a)+4/3*(b*x+a)*sin(b*x+a)+2/9*(b*x+a)*sin(b*x+a)^3+2/27*(2+sin(b*x+a)^2)*cos(b*x+a))+6/b^2*c^2*d^2*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/3*cos(b*x+a)+4/3*(b*x+a)*sin(b*x+a)+2/9*(b*x+a)*sin(b*x+a)^3+2/27*(2+sin(b*x+a)^2)*cos(b*x+a))-4/b^4*a^3*d^4*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/9*sin(b*x+a)^3+2/3*sin(b*x+a))+12/b^3*a^2*c*d^3*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/9*sin(b*x+a)^3+2/3*sin(b*x+a))-12/b^2*a*c^2*d^2*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/9*sin(b*x+a)^3+2/3*sin(b*x+a))+4/b*c^3*d*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/9*sin(b*x+a)^3+2/3*sin(b*x+a))-1/3/b^4*a^4*d^4*(2+sin(b*x+a)^2)*cos(b*x+a)+4/3/b^3*a^3*c*d^3*(2+sin(b*x+a)^2)*cos(b*x+a)-2/b^2*a^2*c^2*d^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/3/b*a*c^3*d*(2+sin(b*x+a)^2)*cos(b*x+a)-1/3*c^4*(2+sin(b*x+a)^2)*cos(b*x+a))","B"
17,1,560,161,0.020000," ","int((d*x+c)^3*sin(b*x+a)^3,x)","\frac{\frac{d^{3} \left(-\frac{\left(b x +a \right)^{3} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+2 \left(b x +a \right)^{2} \sin \left(b x +a \right)-\frac{40 \sin \left(b x +a \right)}{9}+4 \left(b x +a \right) \cos \left(b x +a \right)+\frac{\left(b x +a \right)^{2} \left(\sin^{3}\left(b x +a \right)\right)}{3}+\frac{2 \left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{9}-\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{27}\right)}{b^{3}}-\frac{3 a \,d^{3} \left(-\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{4 \cos \left(b x +a \right)}{3}+\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{27}\right)}{b^{3}}+\frac{3 c \,d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{4 \cos \left(b x +a \right)}{3}+\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{27}\right)}{b^{2}}+\frac{3 a^{2} d^{3} \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \sin \left(b x +a \right)}{3}\right)}{b^{3}}-\frac{6 a c \,d^{2} \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \sin \left(b x +a \right)}{3}\right)}{b^{2}}+\frac{3 c^{2} d \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \sin \left(b x +a \right)}{3}\right)}{b}+\frac{a^{3} d^{3} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3 b^{3}}-\frac{a^{2} c \,d^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{b^{2}}+\frac{a \,c^{2} d \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{b}-\frac{c^{3} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(1/b^3*d^3*(-1/3*(b*x+a)^3*(2+sin(b*x+a)^2)*cos(b*x+a)+2*(b*x+a)^2*sin(b*x+a)-40/9*sin(b*x+a)+4*(b*x+a)*cos(b*x+a)+1/3*(b*x+a)^2*sin(b*x+a)^3+2/9*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)-2/27*sin(b*x+a)^3)-3/b^3*a*d^3*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/3*cos(b*x+a)+4/3*(b*x+a)*sin(b*x+a)+2/9*(b*x+a)*sin(b*x+a)^3+2/27*(2+sin(b*x+a)^2)*cos(b*x+a))+3/b^2*c*d^2*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/3*cos(b*x+a)+4/3*(b*x+a)*sin(b*x+a)+2/9*(b*x+a)*sin(b*x+a)^3+2/27*(2+sin(b*x+a)^2)*cos(b*x+a))+3/b^3*a^2*d^3*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/9*sin(b*x+a)^3+2/3*sin(b*x+a))-6/b^2*a*c*d^2*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/9*sin(b*x+a)^3+2/3*sin(b*x+a))+3/b*c^2*d*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/9*sin(b*x+a)^3+2/3*sin(b*x+a))+1/3/b^3*a^3*d^3*(2+sin(b*x+a)^2)*cos(b*x+a)-1/b^2*a^2*c*d^2*(2+sin(b*x+a)^2)*cos(b*x+a)+1/b*a*c^2*d*(2+sin(b*x+a)^2)*cos(b*x+a)-1/3*c^3*(2+sin(b*x+a)^2)*cos(b*x+a))","B"
18,1,265,111,0.019000," ","int((d*x+c)^2*sin(b*x+a)^3,x)","\frac{\frac{d^{2} \left(-\frac{\left(b x +a \right)^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{4 \cos \left(b x +a \right)}{3}+\frac{4 \left(b x +a \right) \sin \left(b x +a \right)}{3}+\frac{2 \left(b x +a \right) \left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{27}\right)}{b^{2}}-\frac{2 a \,d^{2} \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \sin \left(b x +a \right)}{3}\right)}{b^{2}}+\frac{2 c d \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \sin \left(b x +a \right)}{3}\right)}{b}-\frac{a^{2} d^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3 b^{2}}+\frac{2 a c d \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3 b}-\frac{c^{2} \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(1/b^2*d^2*(-1/3*(b*x+a)^2*(2+sin(b*x+a)^2)*cos(b*x+a)+4/3*cos(b*x+a)+4/3*(b*x+a)*sin(b*x+a)+2/9*(b*x+a)*sin(b*x+a)^3+2/27*(2+sin(b*x+a)^2)*cos(b*x+a))-2/b^2*a*d^2*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/9*sin(b*x+a)^3+2/3*sin(b*x+a))+2/b*c*d*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/9*sin(b*x+a)^3+2/3*sin(b*x+a))-1/3/b^2*a^2*d^2*(2+sin(b*x+a)^2)*cos(b*x+a)+2/3/b*a*c*d*(2+sin(b*x+a)^2)*cos(b*x+a)-1/3*c^2*(2+sin(b*x+a)^2)*cos(b*x+a))","B"
19,1,95,67,0.018000," ","int((d*x+c)*sin(b*x+a)^3,x)","\frac{\frac{d \left(-\frac{\left(b x +a \right) \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}+\frac{\left(\sin^{3}\left(b x +a \right)\right)}{9}+\frac{2 \sin \left(b x +a \right)}{3}\right)}{b}+\frac{d a \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3 b}-\frac{c \left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(1/b*d*(-1/3*(b*x+a)*(2+sin(b*x+a)^2)*cos(b*x+a)+1/9*sin(b*x+a)^3+2/3*sin(b*x+a))+1/3/b*d*a*(2+sin(b*x+a)^2)*cos(b*x+a)-1/3*c*(2+sin(b*x+a)^2)*cos(b*x+a))","A"
20,1,167,113,0.018000," ","int(sin(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) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}-\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{12}+\frac{3 b \left(\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}\right)}{4}}{b}"," ",0,"1/b*(-1/12*b*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d-3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d)+3/4*b*(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d))","A"
21,1,240,137,0.021000," ","int(sin(b*x+a)^3/(d*x+c)^2,x)","\frac{-\frac{b^{2} \left(-\frac{3 \sin \left(3 b x +3 a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{9 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}+\frac{9 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}}{d}\right)}{12}+\frac{3 b^{2} \left(-\frac{\sin \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}+\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}+\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}}{d}\right)}{4}}{b}"," ",0,"1/b*(-1/12*b^2*(-3*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d+3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d+3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d)/d)+3/4*b^2*(-sin(b*x+a)/((b*x+a)*d-d*a+c*b)/d+(Si(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)/d))","A"
22,1,313,172,0.021000," ","int(sin(b*x+a)^3/(d*x+c)^3,x)","\frac{-\frac{b^{3} \left(-\frac{3 \sin \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{9 \cos \left(3 b x +3 a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right) d}-\frac{9 \left(\frac{3 \Si \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \cos \left(\frac{-3 d a +3 c b}{d}\right)}{d}-\frac{3 \Ci \left(3 b x +3 a +\frac{-3 d a +3 c b}{d}\right) \sin \left(\frac{-3 d a +3 c b}{d}\right)}{d}\right)}{2 d}}{d}\right)}{12}+\frac{3 b^{3} \left(-\frac{\sin \left(b x +a \right)}{2 \left(\left(b x +a \right) d -d a +c b \right)^{2} d}+\frac{-\frac{\cos \left(b x +a \right)}{\left(\left(b x +a \right) d -d a +c b \right) d}-\frac{\frac{\Si \left(b x +a +\frac{-d a +c b}{d}\right) \cos \left(\frac{-d a +c b}{d}\right)}{d}-\frac{\Ci \left(b x +a +\frac{-d a +c b}{d}\right) \sin \left(\frac{-d a +c b}{d}\right)}{d}}{d}}{2 d}\right)}{4}}{b}"," ",0,"1/b*(-1/12*b^3*(-3/2*sin(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)^2/d+3/2*(-3*cos(3*b*x+3*a)/((b*x+a)*d-d*a+c*b)/d-3*(3*Si(3*b*x+3*a+3*(-a*d+b*c)/d)*cos(3*(-a*d+b*c)/d)/d-3*Ci(3*b*x+3*a+3*(-a*d+b*c)/d)*sin(3*(-a*d+b*c)/d)/d)/d)/d)+3/4*b^3*(-1/2*sin(b*x+a)/((b*x+a)*d-d*a+c*b)^2/d+1/2*(-cos(b*x+a)/((b*x+a)*d-d*a+c*b)/d-(Si(b*x+a+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d-Ci(b*x+a+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d)/d)/d))","A"
23,1,633,167,0.122000," ","int((d*x+c)^3*csc(b*x+a),x)","\frac{2 d^{3} a^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{6 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{3}}{b^{4}}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{b}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{b^{4}}-\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{b}-\frac{2 c^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{6 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}-\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{3}}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{6 c^{2} d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{6 c \,d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}"," ",0,"2/b^4*d^3*a^3*arctanh(exp(I*(b*x+a)))-6/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+6/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))-6/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x+6/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x-2/b*c^3*arctanh(exp(I*(b*x+a)))-6*I/b^2*c*d^2*polylog(2,exp(I*(b*x+a)))*x+6*I/b^2*c*d^2*polylog(2,-exp(I*(b*x+a)))*x-3/b*c^2*d*ln(exp(I*(b*x+a))+1)*x-3/b^2*c^2*d*ln(exp(I*(b*x+a))+1)*a-3/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2+3/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2-1/b^4*d^3*ln(exp(I*(b*x+a))+1)*a^3+1/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+1/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3-1/b*d^3*ln(exp(I*(b*x+a))+1)*x^3+6/b^2*c^2*d*a*arctanh(exp(I*(b*x+a)))-6/b^3*c*d^2*a^2*arctanh(exp(I*(b*x+a)))+3*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2-3*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2-3*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))+3*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-3/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+3/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))+1)+3/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+3/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-6*I*d^3*polylog(4,-exp(I*(b*x+a)))/b^4+6*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4","B"
24,1,361,111,0.060000," ","int((d*x+c)^2*csc(b*x+a),x)","-\frac{2 c^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{2 d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{2 i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{4 c d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{b^{3}}+\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{3}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}-\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{2 c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{2 c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}"," ",0,"-2/b*c^2*arctanh(exp(I*(b*x+a)))-2/b^3*d^2*a^2*arctanh(exp(I*(b*x+a)))+2*d^2*polylog(3,exp(I*(b*x+a)))/b^3-2*d^2*polylog(3,-exp(I*(b*x+a)))/b^3+2*I/b^2*d^2*polylog(2,-exp(I*(b*x+a)))*x-2*I/b^2*d^2*polylog(2,exp(I*(b*x+a)))*x+4/b^2*c*d*a*arctanh(exp(I*(b*x+a)))-1/b*d^2*ln(exp(I*(b*x+a))+1)*x^2+1/b^3*d^2*ln(exp(I*(b*x+a))+1)*a^2+2*I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))+1/b*d^2*ln(1-exp(I*(b*x+a)))*x^2-1/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2-2*I/b^2*c*d*polylog(2,exp(I*(b*x+a)))-2/b*c*d*ln(exp(I*(b*x+a))+1)*x-2/b^2*c*d*ln(exp(I*(b*x+a))+1)*a+2/b*c*d*ln(1-exp(I*(b*x+a)))*x+2/b^2*c*d*ln(1-exp(I*(b*x+a)))*a","B"
25,1,164,59,0.007000," ","int((d*x+c)*csc(b*x+a),x)","\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{i d \dilog \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}+\frac{i d \dilog \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{d a \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b^{2}}+\frac{c \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b}"," ",0,"1/b*d*ln(1-exp(I*(b*x+a)))*x-1/b*d*ln(exp(I*(b*x+a))+1)*x-I/b^2*d*dilog(1-exp(I*(b*x+a)))+1/b^2*d*ln(1-exp(I*(b*x+a)))*a-1/b^2*d*ln(exp(I*(b*x+a))+1)*a+I/b^2*d*dilog(exp(I*(b*x+a))+1)-1/b^2*d*a*ln(csc(b*x+a)-cot(b*x+a))+1/b*c*ln(csc(b*x+a)-cot(b*x+a))","B"
26,0,0,16,0.089000," ","int(csc(b*x+a)/(d*x+c),x)","\int \frac{\csc \left(b x +a \right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)/(d*x+c),x)","F"
27,0,0,16,0.070000," ","int(csc(b*x+a)/(d*x+c)^2,x)","\int \frac{\csc \left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)/(d*x+c)^2,x)","F"
28,1,541,103,0.108000," ","int((d*x+c)^3*csc(b*x+a)^2,x)","-\frac{6 d^{3} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 d^{3} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{4}}+\frac{3 d \,c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{b^{2}}-\frac{6 d \,c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{3 d \,c^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{2}}+\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{b^{2}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{b^{2}}-\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{b^{4}}+\frac{4 i d^{3} a^{3}}{b^{4}}-\frac{2 i d^{3} x^{3}}{b}-\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{6 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{6 d^{2} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{6 d^{2} c \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}+\frac{12 d^{2} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 d^{2} c a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}+\frac{6 d^{2} c \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{2}}+\frac{6 i d^{3} a^{2} x}{b^{3}}-\frac{6 i d^{2} c \,x^{2}}{b}-\frac{6 i d^{2} c \,a^{2}}{b^{3}}-\frac{6 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{6 i d^{2} c \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{6 i d^{2} c \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{12 i d^{2} c a x}{b^{2}}"," ",0,"-6/b^4*d^3*a^2*ln(exp(I*(b*x+a)))+3/b^4*d^3*a^2*ln(exp(I*(b*x+a))-1)+3/b^2*d*c^2*ln(exp(I*(b*x+a))+1)-6/b^2*d*c^2*ln(exp(I*(b*x+a)))+3/b^2*d*c^2*ln(exp(I*(b*x+a))-1)+3/b^2*d^3*ln(exp(I*(b*x+a))+1)*x^2+3/b^2*d^3*ln(1-exp(I*(b*x+a)))*x^2-3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^2+4*I/b^4*d^3*a^3-2*I/b*d^3*x^3-2*I*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/b/(exp(2*I*(b*x+a))-1)+6/b^4*d^3*polylog(3,-exp(I*(b*x+a)))+6/b^4*d^3*polylog(3,exp(I*(b*x+a)))+6/b^2*d^2*c*ln(1-exp(I*(b*x+a)))*x+6/b^3*d^2*c*ln(1-exp(I*(b*x+a)))*a+12/b^3*d^2*c*a*ln(exp(I*(b*x+a)))-6/b^3*d^2*c*a*ln(exp(I*(b*x+a))-1)+6/b^2*d^2*c*ln(exp(I*(b*x+a))+1)*x+6*I/b^3*d^3*a^2*x-6*I/b*d^2*c*x^2-6*I/b^3*d^2*c*a^2-6*I/b^3*d^3*polylog(2,exp(I*(b*x+a)))*x-6*I/b^3*d^3*polylog(2,-exp(I*(b*x+a)))*x-6*I/b^3*d^2*c*polylog(2,-exp(I*(b*x+a)))-6*I/b^3*d^2*c*polylog(2,exp(I*(b*x+a)))-12*I/b^2*d^2*c*a*x","B"
29,1,276,77,0.066000," ","int((d*x+c)^2*csc(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}^{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 d c \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\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}^{i \left(b x +a \right)}+1\right) x}{b^{2}}-\frac{2 i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{2 d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{3}}-\frac{2 i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{4 d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 d^{2} a \ln \left({\mathrm e}^{i \left(b x +a \right)}-1\right)}{b^{3}}"," ",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(I*(b*x+a))+1)-4/b^2*d*c*ln(exp(I*(b*x+a)))+2/b^2*d*c*ln(exp(I*(b*x+a))-1)-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(I*(b*x+a))+1)*x-2*I/b^3*d^2*polylog(2,-exp(I*(b*x+a)))+2/b^2*d^2*ln(1-exp(I*(b*x+a)))*x+2/b^3*d^2*ln(1-exp(I*(b*x+a)))*a-2*I/b^3*d^2*polylog(2,exp(I*(b*x+a)))+4/b^3*d^2*a*ln(exp(I*(b*x+a)))-2/b^3*d^2*a*ln(exp(I*(b*x+a))-1)","B"
30,1,39,29,0.018000," ","int((d*x+c)*csc(b*x+a)^2,x)","-\frac{d \cot \left(b x +a \right) x}{b}+\frac{d \ln \left(\sin \left(b x +a \right)\right)}{b^{2}}-\frac{c \cot \left(b x +a \right)}{b}"," ",0,"-1/b*d*cot(b*x+a)*x+d*ln(sin(b*x+a))/b^2-1/b*c*cot(b*x+a)","A"
31,0,0,18,0.243000," ","int(csc(b*x+a)^2/(d*x+c),x)","\int \frac{\csc^{2}\left(b x +a \right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)^2/(d*x+c),x)","F"
32,0,0,18,0.388000," ","int(csc(b*x+a)^2/(d*x+c)^2,x)","\int \frac{\csc^{2}\left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)^2/(d*x+c)^2,x)","F"
33,1,1056,275,0.192000," ","int((d*x+c)^3*csc(b*x+a)^3,x)","\frac{d^{3} a^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 c \,d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 c \,d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 d^{3} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}-\frac{3 i d^{3} \polylog \left(4, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 i d^{3} \polylog \left(4, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{3}}{2 b^{4}}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{3}}{2 b}+\frac{d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{3}}{2 b^{4}}-\frac{d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{3}}{2 b}-\frac{c^{3} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}+\frac{d^{3} x^{3} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 c \,d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+3 c^{2} d x b \,{\mathrm e}^{3 i \left(b x +a \right)}+d^{3} x^{3} b \,{\mathrm e}^{i \left(b x +a \right)}+b \,c^{3} {\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)}+b \,c^{3} {\mathrm e}^{i \left(b x +a \right)}-3 i c^{2} d \,{\mathrm e}^{3 i \left(b x +a \right)}+3 i d^{3} x^{2} {\mathrm e}^{i \left(b x +a \right)}+6 i c \,d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}+3 i c^{2} d \,{\mathrm e}^{i \left(b x +a \right)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}-\frac{3 i c \,d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 i c \,d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}-\frac{3 i c^{2} d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{3 i c^{2} d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}-\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{2 b}-\frac{3 c^{2} d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{2 b^{2}}-\frac{3 c \,d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{2 b}+\frac{3 c \,d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}-\frac{3 c \,d^{2} a^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{3}}+\frac{3 c \,d^{2} a^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right)}{2 b^{3}}+\frac{3 c^{2} d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}+\frac{3 c^{2} d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{3 c \,d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b^{2}}-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{4}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{3}}+\frac{3 d^{3} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{4}}+\frac{6 d^{3} a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{6 c \,d^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{3 i d^{3} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}+\frac{3 i d^{3} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{4}}-\frac{3 d^{3} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b^{3}}"," ",0,"1/b^4*d^3*a^3*arctanh(exp(I*(b*x+a)))-3/b^3*c*d^2*polylog(3,-exp(I*(b*x+a)))+3/b^3*c*d^2*polylog(3,exp(I*(b*x+a)))-3/b^3*d^3*polylog(3,-exp(I*(b*x+a)))*x+3/b^3*d^3*polylog(3,exp(I*(b*x+a)))*x-1/b*c^3*arctanh(exp(I*(b*x+a)))-3/b^4*d^3*ln(exp(I*(b*x+a))+1)*a+3/b^3*d^3*ln(1-exp(I*(b*x+a)))*x+3/b^4*d^3*ln(1-exp(I*(b*x+a)))*a+6/b^4*d^3*a*arctanh(exp(I*(b*x+a)))-6/b^3*c*d^2*arctanh(exp(I*(b*x+a)))-3/b^3*d^3*ln(exp(I*(b*x+a))+1)*x+1/b^2/(exp(2*I*(b*x+a))-1)^2*(d^3*x^3*b*exp(3*I*(b*x+a))+3*c*d^2*x^2*b*exp(3*I*(b*x+a))+3*c^2*d*x*b*exp(3*I*(b*x+a))+d^3*x^3*b*exp(I*(b*x+a))+b*c^3*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))+b*c^3*exp(I*(b*x+a))-3*I*c^2*d*exp(3*I*(b*x+a))+3*I*d^3*x^2*exp(I*(b*x+a))+6*I*c*d^2*x*exp(I*(b*x+a))+3*I*c^2*d*exp(I*(b*x+a)))+3/2*I/b^2*c^2*d*polylog(2,-exp(I*(b*x+a)))-3/2*I/b^2*c^2*d*polylog(2,exp(I*(b*x+a)))+3/2*I/b^2*d^3*polylog(2,-exp(I*(b*x+a)))*x^2-3/2*I/b^2*d^3*polylog(2,exp(I*(b*x+a)))*x^2+3*I/b^2*polylog(2,-exp(I*(b*x+a)))*c*d^2*x-3*I/b^2*polylog(2,exp(I*(b*x+a)))*c*d^2*x-3/2/b*c^2*d*ln(exp(I*(b*x+a))+1)*x-3/2/b^2*c^2*d*ln(exp(I*(b*x+a))+1)*a-3/2/b*c*d^2*ln(exp(I*(b*x+a))+1)*x^2+3/2/b*c*d^2*ln(1-exp(I*(b*x+a)))*x^2-1/2/b^4*d^3*ln(exp(I*(b*x+a))+1)*a^3+1/2/b*d^3*ln(1-exp(I*(b*x+a)))*x^3+1/2/b^4*d^3*ln(1-exp(I*(b*x+a)))*a^3-1/2/b*d^3*ln(exp(I*(b*x+a))+1)*x^3+3/b^2*c^2*d*a*arctanh(exp(I*(b*x+a)))-3/b^3*c*d^2*a^2*arctanh(exp(I*(b*x+a)))-3/2/b^3*c*d^2*a^2*ln(1-exp(I*(b*x+a)))+3/2/b^3*c*d^2*a^2*ln(exp(I*(b*x+a))+1)+3/2/b*c^2*d*ln(1-exp(I*(b*x+a)))*x+3/2/b^2*c^2*d*ln(1-exp(I*(b*x+a)))*a-3*I*d^3*polylog(4,-exp(I*(b*x+a)))/b^4-3*I*d^3*polylog(2,exp(I*(b*x+a)))/b^4+3*I*d^3*polylog(2,-exp(I*(b*x+a)))/b^4+3*I*d^3*polylog(4,exp(I*(b*x+a)))/b^4","B"
34,1,548,166,0.115000," ","int((d*x+c)^2*csc(b*x+a)^3,x)","\frac{d^{2} x^{2} b \,{\mathrm e}^{3 i \left(b x +a \right)}+2 c d x b \,{\mathrm e}^{3 i \left(b x +a \right)}+b \,c^{2} {\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)}+b \,c^{2} {\mathrm e}^{i \left(b x +a \right)}-2 i d c \,{\mathrm e}^{3 i \left(b x +a \right)}+2 i d^{2} x \,{\mathrm e}^{i \left(b x +a \right)}+2 i d c \,{\mathrm e}^{i \left(b x +a \right)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}+\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a^{2}}{2 b^{3}}-\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a^{2}}{2 b^{3}}-\frac{c^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{d^{2} a^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{d^{2} \polylog \left(3, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}+\frac{d^{2} \polylog \left(3, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{2 d^{2} \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{3}}-\frac{d^{2} \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x^{2}}{2 b}-\frac{i d^{2} \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{d^{2} \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x^{2}}{2 b}-\frac{i c d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}-\frac{c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{b}-\frac{c d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{b^{2}}+\frac{c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{b}+\frac{c d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{b^{2}}+\frac{2 c d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}+\frac{i d^{2} \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right) x}{b^{2}}+\frac{i c d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"1/b^2/(exp(2*I*(b*x+a))-1)^2*(d^2*x^2*b*exp(3*I*(b*x+a))+2*c*d*x*b*exp(3*I*(b*x+a))+b*c^2*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))+b*c^2*exp(I*(b*x+a))-2*I*d*c*exp(3*I*(b*x+a))+2*I*d^2*x*exp(I*(b*x+a))+2*I*d*c*exp(I*(b*x+a)))+1/2/b^3*d^2*ln(exp(I*(b*x+a))+1)*a^2-1/2/b^3*d^2*ln(1-exp(I*(b*x+a)))*a^2-1/b*c^2*arctanh(exp(I*(b*x+a)))-1/b^3*d^2*a^2*arctanh(exp(I*(b*x+a)))-d^2*polylog(3,-exp(I*(b*x+a)))/b^3+d^2*polylog(3,exp(I*(b*x+a)))/b^3-2/b^3*d^2*arctanh(exp(I*(b*x+a)))-1/2/b*d^2*ln(exp(I*(b*x+a))+1)*x^2-I/b^2*c*d*polylog(2,exp(I*(b*x+a)))+1/2/b*d^2*ln(1-exp(I*(b*x+a)))*x^2+I/b^2*c*d*polylog(2,-exp(I*(b*x+a)))-1/b*c*d*ln(exp(I*(b*x+a))+1)*x-1/b^2*c*d*ln(exp(I*(b*x+a))+1)*a+1/b*c*d*ln(1-exp(I*(b*x+a)))*x+1/b^2*c*d*ln(1-exp(I*(b*x+a)))*a+2/b^2*c*d*a*arctanh(exp(I*(b*x+a)))-I/b^2*polylog(2,exp(I*(b*x+a)))*d^2*x+I/b^2*polylog(2,-exp(I*(b*x+a)))*d^2*x","B"
35,1,246,93,0.088000," ","int((d*x+c)*csc(b*x+a)^3,x)","\frac{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)}}{b^{2} \left({\mathrm e}^{2 i \left(b x +a \right)}-1\right)^{2}}-\frac{c \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) x}{2 b}-\frac{d \ln \left({\mathrm e}^{i \left(b x +a \right)}+1\right) a}{2 b^{2}}+\frac{i d \polylog \left(2, -{\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) x}{2 b}+\frac{d \ln \left(1-{\mathrm e}^{i \left(b x +a \right)}\right) a}{2 b^{2}}-\frac{i d \polylog \left(2, {\mathrm e}^{i \left(b x +a \right)}\right)}{2 b^{2}}+\frac{d a \arctanh \left({\mathrm e}^{i \left(b x +a \right)}\right)}{b^{2}}"," ",0,"1/b^2/(exp(2*I*(b*x+a))-1)^2*(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)))-1/b*c*arctanh(exp(I*(b*x+a)))-1/2/b*d*ln(exp(I*(b*x+a))+1)*x-1/2/b^2*d*ln(exp(I*(b*x+a))+1)*a+1/2*I*d*polylog(2,-exp(I*(b*x+a)))/b^2+1/2/b*d*ln(1-exp(I*(b*x+a)))*x+1/2/b^2*d*ln(1-exp(I*(b*x+a)))*a-1/2*I*d*polylog(2,exp(I*(b*x+a)))/b^2+1/b^2*d*a*arctanh(exp(I*(b*x+a)))","B"
36,0,0,18,2.905000," ","int(csc(b*x+a)^3/(d*x+c),x)","\int \frac{\csc^{3}\left(b x +a \right)}{d x +c}\, dx"," ",0,"int(csc(b*x+a)^3/(d*x+c),x)","F"
37,0,0,18,4.458000," ","int(csc(b*x+a)^3/(d*x+c)^2,x)","\int \frac{\csc^{3}\left(b x +a \right)}{\left(d x +c \right)^{2}}\, dx"," ",0,"int(csc(b*x+a)^3/(d*x+c)^2,x)","F"
38,1,233,149,0.019000," ","int((d*x+c)^(5/2)*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{b}+\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{b}}{d}"," ",0,"2/d*(-1/2/b*d*(d*x+c)^(5/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+5/2/b*d*(1/2/b*d*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/2/b*d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
39,1,188,128,0.012000," ","int((d*x+c)^(3/2)*sin(b*x+a),x)","\frac{-\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{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)}{b}}{d}"," ",0,"2/d*(-1/2/b*d*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/2/b*d*(1/2/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
40,1,145,109,0.010000," ","int((d*x+c)^(1/2)*sin(b*x+a),x)","\frac{-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{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)}{2 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
41,1,99,89,0.012000," ","int(sin(b*x+a)/(d*x+c)^(1/2),x)","\frac{\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}}}"," ",0,"1/d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))","A"
42,1,140,109,0.010000," ","int(sin(b*x+a)/(d*x+c)^(3/2),x)","\frac{-\frac{2 \sin \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) \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}}}}{d}"," ",0,"2/d*(-1/(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+b/d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
43,1,180,128,0.011000," ","int(sin(b*x+a)/(d*x+c)^(5/2),x)","\frac{-\frac{2 \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{4 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}}{d}"," ",0,"2/d*(-1/3/(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+2/3*b/d*(-1/(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-b/d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
44,1,220,149,0.010000," ","int(sin(b*x+a)/(d*x+c)^(7/2),x)","\frac{-\frac{2 \sin \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{\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{2 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}\right)}{5 d}}{d}"," ",0,"2/d*(-1/5/(d*x+c)^(5/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+2/5*b/d*(-1/3/(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-2/3*b/d*(-1/(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+b/d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
45,1,242,179,0.040000," ","int((d*x+c)^(5/2)*sin(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/b*d*(d*x+c)^(5/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+5/8/b*d*(-1/4/b*d*(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/4/b*d*(1/4/b*d*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
46,1,197,155,0.033000," ","int((d*x+c)^(3/2)*sin(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/b*d*(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+3/8/b*d*(-1/4/b*d*(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/8/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
47,1,150,118,0.033000," ","int((d*x+c)^(1/2)*sin(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/b*d*(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+1/16/b*d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
48,1,108,96,0.036000," ","int(sin(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)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
49,1,145,105,0.034000," ","int(sin(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)+b/d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
50,1,189,130,0.035000," ","int(sin(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*b/d*(-1/(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+2*b/d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
51,1,230,168,0.034000," ","int(sin(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*b/d*(-1/3/(d*x+c)^(3/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+4/3*b/d*(-1/(d*x+c)^(1/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-2*b/d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
52,1,273,195,0.034000," ","int(sin(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*b/d*(-1/5/(d*x+c)^(5/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+4/5*b/d*(-1/3/(d*x+c)^(3/2)*cos(2/d*(d*x+c)*b+2*(a*d-b*c)/d)-4/3*b/d*(-1/(d*x+c)^(1/2)*sin(2/d*(d*x+c)*b+2*(a*d-b*c)/d)+2*b/d*Pi^(1/2)/(b/d)^(1/2)*(cos(2*(a*d-b*c)/d)*FresnelC(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(2*(a*d-b*c)/d)*FresnelS(2/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))))","A"
53,1,476,314,0.029000," ","int((d*x+c)^(5/2)*sin(b*x+a)^3,x)","\frac{-\frac{3 d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}+\frac{15 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{3 d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{4 b}+\frac{d \left(d x +c \right)^{\frac{5}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}-\frac{5 d \left(\frac{d \left(d x +c \right)^{\frac{3}{2}} \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \left(-\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{2 b}\right)}{12 b}}{d}"," ",0,"2/d*(-3/8/b*d*(d*x+c)^(5/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+15/8/b*d*(1/2/b*d*(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-3/2/b*d*(-1/2/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))+1/24/b*d*(d*x+c)^(5/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-5/24/b*d*(1/6/b*d*(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/2/b*d*(-1/6/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
54,1,384,268,0.022000," ","int((d*x+c)^(3/2)*sin(b*x+a)^3,x)","\frac{-\frac{3 d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}+\frac{9 d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{2 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{4 b \sqrt{\frac{b}{d}}}\right)}{4 b}+\frac{d \left(d x +c \right)^{\frac{3}{2}} \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}-\frac{d \left(\frac{d \sqrt{d x +c}\, \sin \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{6 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)+\sin \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{36 b \sqrt{\frac{b}{d}}}\right)}{4 b}}{d}"," ",0,"2/d*(-3/8/b*d*(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+9/8/b*d*(1/2/b*d*(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)-1/4/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))+1/24/b*d*(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/8/b*d*(1/6/b*d*(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/36/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
55,1,296,224,0.020000," ","int((d*x+c)^(1/2)*sin(b*x+a)^3,x)","\frac{-\frac{3 d \sqrt{d x +c}\, \cos \left(\frac{\left(d x +c \right) b}{d}+\frac{d a -c b}{d}\right)}{4 b}+\frac{3 d \sqrt{2}\, \sqrt{\pi}\, \left(\cos \left(\frac{d a -c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{d a -c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{8 b \sqrt{\frac{b}{d}}}+\frac{d \sqrt{d x +c}\, \cos \left(\frac{3 \left(d x +c \right) b}{d}+\frac{3 d a -3 c b}{d}\right)}{12 b}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \left(\cos \left(\frac{3 d a -3 c b}{d}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)-\sin \left(\frac{3 d a -3 c b}{d}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{d x +c}\, b}{\sqrt{\pi}\, \sqrt{\frac{b}{d}}\, d}\right)\right)}{72 b \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-3/8/b*d*(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/16/b*d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))+1/24/b*d*(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/144/b*d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
56,1,210,185,0.024000," ","int(sin(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) \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 \sqrt{\frac{b}{d}}}-\frac{\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)}{12 \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(3/8*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))-1/24*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
57,1,288,205,0.023000," ","int(sin(b*x+a)^3/(d*x+c)^(3/2),x)","\frac{-\frac{3 \sin \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) \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)}{2 d \sqrt{\frac{b}{d}}}+\frac{\sin \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) \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)}{2 d \sqrt{\frac{b}{d}}}}{d}"," ",0,"2/d*(-3/4/(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/4*b/d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))+1/4/(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/4*b/d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))","A"
58,1,368,230,0.021000," ","int(sin(b*x+a)^3/(d*x+c)^(5/2),x)","\frac{-\frac{\sin \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{\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)}{d}+\frac{\sin \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{\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}}{d}"," ",0,"2/d*(-1/4/(d*x+c)^(3/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+1/2*b/d*(-1/(d*x+c)^(1/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-b/d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))+1/12/(d*x+c)^(3/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-1/2*b/d*(-1/(d*x+c)^(1/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-b/d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)+sin(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))","A"
59,1,450,276,0.023000," ","int(sin(b*x+a)^3/(d*x+c)^(7/2),x)","\frac{-\frac{3 \sin \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{\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{2 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}\right)}{5 d}+\frac{\sin \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{\cos \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{\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}\right)}{5 d}}{d}"," ",0,"2/d*(-3/20/(d*x+c)^(5/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+3/10*b/d*(-1/3/(d*x+c)^(3/2)*cos(1/d*(d*x+c)*b+(a*d-b*c)/d)-2/3*b/d*(-1/(d*x+c)^(1/2)*sin(1/d*(d*x+c)*b+(a*d-b*c)/d)+b/d*2^(1/2)*Pi^(1/2)/(b/d)^(1/2)*(cos((a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin((a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d))))+1/20/(d*x+c)^(5/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-3/10*b/d*(-1/3/(d*x+c)^(3/2)*cos(3/d*(d*x+c)*b+3*(a*d-b*c)/d)-2*b/d*(-1/(d*x+c)^(1/2)*sin(3/d*(d*x+c)*b+3*(a*d-b*c)/d)+b/d*2^(1/2)*Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(cos(3*(a*d-b*c)/d)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)-sin(3*(a*d-b*c)/d)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(b/d)^(1/2)*(d*x+c)^(1/2)*b/d)))))","A"
60,1,87,63,0.020000," ","int((d*x)^(3/2)*sin(f*x),x)","\frac{-\frac{d \left(d x \right)^{\frac{3}{2}} \cos \left(f x \right)}{f}+\frac{3 d \left(\frac{d \sqrt{d x}\, \sin \left(f x \right)}{2 f}-\frac{d \sqrt{2}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x}\, f}{\sqrt{\pi}\, \sqrt{\frac{f}{d}}\, d}\right)}{4 f \sqrt{\frac{f}{d}}}\right)}{f}}{d}"," ",0,"2/d*(-1/2*d/f*(d*x)^(3/2)*cos(f*x)+3/2*d/f*(1/2*d/f*(d*x)^(1/2)*sin(f*x)-1/4*d/f*2^(1/2)*Pi^(1/2)/(1/d*f)^(1/2)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*f)^(1/2)*(d*x)^(1/2)/d*f)))","A"
61,1,65,48,0.010000," ","int((d*x)^(1/2)*sin(f*x),x)","\frac{-\frac{d \sqrt{d x}\, \cos \left(f x \right)}{f}+\frac{d \sqrt{2}\, \sqrt{\pi}\, \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x}\, f}{\sqrt{\pi}\, \sqrt{\frac{f}{d}}\, d}\right)}{2 f \sqrt{\frac{f}{d}}}}{d}"," ",0,"2/d*(-1/2*d/f*(d*x)^(1/2)*cos(f*x)+1/4*d/f*2^(1/2)*Pi^(1/2)/(1/d*f)^(1/2)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*f)^(1/2)*(d*x)^(1/2)/d*f))","A"
62,1,42,32,0.011000," ","int(sin(f*x)/(d*x)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x}\, f}{\sqrt{\pi}\, \sqrt{\frac{f}{d}}\, d}\right)}{d \sqrt{\frac{f}{d}}}"," ",0,"1/d*2^(1/2)*Pi^(1/2)/(1/d*f)^(1/2)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*f)^(1/2)*(d*x)^(1/2)/d*f)","A"
63,1,60,48,0.010000," ","int(sin(f*x)/(d*x)^(3/2),x)","\frac{-\frac{2 \sin \left(f x \right)}{\sqrt{d x}}+\frac{2 f \sqrt{2}\, \sqrt{\pi}\, \FresnelC \left(\frac{\sqrt{2}\, \sqrt{d x}\, f}{\sqrt{\pi}\, \sqrt{\frac{f}{d}}\, d}\right)}{d \sqrt{\frac{f}{d}}}}{d}"," ",0,"2/d*(-sin(f*x)/(d*x)^(1/2)+1/d*f*2^(1/2)*Pi^(1/2)/(1/d*f)^(1/2)*FresnelC(2^(1/2)/Pi^(1/2)/(1/d*f)^(1/2)*(d*x)^(1/2)/d*f))","A"
64,1,79,63,0.011000," ","int(sin(f*x)/(d*x)^(5/2),x)","\frac{-\frac{2 \sin \left(f x \right)}{3 \left(d x \right)^{\frac{3}{2}}}+\frac{4 f \left(-\frac{\cos \left(f x \right)}{\sqrt{d x}}-\frac{f \sqrt{2}\, \sqrt{\pi}\, \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{d x}\, f}{\sqrt{\pi}\, \sqrt{\frac{f}{d}}\, d}\right)}{d \sqrt{\frac{f}{d}}}\right)}{3 d}}{d}"," ",0,"2/d*(-1/3*sin(f*x)/(d*x)^(3/2)+2/3/d*f*(-1/(d*x)^(1/2)*cos(f*x)-1/d*f*2^(1/2)*Pi^(1/2)/(1/d*f)^(1/2)*FresnelS(2^(1/2)/Pi^(1/2)/(1/d*f)^(1/2)*(d*x)^(1/2)/d*f)))","A"
65,0,0,16,0.086000," ","int(csc(b*x+a)*(d*x+c)^(1/2),x)","\int \csc \left(b x +a \right) \sqrt{d x +c}\, dx"," ",0,"int(csc(b*x+a)*(d*x+c)^(1/2),x)","F"
66,0,0,16,0.089000," ","int(csc(b*x+a)/(d*x+c)^(1/2),x)","\int \frac{\csc \left(b x +a \right)}{\sqrt{d x +c}}\, dx"," ",0,"int(csc(b*x+a)/(d*x+c)^(1/2),x)","F"
67,0,0,34,0.237000," ","int(x/sin(f*x+e)^(3/2)+x*sin(f*x+e)^(1/2),x)","\int \frac{x}{\sin \left(f x +e \right)^{\frac{3}{2}}}+x \left(\sqrt{\sin}\left(f x +e \right)\right)\, dx"," ",0,"int(x/sin(f*x+e)^(3/2)+x*sin(f*x+e)^(1/2),x)","F"
68,0,0,88,0.205000," ","int(x^2/sin(f*x+e)^(3/2)+x^2*sin(f*x+e)^(1/2),x)","\int \frac{x^{2}}{\sin \left(f x +e \right)^{\frac{3}{2}}}+x^{2} \left(\sqrt{\sin}\left(f x +e \right)\right)\, dx"," ",0,"int(x^2/sin(f*x+e)^(3/2)+x^2*sin(f*x+e)^(1/2),x)","F"
69,0,0,34,0.215000," ","int(x/sin(f*x+e)^(5/2)-1/3*x/sin(f*x+e)^(1/2),x)","\int \frac{x}{\sin \left(f x +e \right)^{\frac{5}{2}}}-\frac{x}{3 \sqrt{\sin \left(f x +e \right)}}\, dx"," ",0,"int(x/sin(f*x+e)^(5/2)-1/3*x/sin(f*x+e)^(1/2),x)","F"
70,0,0,67,0.270000," ","int(x/sin(f*x+e)^(7/2)+3/5*x*sin(f*x+e)^(1/2),x)","\int \frac{x}{\sin \left(f x +e \right)^{\frac{7}{2}}}+\frac{3 x \left(\sqrt{\sin}\left(f x +e \right)\right)}{5}\, dx"," ",0,"int(x/sin(f*x+e)^(7/2)+3/5*x*sin(f*x+e)^(1/2),x)","F"
71,0,0,20,0.336000," ","int((d*x+c)^m*(b*sin(f*x+e))^n,x)","\int \left(d x +c \right)^{m} \left(b \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((d*x+c)^m*(b*sin(f*x+e))^n,x)","F"
72,0,0,247,0.312000," ","int((d*x+c)^m*sin(b*x+a)^3,x)","\int \left(d x +c \right)^{m} \left(\sin^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*sin(b*x+a)^3,x)","F"
73,0,0,152,0.202000," ","int((d*x+c)^m*sin(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*sin(b*x+a)^2,x)","F"
74,0,0,117,0.083000," ","int((d*x+c)^m*sin(b*x+a),x)","\int \left(d x +c \right)^{m} \sin \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*sin(b*x+a),x)","F"
75,0,0,16,0.056000," ","int((d*x+c)^m*csc(b*x+a),x)","\int \left(d x +c \right)^{m} \csc \left(b x +a \right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a),x)","F"
76,0,0,18,0.052000," ","int((d*x+c)^m*csc(b*x+a)^2,x)","\int \left(d x +c \right)^{m} \left(\csc^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*x+c)^m*csc(b*x+a)^2,x)","F"
77,1,454,67,0.159000," ","int(x^(3+m)*sin(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) \sin \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) \cos \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))*sin(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))*cos(a)","C"
78,1,353,65,0.090000," ","int(x^(2+m)*sin(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) \sin \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) \cos \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))*sin(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))*cos(a)","C"
79,1,290,67,0.088000," ","int(x^(1+m)*sin(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) \sin \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) \cos \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))*sin(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))*cos(a)","C"
80,1,378,65,0.084000," ","int(x^m*sin(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) \sin \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) \cos \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))*sin(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))*cos(a)","C"
81,1,426,57,0.088000," ","int(x^(-1+m)*sin(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) \sin \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) \cos \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))*sin(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))*cos(a)","C"
82,1,529,61,0.094000," ","int(x^(m-2)*sin(b*x+a),x)","2^{m -2} \left(b^{2}\right)^{-\frac{1}{2}-\frac{m}{2}} b^{2} \sqrt{\pi}\, \left(\frac{3 \,2^{1-m} x^{m -2} \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^{m -2} \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) \sin \left(a \right)+2^{m -2} 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) \cos \left(a \right)"," ",0,"2^(m-2)*(b^2)^(-1/2-1/2*m)*b^2*Pi^(1/2)*(3*2^(1-m)/Pi^(1/2)/(-1+m)*x^(m-2)*(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^(m-2)*(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))*sin(a)+2^(m-2)*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))*cos(a)","C"
83,1,599,67,0.099000," ","int(x^(m-3)*sin(b*x+a),x)","2^{m -3} \left(b^{2}\right)^{-\frac{m}{2}} b^{2} \sqrt{\pi}\, \left(\frac{2^{2-m} x^{m -3} \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(m -2\right) b^{3} m \left(2+m \right) \left(-1+m \right)}-\frac{2^{-m +3} x^{m -3} \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(m -2\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(m -2\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(m -2\right) m \left(-1+m \right)}\right) \sin \left(a \right)+2^{m -3} b^{2-m} \sqrt{\pi}\, \left(\frac{2^{2-m} x^{m -2} b^{m -2} \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(m -2\right)}+\frac{2^{-m +3} x^{m -2} b^{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) \left(1+m \right) \left(m -2\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(m -2\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(m -2\right) m}\right) \cos \left(a \right)"," ",0,"2^(m-3)*(b^2)^(-1/2*m)*b^2*Pi^(1/2)*(2^(2-m)/Pi^(1/2)/(m-2)*x^(m-3)/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)/(m-2)*x^(m-3)/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)/(m-2)*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)/(m-2)*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))*sin(a)+2^(m-3)*b^(2-m)*Pi^(1/2)*(2^(2-m)/Pi^(1/2)/(-1+m)*x^(m-2)*b^(m-2)*(-2*b^2*x^2+2*m^2-2*m-4)/(1+m)/(m-2)*sin(b*x)+2^(-m+3)/Pi^(1/2)/(-1+m)*x^(m-2)*b^(m-2)*(b^2*x^2-m^2-m)/(1+m)/(m-2)/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)/(m-2)*(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)/(m-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)","C"
84,0,0,89,0.139000," ","int(x^(3+m)*sin(b*x+a)^2,x)","\int x^{3+m} \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(3+m)*sin(b*x+a)^2,x)","F"
85,0,0,93,0.120000," ","int(x^(2+m)*sin(b*x+a)^2,x)","\int x^{2+m} \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(2+m)*sin(b*x+a)^2,x)","F"
86,0,0,91,0.188000," ","int(x^(1+m)*sin(b*x+a)^2,x)","\int x^{1+m} \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(1+m)*sin(b*x+a)^2,x)","F"
87,0,0,93,0.135000," ","int(x^m*sin(b*x+a)^2,x)","\int x^{m} \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^m*sin(b*x+a)^2,x)","F"
88,0,0,75,0.201000," ","int(x^(-1+m)*sin(b*x+a)^2,x)","\int x^{-1+m} \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(-1+m)*sin(b*x+a)^2,x)","F"
89,0,0,91,0.150000," ","int(x^(m-2)*sin(b*x+a)^2,x)","\int x^{m -2} \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(m-2)*sin(b*x+a)^2,x)","F"
90,0,0,89,0.155000," ","int(x^(m-3)*sin(b*x+a)^2,x)","\int x^{m -3} \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(x^(m-3)*sin(b*x+a)^2,x)","F"
91,0,0,34,0.232000," ","int(x/csc(f*x+e)^(3/2)-1/3*x*csc(f*x+e)^(1/2),x)","\int \frac{x}{\csc \left(f x +e \right)^{\frac{3}{2}}}-\frac{x \left(\sqrt{\csc}\left(f x +e \right)\right)}{3}\, dx"," ",0,"int(x/csc(f*x+e)^(3/2)-1/3*x*csc(f*x+e)^(1/2),x)","F"
92,0,0,123,0.218000," ","int(x^2/csc(f*x+e)^(3/2)-1/3*x^2*csc(f*x+e)^(1/2),x)","\int \frac{x^{2}}{\csc \left(f x +e \right)^{\frac{3}{2}}}-\frac{x^{2} \left(\sqrt{\csc}\left(f x +e \right)\right)}{3}\, dx"," ",0,"int(x^2/csc(f*x+e)^(3/2)-1/3*x^2*csc(f*x+e)^(1/2),x)","F"
93,0,0,34,0.201000," ","int(x/csc(f*x+e)^(5/2)-3/5*x/csc(f*x+e)^(1/2),x)","\int \frac{x}{\csc \left(f x +e \right)^{\frac{5}{2}}}-\frac{3 x}{5 \sqrt{\csc \left(f x +e \right)}}\, dx"," ",0,"int(x/csc(f*x+e)^(5/2)-3/5*x/csc(f*x+e)^(1/2),x)","F"
94,0,0,67,0.232000," ","int(x/csc(f*x+e)^(7/2)-5/21*x*csc(f*x+e)^(1/2),x)","\int \frac{x}{\csc \left(f x +e \right)^{\frac{7}{2}}}-\frac{5 x \left(\sqrt{\csc}\left(f x +e \right)\right)}{21}\, dx"," ",0,"int(x/csc(f*x+e)^(7/2)-5/21*x*csc(f*x+e)^(1/2),x)","F"
95,1,482,88,0.038000," ","int((d*x+c)^3*(a+a*sin(f*x+e)),x)","\frac{\frac{a \,d^{3} \left(-\left(f x +e \right)^{3} \cos \left(f x +e \right)+3 \left(f x +e \right)^{2} \sin \left(f x +e \right)-6 \sin \left(f x +e \right)+6 \left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{3}}+\frac{3 a c \,d^{2} \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}-\frac{3 a \,d^{3} e \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{3}}+\frac{3 a \,c^{2} d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}-\frac{6 a c \,d^{2} e \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}+\frac{3 a \,d^{3} e^{2} \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{3}}-a \,c^{3} \cos \left(f x +e \right)+\frac{3 a \,c^{2} d e \cos \left(f x +e \right)}{f}-\frac{3 a c \,d^{2} e^{2} \cos \left(f x +e \right)}{f^{2}}+\frac{a \,d^{3} e^{3} \cos \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*cos(f*x+e)+3*(f*x+e)^2*sin(f*x+e)-6*sin(f*x+e)+6*(f*x+e)*cos(f*x+e))+3*a/f^2*c*d^2*(-(f*x+e)^2*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))-3*a/f^3*d^3*e*(-(f*x+e)^2*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))+3*a/f*c^2*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-6*a/f^2*c*d^2*e*(sin(f*x+e)-(f*x+e)*cos(f*x+e))+3*a/f^3*d^3*e^2*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-a*c^3*cos(f*x+e)+3*a/f*c^2*d*e*cos(f*x+e)-3*a/f^2*c*d^2*e^2*cos(f*x+e)+a/f^3*d^3*e^3*cos(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"
96,1,241,66,0.026000," ","int((d*x+c)^2*(a+a*sin(f*x+e)),x)","\frac{\frac{a \,d^{2} \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}+\frac{2 a c d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}-\frac{2 a \,d^{2} e \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}-a \,c^{2} \cos \left(f x +e \right)+\frac{2 a c d e \cos \left(f x +e \right)}{f}-\frac{a \,d^{2} e^{2} \cos \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*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))+2*a/f*c*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-2*a/f^2*d^2*e*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-a*c^2*cos(f*x+e)+2*a/f*c*d*e*cos(f*x+e)-a/f^2*d^2*e^2*cos(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"
97,1,90,43,0.024000," ","int((d*x+c)*(a+a*sin(f*x+e)),x)","\frac{\frac{a d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}-a c \cos \left(f x +e \right)+\frac{a d e \cos \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*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-a*c*cos(f*x+e)+a/f*d*e*cos(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"
98,1,96,67,0.031000," ","int((a+a*sin(f*x+e))/(d*x+c),x)","\frac{a \Si \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}-\frac{a \Ci \left(f x +e +\frac{c f -d e}{d}\right) \sin \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)*cos((c*f-d*e)/d)/d-a*Ci(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d+a*ln((f*x+e)*d+c*f-d*e)/d","A"
99,1,141,89,0.029000," ","int((a+a*sin(f*x+e))/(d*x+c)^2,x)","\frac{a \,f^{2} \left(-\frac{\sin \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) \sin \left(\frac{c f -d e}{d}\right)}{d}+\frac{\Ci \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}}{d}\right)-\frac{a \,f^{2}}{\left(\left(f x +e \right) d +c f -d e \right) d}}{f}"," ",0,"1/f*(a*f^2*(-sin(f*x+e)/((f*x+e)*d+c*f-d*e)/d+(Si(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d+Ci(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d)/d)-a*f^2/((f*x+e)*d+c*f-d*e)/d)","A"
100,1,177,115,0.026000," ","int((a+a*sin(f*x+e))/(d*x+c)^3,x)","\frac{a \,f^{3} \left(-\frac{\sin \left(f x +e \right)}{2 \left(\left(f x +e \right) d +c f -d e \right)^{2} d}+\frac{-\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}}{2 d}\right)-\frac{a \,f^{3}}{2 \left(\left(f x +e \right) d +c f -d e \right)^{2} d}}{f}"," ",0,"1/f*(a*f^3*(-1/2*sin(f*x+e)/((f*x+e)*d+c*f-d*e)^2/d+1/2*(-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)/d)-1/2*a*f^3/((f*x+e)*d+c*f-d*e)^2/d)","A"
101,1,1135,223,0.049000," ","int((d*x+c)^3*(a+a*sin(f*x+e))^2,x)","\frac{\frac{a^{2} d^{3} \left(\left(f x +e \right)^{3} \left(-\frac{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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{2 a^{2} d^{3} \left(-\left(f x +e \right)^{3} \cos \left(f x +e \right)+3 \left(f x +e \right)^{2} \sin \left(f x +e \right)-6 \sin \left(f x +e \right)+6 \left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{3}}+a^{2} c^{3} \left(f x +e \right)-2 a^{2} c^{3} \cos \left(f x +e \right)+a^{2} c^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{6 a^{2} d^{3} e \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \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^{3} \left(f x +e \right)}{f^{3}}+\frac{6 a^{2} c \,d^{2} \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}+\frac{6 a^{2} c^{2} d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}+\frac{2 a^{2} d^{3} e^{3} \cos \left(f x +e \right)}{f^{3}}+\frac{6 a^{2} d^{3} e^{2} \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{3}}-\frac{a^{2} d^{3} e^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f^{3}}+\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{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{\sin \left(f x +e \right) \cos \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} c \,d^{2} \left(\left(f x +e \right)^{2} \left(-\frac{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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{3 a^{2} d^{3} e \left(\left(f x +e \right)^{2} \left(-\frac{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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} \cos \left(f x +e \right)}{f^{2}}+\frac{6 a^{2} c^{2} d e \cos \left(f x +e \right)}{f}-\frac{3 a^{2} c \,d^{2} e \left(f x +e \right)^{2}}{f^{2}}+\frac{3 a^{2} c \,d^{2} e^{2} \left(f x +e \right)}{f^{2}}-\frac{12 a^{2} c \,d^{2} e \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}-\frac{3 a^{2} c^{2} d e \left(f x +e \right)}{f}-\frac{3 a^{2} c^{2} d e \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}+\frac{3 a^{2} c \,d^{2} e^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f^{2}}-\frac{6 a^{2} c \,d^{2} e \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \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}}}{f}"," ",0,"1/f*(a^2/f^3*d^3*((f*x+e)^3*(-1/2*sin(f*x+e)*cos(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*sin(f*x+e)*cos(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)+1/4*a^2/f^3*d^3*(f*x+e)^4+2*a^2/f^3*d^3*(-(f*x+e)^3*cos(f*x+e)+3*(f*x+e)^2*sin(f*x+e)-6*sin(f*x+e)+6*(f*x+e)*cos(f*x+e))+a^2*c^3*(f*x+e)-2*a^2*c^3*cos(f*x+e)+a^2*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+3*a^2/f^3*d^3*e^2*((f*x+e)*(-1/2*sin(f*x+e)*cos(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*cos(f*x+e)+2*cos(f*x+e)+2*(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^3*(f*x+e)+3*a^2/f^2*c*d^2*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/2*(f*x+e)*cos(f*x+e)^2+1/4*sin(f*x+e)*cos(f*x+e)+1/4*f*x+1/4*e-1/3*(f*x+e)^3)+6*a^2/f^2*c*d^2*(-(f*x+e)^2*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))+6*a^2/f*c^2*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))+2*a^2/f^3*d^3*e^3*cos(f*x+e)+3*a^2/f*c^2*d*((f*x+e)*(-1/2*sin(f*x+e)*cos(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^2*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-3*a^2/f^3*d^3*e*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/2*(f*x+e)*cos(f*x+e)^2+1/4*sin(f*x+e)*cos(f*x+e)+1/4*f*x+1/4*e-1/3*(f*x+e)^3)-a^2/f^3*d^3*e^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*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-a^2/f^3*d^3*e*(f*x+e)^3-6*a^2/f^2*c*d^2*e^2*cos(f*x+e)+6*a^2/f*c^2*d*e*cos(f*x+e)-3*a^2/f^2*c*d^2*e*(f*x+e)^2+3*a^2/f^2*c*d^2*e^2*(f*x+e)-6*a^2/f^2*c*d^2*e*((f*x+e)*(-1/2*sin(f*x+e)*cos(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*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-3*a^2/f*c^2*d*e*(f*x+e)-3*a^2/f*c^2*d*e*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+3*a^2/f^2*c*d^2*e^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","B"
102,1,567,158,0.052000," ","int((d*x+c)^2*(a+a*sin(f*x+e))^2,x)","\frac{\frac{a^{2} d^{2} \left(\left(f x +e \right)^{2} \left(-\frac{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{2 a^{2} c d e \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}+\frac{a^{2} d^{2} e^{2} \left(-\frac{\sin \left(f x +e \right) \cos \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} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}+\frac{4 a^{2} c d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}-\frac{4 a^{2} d^{2} e \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}-2 a^{2} c^{2} \cos \left(f x +e \right)+\frac{4 a^{2} c d e \cos \left(f x +e \right)}{f}-\frac{2 a^{2} d^{2} e^{2} \cos \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*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/2*(f*x+e)*cos(f*x+e)^2+1/4*sin(f*x+e)*cos(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*sin(f*x+e)*cos(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*sin(f*x+e)*cos(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*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a^2/f*c*d*e*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^2/f^2*d^2*e^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2*a^2/f^2*d^2*(-(f*x+e)^2*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))+4*a^2/f*c*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-4*a^2/f^2*d^2*e*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-2*a^2*c^2*cos(f*x+e)+4*a^2/f*c*d*e*cos(f*x+e)-2*a^2/f^2*d^2*e^2*cos(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"
103,1,219,108,0.045000," ","int((d*x+c)*(a+a*sin(f*x+e))^2,x)","\frac{\frac{a^{2} d \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{a^{2} d e \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}+\frac{2 a^{2} d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}-2 a^{2} c \cos \left(f x +e \right)+\frac{2 a^{2} d e \cos \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*sin(f*x+e)*cos(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*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^2/f*d*e*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2*a^2/f*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-2*a^2*c*cos(f*x+e)+2*a^2/f*d*e*cos(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"
104,1,192,141,0.051000," ","int((a+a*sin(f*x+e))^2/(d*x+c),x)","\frac{3 a^{2} \ln \left(\left(f x +e \right) d +c f -d e \right)}{2 d}-\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{2 a^{2} \Si \left(f x +e +\frac{c f -d e}{d}\right) \cos \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) \sin \left(\frac{c f -d e}{d}\right)}{d}"," ",0,"3/2*a^2*ln((f*x+e)*d+c*f-d*e)/d-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+2*a^2*Si(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d-2*a^2*Ci(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d","A"
105,1,274,159,0.054000," ","int((a+a*sin(f*x+e))^2/(d*x+c)^2,x)","\frac{-\frac{3 a^{2} f^{2}}{2 \left(\left(f x +e \right) d +c f -d e \right) d}-\frac{a^{2} f^{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}+2 a^{2} f^{2} \left(-\frac{\sin \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) \sin \left(\frac{c f -d e}{d}\right)}{d}+\frac{\Ci \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}}{d}\right)}{f}"," ",0,"1/f*(-3/2*a^2*f^2/((f*x+e)*d+c*f-d*e)/d-1/4*a^2*f^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)+2*a^2*f^2*(-sin(f*x+e)/((f*x+e)*d+c*f-d*e)/d+(Si(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d+Ci(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d)/d))","A"
106,1,347,207,0.053000," ","int((a+a*sin(f*x+e))^2/(d*x+c)^3,x)","\frac{-\frac{3 a^{2} f^{3}}{4 \left(\left(f x +e \right) d +c f -d e \right)^{2} d}-\frac{a^{2} f^{3} \left(-\frac{\cos \left(2 f x +2 e \right)}{\left(\left(f x +e \right) d +c f -d e \right)^{2} d}-\frac{-\frac{2 \sin \left(2 f x +2 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\frac{4 \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)}{d}+\frac{4 \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)}{d}}{d}}{d}\right)}{4}+2 a^{2} f^{3} \left(-\frac{\sin \left(f x +e \right)}{2 \left(\left(f x +e \right) d +c f -d e \right)^{2} d}+\frac{-\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}}{2 d}\right)}{f}"," ",0,"1/f*(-3/4*a^2*f^3/((f*x+e)*d+c*f-d*e)^2/d-1/4*a^2*f^3*(-cos(2*f*x+2*e)/((f*x+e)*d+c*f-d*e)^2/d-(-2*sin(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)*sin(2*(c*f-d*e)/d)/d+2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d)/d)/d)+2*a^2*f^3*(-1/2*sin(f*x+e)/((f*x+e)*d+c*f-d*e)^2/d+1/2*(-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)/d))","A"
107,1,484,131,0.199000," ","int((d*x+c)^3/(a+a*sin(f*x+e)),x)","-\frac{2 \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)}+i\right)}+\frac{6 d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}+i\right)}{a \,f^{4}}+\frac{12 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{4}}+\frac{12 c \,d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}-\frac{6 \ln \left({\mathrm e}^{i \left(f x +e \right)}\right) c^{2} d}{a \,f^{2}}-\frac{12 c \,d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}+i\right)}{a \,f^{3}}+\frac{6 d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{a \,f^{2}}-\frac{6 d^{3} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e^{2}}{a \,f^{4}}+\frac{6 \ln \left({\mathrm e}^{i \left(f x +e \right)}+i\right) c^{2} d}{a \,f^{2}}+\frac{4 i d^{3} e^{3}}{a \,f^{4}}-\frac{12 i c \,d^{2} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}-\frac{6 d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{4}}-\frac{6 i c \,d^{2} e^{2}}{a \,f^{3}}-\frac{12 i d^{3} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{3}}+\frac{6 i d^{3} e^{2} x}{a \,f^{3}}-\frac{6 i c \,d^{2} x^{2}}{a f}-\frac{2 i d^{3} x^{3}}{a f}-\frac{12 i c \,d^{2} e x}{a \,f^{2}}+\frac{12 c \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{2}}+\frac{12 c \,d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{a \,f^{3}}"," ",0,"-2*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/f/a/(exp(I*(f*x+e))+I)+6/a/f^4*d^3*e^2*ln(exp(I*(f*x+e))+I)+12*d^3*polylog(3,I*exp(I*(f*x+e)))/a/f^4+12/a/f^3*c*d^2*e*ln(exp(I*(f*x+e)))-6/a/f^2*ln(exp(I*(f*x+e)))*c^2*d-12/a/f^3*c*d^2*e*ln(exp(I*(f*x+e))+I)+6/a/f^2*d^3*ln(1-I*exp(I*(f*x+e)))*x^2-6/a/f^4*d^3*ln(1-I*exp(I*(f*x+e)))*e^2+6/a/f^2*ln(exp(I*(f*x+e))+I)*c^2*d+4*I/a/f^4*d^3*e^3-6*I/a/f^3*c*d^2*e^2-6/a/f^4*d^3*e^2*ln(exp(I*(f*x+e)))-12*I/a/f^3*d^3*polylog(2,I*exp(I*(f*x+e)))*x+6*I/a/f^3*d^3*e^2*x-6*I/a/f*c*d^2*x^2-2*I/a/f*d^3*x^3-12*I/a/f^2*c*d^2*e*x-12*I/a/f^3*c*d^2*polylog(2,I*exp(I*(f*x+e)))+12/a/f^2*c*d^2*ln(1-I*exp(I*(f*x+e)))*x+12/a/f^3*c*d^2*ln(1-I*exp(I*(f*x+e)))*e","B"
108,1,254,99,0.107000," ","int((d*x+c)^2/(a+a*sin(f*x+e)),x)","-\frac{2 \left(d^{2} x^{2}+2 c d x +c^{2}\right)}{f a \left({\mathrm e}^{i \left(f x +e \right)}+i\right)}+\frac{4 \ln \left({\mathrm e}^{i \left(f x +e \right)}+i\right) c d}{a \,f^{2}}-\frac{4 \ln \left({\mathrm e}^{i \left(f x +e \right)}\right) c d}{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-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{2}}+\frac{4 d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{a \,f^{3}}-\frac{4 i d^{2} \polylog \left(2, i {\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)}+i\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*(d^2*x^2+2*c*d*x+c^2)/f/a/(exp(I*(f*x+e))+I)+4/a/f^2*ln(exp(I*(f*x+e))+I)*c*d-4/a/f^2*ln(exp(I*(f*x+e)))*c*d-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(1-I*exp(I*(f*x+e)))*x+4/a/f^3*d^2*ln(1-I*exp(I*(f*x+e)))*e-4*I*d^2*polylog(2,I*exp(I*(f*x+e)))/a/f^3-4/a/f^3*d^2*e*ln(exp(I*(f*x+e))+I)+4/a/f^3*d^2*e*ln(exp(I*(f*x+e)))","B"
109,1,122,48,0.081000," ","int((d*x+c)/(a+a*sin(f*x+e)),x)","-\frac{2 c}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{d x \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right) f}-\frac{d x}{a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right) f}+\frac{2 d \ln \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}{a \,f^{2}}-\frac{d \ln \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a \,f^{2}}"," ",0,"-2/a*c/f/(tan(1/2*f*x+1/2*e)+1)+1/a*d/(tan(1/2*f*x+1/2*e)+1)*x/f*tan(1/2*f*x+1/2*e)-1/a*d/(tan(1/2*f*x+1/2*e)+1)*x/f+2/a*d/f^2*ln(tan(1/2*f*x+1/2*e)+1)-1/a*d/f^2*ln(1+tan(1/2*f*x+1/2*e)^2)","B"
110,0,0,22,0.217000," ","int(1/(d*x+c)/(a+a*sin(f*x+e)),x)","\int \frac{1}{\left(d x +c \right) \left(a +a \sin \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)/(a+a*sin(f*x+e)),x)","F"
111,0,0,22,0.418000," ","int(1/(d*x+c)^2/(a+a*sin(f*x+e)),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +a \sin \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)^2/(a+a*sin(f*x+e)),x)","F"
112,1,807,254,1.231000," ","int((d*x+c)^3/(a+a*sin(f*x+e))^2,x)","-\frac{4 i \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right) d^{3} x}{a^{2} f^{3}}+\frac{2 \ln \left({\mathrm e}^{i \left(f x +e \right)}+i\right) c^{2} d}{a^{2} f^{2}}-\frac{2 \ln \left({\mathrm e}^{i \left(f x +e \right)}\right) c^{2} d}{a^{2} f^{2}}-\frac{2 \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) d^{3} e^{2}}{a^{2} f^{4}}+\frac{2 \ln \left({\mathrm e}^{i \left(f x +e \right)}+i\right) d^{3} e^{2}}{a^{2} f^{4}}-\frac{2 \ln \left({\mathrm e}^{i \left(f x +e \right)}\right) d^{3} e^{2}}{a^{2} f^{4}}-\frac{2 i c \,d^{2} e^{2}}{a^{2} f^{3}}-\frac{4 i c \,d^{2} \polylog \left(2, i {\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{3}}+\frac{4 i d^{3} e^{3}}{3 a^{2} f^{4}}-\frac{4 \ln \left({\mathrm e}^{i \left(f x +e \right)}+i\right) c \,d^{2} e}{a^{2} f^{3}}+\frac{4 \ln \left({\mathrm e}^{i \left(f x +e \right)}\right) c \,d^{2} e}{a^{2} f^{3}}+\frac{4 \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) c \,d^{2} x}{a^{2} f^{2}}+\frac{4 \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) c \,d^{2} e}{a^{2} f^{3}}+\frac{2 i d^{3} e^{2} x}{a^{2} f^{3}}-\frac{2 i \left(i d^{3} f^{2} x^{3}+3 d^{3} f^{2} x^{3} {\mathrm e}^{i \left(f x +e \right)}+3 i c \,d^{2} f^{2} x^{2}+6 i d^{3} x +9 c \,d^{2} f^{2} x^{2} {\mathrm e}^{i \left(f x +e \right)}+3 f \,d^{3} x^{2} {\mathrm e}^{2 i \left(f x +e \right)}+6 i c \,d^{2}-6 i c \,d^{2} {\mathrm e}^{2 i \left(f x +e \right)}+i c^{3} f^{2}+9 c^{2} d \,f^{2} x \,{\mathrm e}^{i \left(f x +e \right)}+6 f c \,d^{2} x \,{\mathrm e}^{2 i \left(f x +e \right)}+3 i f \,d^{3} x^{2} {\mathrm e}^{i \left(f x +e \right)}+3 i f \,c^{2} d \,{\mathrm e}^{i \left(f x +e \right)}+3 i c^{2} d \,f^{2} x +3 c^{3} f^{2} {\mathrm e}^{i \left(f x +e \right)}+3 f \,c^{2} d \,{\mathrm e}^{2 i \left(f x +e \right)}-6 i d^{3} x \,{\mathrm e}^{2 i \left(f x +e \right)}+12 d^{3} x \,{\mathrm e}^{i \left(f x +e \right)}+6 i f c \,d^{2} x \,{\mathrm e}^{i \left(f x +e \right)}+12 c \,d^{2} {\mathrm e}^{i \left(f x +e \right)}\right)}{3 \left({\mathrm e}^{i \left(f x +e \right)}+i\right)^{3} f^{3} a^{2}}-\frac{2 i d^{3} x^{3}}{3 a^{2} f}-\frac{2 i c \,d^{2} x^{2}}{a^{2} f}-\frac{4 i c \,d^{2} e x}{a^{2} f^{2}}+\frac{2 \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) d^{3} x^{2}}{a^{2} f^{2}}+\frac{4 \ln \left({\mathrm e}^{i \left(f x +e \right)}+i\right) d^{3}}{a^{2} f^{4}}-\frac{4 \ln \left({\mathrm e}^{i \left(f x +e \right)}\right) d^{3}}{a^{2} f^{4}}+\frac{4 d^{3} \polylog \left(3, i {\mathrm e}^{i \left(f x +e \right)}\right)}{a^{2} f^{4}}"," ",0,"-2*I/a^2/f^3*c*d^2*e^2+2/a^2/f^2*ln(exp(I*(f*x+e))+I)*c^2*d-2/a^2/f^2*ln(exp(I*(f*x+e)))*c^2*d-2/a^2/f^4*ln(1-I*exp(I*(f*x+e)))*d^3*e^2+2/a^2/f^4*ln(exp(I*(f*x+e))+I)*d^3*e^2-2/a^2/f^4*ln(exp(I*(f*x+e)))*d^3*e^2-4*I/a^2/f^3*c*d^2*polylog(2,I*exp(I*(f*x+e)))+4/3*I/a^2/f^4*d^3*e^3+2*I/a^2/f^3*d^3*e^2*x-4/a^2/f^3*ln(exp(I*(f*x+e))+I)*c*d^2*e+4/a^2/f^3*ln(exp(I*(f*x+e)))*c*d^2*e+4/a^2/f^2*ln(1-I*exp(I*(f*x+e)))*c*d^2*x+4/a^2/f^3*ln(1-I*exp(I*(f*x+e)))*c*d^2*e-2/3*I*(I*d^3*f^2*x^3+3*d^3*f^2*x^3*exp(I*(f*x+e))+3*I*c*d^2*f^2*x^2+6*I*d^3*x+9*c*d^2*f^2*x^2*exp(I*(f*x+e))+3*f*d^3*x^2*exp(2*I*(f*x+e))+6*I*c*d^2-6*I*c*d^2*exp(2*I*(f*x+e))+I*c^3*f^2+9*c^2*d*f^2*x*exp(I*(f*x+e))+6*f*c*d^2*x*exp(2*I*(f*x+e))+3*I*f*d^3*x^2*exp(I*(f*x+e))+3*I*f*c^2*d*exp(I*(f*x+e))+3*I*c^2*d*f^2*x+3*c^3*f^2*exp(I*(f*x+e))+3*f*c^2*d*exp(2*I*(f*x+e))-6*I*d^3*x*exp(2*I*(f*x+e))+12*d^3*x*exp(I*(f*x+e))+6*I*f*c*d^2*x*exp(I*(f*x+e))+12*c*d^2*exp(I*(f*x+e)))/(exp(I*(f*x+e))+I)^3/f^3/a^2-2/3*I/a^2/f*d^3*x^3-2*I/a^2/f*c*d^2*x^2-4*I/a^2/f^2*c*d^2*e*x-4*I/a^2/f^3*polylog(2,I*exp(I*(f*x+e)))*d^3*x+2/a^2/f^2*ln(1-I*exp(I*(f*x+e)))*d^3*x^2+4/a^2/f^4*ln(exp(I*(f*x+e))+I)*d^3-4/a^2/f^4*ln(exp(I*(f*x+e)))*d^3+4*d^3*polylog(3,I*exp(I*(f*x+e)))/a^2/f^4","B"
113,1,421,191,0.952000," ","int((d*x+c)^2/(a+a*sin(f*x+e))^2,x)","-\frac{2 i \left(i d^{2} f^{2} x^{2}+3 d^{2} f^{2} x^{2} {\mathrm e}^{i \left(f x +e \right)}+2 i c d \,f^{2} x +2 i f \,d^{2} x \,{\mathrm e}^{i \left(f x +e \right)}+6 c d \,f^{2} x \,{\mathrm e}^{i \left(f x +e \right)}+2 f \,d^{2} x \,{\mathrm e}^{2 i \left(f x +e \right)}+i c^{2} f^{2}+2 i f c d \,{\mathrm e}^{i \left(f x +e \right)}-2 i d^{2} {\mathrm e}^{2 i \left(f x +e \right)}+3 c^{2} f^{2} {\mathrm e}^{i \left(f x +e \right)}+2 f c d \,{\mathrm e}^{2 i \left(f x +e \right)}+2 i d^{2}+4 d^{2} {\mathrm e}^{i \left(f x +e \right)}\right)}{3 \left({\mathrm e}^{i \left(f x +e \right)}+i\right)^{3} f^{3} a^{2}}+\frac{4 \ln \left({\mathrm e}^{i \left(f x +e \right)}+i\right) c d}{3 a^{2} f^{2}}-\frac{4 \ln \left({\mathrm e}^{i \left(f x +e \right)}\right) c d}{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(1-i {\mathrm e}^{i \left(f x +e \right)}\right) x}{3 a^{2} f^{2}}+\frac{4 d^{2} \ln \left(1-i {\mathrm e}^{i \left(f x +e \right)}\right) e}{3 a^{2} f^{3}}-\frac{4 i d^{2} \polylog \left(2, i {\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)}+i\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*(I*d^2*f^2*x^2+3*d^2*f^2*x^2*exp(I*(f*x+e))+2*I*c*d*f^2*x+2*I*f*d^2*x*exp(I*(f*x+e))+6*c*d*f^2*x*exp(I*(f*x+e))+2*f*d^2*x*exp(2*I*(f*x+e))+I*c^2*f^2+2*I*f*c*d*exp(I*(f*x+e))-2*I*d^2*exp(2*I*(f*x+e))+3*c^2*f^2*exp(I*(f*x+e))+2*f*c*d*exp(2*I*(f*x+e))+2*I*d^2+4*d^2*exp(I*(f*x+e)))/(exp(I*(f*x+e))+I)^3/f^3/a^2+4/3/a^2/f^2*ln(exp(I*(f*x+e))+I)*c*d-4/3/a^2/f^2*ln(exp(I*(f*x+e)))*c*d-2/3*I/a^2/f*d^2*x^2-4/3*I/a^2/f^2*d^2*e*x-2/3*I/a^2/f^3*d^2*e^2+4/3/a^2/f^2*d^2*ln(1-I*exp(I*(f*x+e)))*x+4/3/a^2/f^3*d^2*ln(1-I*exp(I*(f*x+e)))*e-4/3*I*d^2*polylog(2,I*exp(I*(f*x+e)))/a^2/f^3-4/3/a^2/f^3*d^2*e*ln(exp(I*(f*x+e))+I)+4/3/a^2/f^3*d^2*e*ln(exp(I*(f*x+e)))","B"
114,1,233,110,0.392000," ","int((d*x+c)/(a+a*sin(f*x+e))^2,x)","\frac{2 c}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 c}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 c}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{2 x d}{3 a^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3} f}+\frac{2 d \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{3 a^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3} f^{2}}+\frac{2 d \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{3 a^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3} f^{2}}+\frac{2 x d \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{3 a^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3} f}+\frac{2 d \ln \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}{3 a^{2} f^{2}}-\frac{d \ln \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{3 a^{2} f^{2}}"," ",0,"2/a^2*c/f/(tan(1/2*f*x+1/2*e)+1)^2-4/3/a^2*c/f/(tan(1/2*f*x+1/2*e)+1)^3-2/a^2*c/f/(tan(1/2*f*x+1/2*e)+1)-2/3/a^2/(tan(1/2*f*x+1/2*e)+1)^3/f*x*d+2/3/a^2/(tan(1/2*f*x+1/2*e)+1)^3*d/f^2*tan(1/2*f*x+1/2*e)+2/3/a^2/(tan(1/2*f*x+1/2*e)+1)^3*d/f^2*tan(1/2*f*x+1/2*e)^2+2/3/a^2/(tan(1/2*f*x+1/2*e)+1)^3/f*x*d*tan(1/2*f*x+1/2*e)^3+2/3/a^2*d/f^2*ln(tan(1/2*f*x+1/2*e)+1)-1/3/a^2*d/f^2*ln(1+tan(1/2*f*x+1/2*e)^2)","B"
115,0,0,22,4.727000," ","int(1/(d*x+c)/(a+a*sin(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right) \left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)/(a+a*sin(f*x+e))^2,x)","F"
116,0,0,22,7.202000," ","int(1/(d*x+c)^2/(a+a*sin(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)^2/(a+a*sin(f*x+e))^2,x)","F"
117,1,484,130,0.202000," ","int((d*x+c)^3/(a-a*sin(f*x+e)),x)","\frac{2 d^{3} x^{3}+6 c \,d^{2} x^{2}+6 c^{2} d x +2 c^{3}}{f a \left({\mathrm e}^{i \left(f x +e \right)}-i\right)}+\frac{12 c \,d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}-\frac{6 \ln \left({\mathrm e}^{i \left(f x +e \right)}\right) c^{2} d}{a \,f^{2}}-\frac{2 i d^{3} x^{3}}{a f}+\frac{4 i d^{3} e^{3}}{a \,f^{4}}-\frac{6 i c \,d^{2} x^{2}}{a f}-\frac{12 i c \,d^{2} e x}{a \,f^{2}}-\frac{12 i d^{3} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{3}}-\frac{12 c \,d^{2} e \ln \left({\mathrm e}^{i \left(f x +e \right)}-i\right)}{a \,f^{3}}-\frac{6 d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{4}}+\frac{6 \ln \left({\mathrm e}^{i \left(f x +e \right)}-i\right) c^{2} d}{a \,f^{2}}+\frac{6 d^{3} e^{2} \ln \left({\mathrm e}^{i \left(f x +e \right)}-i\right)}{a \,f^{4}}+\frac{12 d^{3} \polylog \left(3, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{4}}+\frac{6 d^{3} \ln \left(1+i {\mathrm e}^{i \left(f x +e \right)}\right) x^{2}}{a \,f^{2}}-\frac{6 d^{3} \ln \left(1+i {\mathrm e}^{i \left(f x +e \right)}\right) e^{2}}{a \,f^{4}}+\frac{6 i d^{3} e^{2} x}{a \,f^{3}}-\frac{12 i c \,d^{2} \polylog \left(2, -i {\mathrm e}^{i \left(f x +e \right)}\right)}{a \,f^{3}}-\frac{6 i c \,d^{2} e^{2}}{a \,f^{3}}+\frac{12 c \,d^{2} \ln \left(1+i {\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{2}}+\frac{12 c \,d^{2} \ln \left(1+i {\mathrm e}^{i \left(f x +e \right)}\right) e}{a \,f^{3}}"," ",0,"2*(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3)/f/a/(exp(I*(f*x+e))-I)+12/a/f^3*c*d^2*e*ln(exp(I*(f*x+e)))-6/a/f^2*ln(exp(I*(f*x+e)))*c^2*d-2*I/a/f*d^3*x^3-12*I/a/f^3*d^3*polylog(2,-I*exp(I*(f*x+e)))*x+4*I/a/f^4*d^3*e^3-6*I/a/f*c*d^2*x^2-12*I/a/f^2*c*d^2*e*x-12/a/f^3*c*d^2*e*ln(exp(I*(f*x+e))-I)-6/a/f^4*d^3*e^2*ln(exp(I*(f*x+e)))+6/a/f^2*ln(exp(I*(f*x+e))-I)*c^2*d+6/a/f^4*d^3*e^2*ln(exp(I*(f*x+e))-I)+12*d^3*polylog(3,-I*exp(I*(f*x+e)))/a/f^4+6/a/f^2*d^3*ln(1+I*exp(I*(f*x+e)))*x^2-6/a/f^4*d^3*ln(1+I*exp(I*(f*x+e)))*e^2+6*I/a/f^3*d^3*e^2*x-12*I/a/f^3*c*d^2*polylog(2,-I*exp(I*(f*x+e)))-6*I/a/f^3*c*d^2*e^2+12/a/f^2*c*d^2*ln(1+I*exp(I*(f*x+e)))*x+12/a/f^3*c*d^2*ln(1+I*exp(I*(f*x+e)))*e","B"
118,1,254,98,0.143000," ","int((d*x+c)^2/(a-a*sin(f*x+e)),x)","\frac{2 d^{2} x^{2}+4 c d x +2 c^{2}}{f a \left({\mathrm e}^{i \left(f x +e \right)}-i\right)}+\frac{4 \ln \left({\mathrm e}^{i \left(f x +e \right)}-i\right) c d}{a \,f^{2}}-\frac{4 \ln \left({\mathrm e}^{i \left(f x +e \right)}\right) c d}{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+i {\mathrm e}^{i \left(f x +e \right)}\right) x}{a \,f^{2}}+\frac{4 d^{2} \ln \left(1+i {\mathrm e}^{i \left(f x +e \right)}\right) e}{a \,f^{3}}-\frac{4 i d^{2} \polylog \left(2, -i {\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)}-i\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*(d^2*x^2+2*c*d*x+c^2)/f/a/(exp(I*(f*x+e))-I)+4/a/f^2*ln(exp(I*(f*x+e))-I)*c*d-4/a/f^2*ln(exp(I*(f*x+e)))*c*d-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(1+I*exp(I*(f*x+e)))*x+4/a/f^3*d^2*ln(1+I*exp(I*(f*x+e)))*e-4*I*d^2*polylog(2,-I*exp(I*(f*x+e)))/a/f^3-4/a/f^3*d^2*e*ln(exp(I*(f*x+e))-I)+4/a/f^3*d^2*e*ln(exp(I*(f*x+e)))","B"
119,1,123,47,0.116000," ","int((d*x+c)/(a-a*sin(f*x+e)),x)","-\frac{2 c}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{d x}{a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right) f}-\frac{d x \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right) f}-\frac{d \ln \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a \,f^{2}}+\frac{2 d \ln \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}{a \,f^{2}}"," ",0,"-2/a*c/f/(tan(1/2*f*x+1/2*e)-1)-1/a*d/(tan(1/2*f*x+1/2*e)-1)*x/f-1/a*d/(tan(1/2*f*x+1/2*e)-1)*x/f*tan(1/2*f*x+1/2*e)-1/a*d/f^2*ln(1+tan(1/2*f*x+1/2*e)^2)+2/a*d/f^2*ln(tan(1/2*f*x+1/2*e)-1)","B"
120,0,0,23,0.222000," ","int(1/(d*x+c)/(a-a*sin(f*x+e)),x)","\int \frac{1}{\left(d x +c \right) \left(a -a \sin \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)/(a-a*sin(f*x+e)),x)","F"
121,0,0,23,0.427000," ","int(1/(d*x+c)^2/(a-a*sin(f*x+e)),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a -a \sin \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)^2/(a-a*sin(f*x+e)),x)","F"
122,1,145,100,0.139000," ","int(x^3*(a+a*sin(d*x+c))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{-a \left(-2-2 \sin \left(d x +c \right)\right)}\, \left(-i x^{3} d^{3}+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)}-6 d^{2} x^{2}+24 i d x -24 d x \,{\mathrm e}^{i \left(d x +c \right)}-48 i {\mathrm e}^{i \left(d x +c \right)}+48\right) \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{\left({\mathrm e}^{2 i \left(d x +c \right)}-1+2 i {\mathrm e}^{i \left(d x +c \right)}\right) d^{4}}"," ",0,"-I*2^(1/2)*(-a*(-2-2*sin(d*x+c)))^(1/2)/(exp(2*I*(d*x+c))-1+2*I*exp(I*(d*x+c)))*(-I*x^3*d^3+d^3*x^3*exp(I*(d*x+c))+6*I*d^2*x^2*exp(I*(d*x+c))-6*d^2*x^2+24*I*d*x-24*d*x*exp(I*(d*x+c))-48*I*exp(I*(d*x+c))+48)*(exp(I*(d*x+c))+I)/d^4","C"
123,1,119,80,0.069000," ","int(x^2*(a+a*sin(d*x+c))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{-a \left(-2-2 \sin \left(d x +c \right)\right)}\, \left(-i d^{2} x^{2}+d^{2} x^{2} {\mathrm e}^{i \left(d x +c \right)}+4 i d x \,{\mathrm e}^{i \left(d x +c \right)}-4 d x +8 i-8 \,{\mathrm e}^{i \left(d x +c \right)}\right) \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{\left({\mathrm e}^{2 i \left(d x +c \right)}-1+2 i {\mathrm e}^{i \left(d x +c \right)}\right) d^{3}}"," ",0,"-I*2^(1/2)*(-a*(-2-2*sin(d*x+c)))^(1/2)/(exp(2*I*(d*x+c))-1+2*I*exp(I*(d*x+c)))*(-I*d^2*x^2+d^2*x^2*exp(I*(d*x+c))+4*I*d*x*exp(I*(d*x+c))-4*d*x+8*I-8*exp(I*(d*x+c)))*(exp(I*(d*x+c))+I)/d^3","C"
124,1,93,48,0.062000," ","int(x*(a+a*sin(d*x+c))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{-a \left(-2-2 \sin \left(d x +c \right)\right)}\, \left(-i d x +d x \,{\mathrm e}^{i \left(d x +c \right)}+2 i {\mathrm e}^{i \left(d x +c \right)}-2\right) \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{\left({\mathrm e}^{2 i \left(d x +c \right)}-1+2 i {\mathrm e}^{i \left(d x +c \right)}\right) d^{2}}"," ",0,"-I*2^(1/2)*(-a*(-2-2*sin(d*x+c)))^(1/2)/(exp(2*I*(d*x+c))-1+2*I*exp(I*(d*x+c)))*(-I*d*x+d*x*exp(I*(d*x+c))+2*I*exp(I*(d*x+c))-2)*(exp(I*(d*x+c))+I)/d^2","C"
125,0,0,77,0.332000," ","int((a+a*sin(d*x+c))^(1/2)/x,x)","\int \frac{\sqrt{a +a \sin \left(d x +c \right)}}{x}\, dx"," ",0,"int((a+a*sin(d*x+c))^(1/2)/x,x)","F"
126,0,0,98,0.068000," ","int((a+a*sin(d*x+c))^(1/2)/x^2,x)","\int \frac{\sqrt{a +a \sin \left(d x +c \right)}}{x^{2}}\, dx"," ",0,"int((a+a*sin(d*x+c))^(1/2)/x^2,x)","F"
127,0,0,132,0.065000," ","int((a+a*sin(d*x+c))^(1/2)/x^3,x)","\int \frac{\sqrt{a +a \sin \left(d x +c \right)}}{x^{3}}\, dx"," ",0,"int((a+a*sin(d*x+c))^(1/2)/x^3,x)","F"
128,0,0,259,0.080000," ","int(x^3*(a+a*sin(f*x+e))^(3/2),x)","\int x^{3} \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(x^3*(a+a*sin(f*x+e))^(3/2),x)","F"
129,0,0,205,0.046000," ","int(x^2*(a+a*sin(f*x+e))^(3/2),x)","\int x^{2} \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(x^2*(a+a*sin(f*x+e))^(3/2),x)","F"
130,0,0,125,0.045000," ","int(x*(a+a*sin(f*x+e))^(3/2),x)","\int x \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(x*(a+a*sin(f*x+e))^(3/2),x)","F"
131,0,0,161,0.046000," ","int((a+a*sin(f*x+e))^(3/2)/x,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int((a+a*sin(f*x+e))^(3/2)/x,x)","F"
132,0,0,197,0.046000," ","int((a+a*sin(f*x+e))^(3/2)/x^2,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(3/2)/x^2,x)","F"
133,0,0,248,0.047000," ","int((a+a*sin(f*x+e))^(3/2)/x^3,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(3/2)/x^3,x)","F"
134,0,0,329,0.238000," ","int(x^3/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{x^{3}}{\sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int(x^3/(a+a*sin(d*x+c))^(1/2),x)","F"
135,0,0,231,0.084000," ","int(x^2/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{x^{2}}{\sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int(x^2/(a+a*sin(d*x+c))^(1/2),x)","F"
136,0,0,137,0.077000," ","int(x/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{x}{\sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int(x/(a+a*sin(d*x+c))^(1/2),x)","F"
137,0,0,18,0.064000," ","int(1/x/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{1}{x \sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int(1/x/(a+a*sin(d*x+c))^(1/2),x)","F"
138,0,0,18,0.065000," ","int(1/x^2/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{1}{x^{2} \sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int(1/x^2/(a+a*sin(d*x+c))^(1/2),x)","F"
139,0,0,553,0.055000," ","int(x^3/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{x^{3}}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3/(a+a*sin(f*x+e))^(3/2),x)","F"
140,0,0,347,0.053000," ","int(x^2/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{x^{2}}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2/(a+a*sin(f*x+e))^(3/2),x)","F"
141,0,0,199,0.052000," ","int(x/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{x}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/(a+a*sin(f*x+e))^(3/2),x)","F"
142,0,0,18,0.054000," ","int(1/x/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{1}{x \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x/(a+a*sin(f*x+e))^(3/2),x)","F"
143,0,0,18,0.053000," ","int(1/x^2/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{1}{x^{2} \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x^2/(a+a*sin(f*x+e))^(3/2),x)","F"
144,0,0,18,0.110000," ","int((a+a*sin(d*x+c))^(1/3)/x,x)","\int \frac{\left(a +a \sin \left(d x +c \right)\right)^{\frac{1}{3}}}{x}\, dx"," ",0,"int((a+a*sin(d*x+c))^(1/3)/x,x)","F"
145,0,0,22,0.381000," ","int((d*x+c)^m*(a+a*sin(f*x+e))^n,x)","\int \left(d x +c \right)^{m} \left(a +a \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((d*x+c)^m*(a+a*sin(f*x+e))^n,x)","F"
146,0,0,419,0.426000," ","int((d*x+c)^m*(a+a*sin(f*x+e))^3,x)","\int \left(d x +c \right)^{m} \left(a +a \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*x+c)^m*(a+a*sin(f*x+e))^3,x)","F"
147,0,0,283,0.359000," ","int((d*x+c)^m*(a+a*sin(f*x+e))^2,x)","\int \left(d x +c \right)^{m} \left(a +a \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*x+c)^m*(a+a*sin(f*x+e))^2,x)","F"
148,0,0,138,0.133000," ","int((d*x+c)^m*(a+a*sin(f*x+e)),x)","\int \left(d x +c \right)^{m} \left(a +a \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*x+c)^m*(a+a*sin(f*x+e)),x)","F"
149,0,0,22,0.134000," ","int((d*x+c)^m/(a+a*sin(f*x+e)),x)","\int \frac{\left(d x +c \right)^{m}}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int((d*x+c)^m/(a+a*sin(f*x+e)),x)","F"
150,0,0,22,0.302000," ","int((d*x+c)^m/(a+a*sin(f*x+e))^2,x)","\int \frac{\left(d x +c \right)^{m}}{\left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*x+c)^m/(a+a*sin(f*x+e))^2,x)","F"
151,1,482,88,0.029000," ","int((d*x+c)^3*(a+b*sin(f*x+e)),x)","\frac{\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}}+\frac{b \,d^{3} \left(-\left(f x +e \right)^{3} \cos \left(f x +e \right)+3 \left(f x +e \right)^{2} \sin \left(f x +e \right)-6 \sin \left(f x +e \right)+6 \left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{3}}+\frac{3 b c \,d^{2} \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}-\frac{3 b \,d^{3} e \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{3}}+\frac{3 b \,c^{2} d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}-\frac{6 b c \,d^{2} e \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}+\frac{3 b \,d^{3} e^{2} \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{3}}-b \,c^{3} \cos \left(f x +e \right)+\frac{3 b \,c^{2} d e \cos \left(f x +e \right)}{f}-\frac{3 b c \,d^{2} e^{2} \cos \left(f x +e \right)}{f^{2}}+\frac{b \,d^{3} e^{3} \cos \left(f x +e \right)}{f^{3}}}{f}"," ",0,"1/f*(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)+1/f^3*b*d^3*(-(f*x+e)^3*cos(f*x+e)+3*(f*x+e)^2*sin(f*x+e)-6*sin(f*x+e)+6*(f*x+e)*cos(f*x+e))+3/f^2*b*c*d^2*(-(f*x+e)^2*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))-3/f^3*b*d^3*e*(-(f*x+e)^2*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))+3/f*b*c^2*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-6/f^2*b*c*d^2*e*(sin(f*x+e)-(f*x+e)*cos(f*x+e))+3/f^3*b*d^3*e^2*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-b*c^3*cos(f*x+e)+3/f*b*c^2*d*e*cos(f*x+e)-3/f^2*b*c*d^2*e^2*cos(f*x+e)+1/f^3*b*d^3*e^3*cos(f*x+e))","B"
152,1,241,66,0.019000," ","int((d*x+c)^2*(a+b*sin(f*x+e)),x)","\frac{\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}}+\frac{b \,d^{2} \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}+\frac{2 b c d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}-\frac{2 b \,d^{2} e \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}-b \,c^{2} \cos \left(f x +e \right)+\frac{2 b c d e \cos \left(f x +e \right)}{f}-\frac{b \,d^{2} e^{2} \cos \left(f x +e \right)}{f^{2}}}{f}"," ",0,"1/f*(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)+1/f^2*b*d^2*(-(f*x+e)^2*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))+2/f*b*c*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-2/f^2*b*d^2*e*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-b*c^2*cos(f*x+e)+2/f*b*c*d*e*cos(f*x+e)-1/f^2*b*d^2*e^2*cos(f*x+e))","B"
153,1,90,43,0.018000," ","int((d*x+c)*(a+b*sin(f*x+e)),x)","\frac{\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}+\frac{b d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}-c b \cos \left(f x +e \right)+\frac{b d e \cos \left(f x +e \right)}{f}}{f}"," ",0,"1/f*(1/2*a/f*d*(f*x+e)^2+a*c*(f*x+e)-a/f*d*e*(f*x+e)+1/f*b*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-c*b*cos(f*x+e)+1/f*b*d*e*cos(f*x+e))","B"
154,1,96,67,0.022000," ","int((a+b*sin(f*x+e))/(d*x+c),x)","\frac{a \ln \left(\left(f x +e \right) d +c f -d e \right)}{d}+\frac{b \Si \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}-\frac{b \Ci \left(f x +e +\frac{c f -d e}{d}\right) \sin \left(\frac{c f -d e}{d}\right)}{d}"," ",0,"a*ln((f*x+e)*d+c*f-d*e)/d+b*Si(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d-b*Ci(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d","A"
155,1,141,89,0.025000," ","int((a+b*sin(f*x+e))/(d*x+c)^2,x)","\frac{-\frac{a \,f^{2}}{\left(\left(f x +e \right) d +c f -d e \right) d}+f^{2} b \left(-\frac{\sin \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) \sin \left(\frac{c f -d e}{d}\right)}{d}+\frac{\Ci \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}}{d}\right)}{f}"," ",0,"1/f*(-a*f^2/((f*x+e)*d+c*f-d*e)/d+f^2*b*(-sin(f*x+e)/((f*x+e)*d+c*f-d*e)/d+(Si(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d+Ci(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d)/d))","A"
156,1,177,115,0.024000," ","int((a+b*sin(f*x+e))/(d*x+c)^3,x)","\frac{-\frac{a \,f^{3}}{2 \left(\left(f x +e \right) d +c f -d e \right)^{2} d}+f^{3} b \left(-\frac{\sin \left(f x +e \right)}{2 \left(\left(f x +e \right) d +c f -d e \right)^{2} d}+\frac{-\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}}{2 d}\right)}{f}"," ",0,"1/f*(-1/2*a*f^3/((f*x+e)*d+c*f-d*e)^2/d+f^3*b*(-1/2*sin(f*x+e)/((f*x+e)*d+c*f-d*e)^2/d+1/2*(-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)/d))","A"
157,1,1125,234,0.045000," ","int((d*x+c)^3*(a+b*sin(f*x+e))^2,x)","\frac{\frac{b^{2} d^{3} \left(\left(f x +e \right)^{3} \left(-\frac{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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}}-2 a b \,c^{3} \cos \left(f x +e \right)+\frac{a^{2} d^{3} \left(f x +e \right)^{4}}{4 f^{3}}-\frac{6 a b c \,d^{2} e^{2} \cos \left(f x +e \right)}{f^{2}}+\frac{6 a b \,c^{2} d e \cos \left(f x +e \right)}{f}-\frac{12 a b c \,d^{2} e \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}+a^{2} c^{3} \left(f x +e \right)+b^{2} c^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+\frac{3 a^{2} c^{2} d \left(f x +e \right)^{2}}{2 f}-\frac{a^{2} d^{3} e^{3} \left(f x +e \right)}{f^{3}}-\frac{3 b^{2} d^{3} e \left(\left(f x +e \right)^{2} \left(-\frac{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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{3 b^{2} d^{3} e^{2} \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \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 b^{2} c \,d^{2} \left(\left(f x +e \right)^{2} \left(-\frac{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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 b^{2} c^{2} d \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \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{b^{2} d^{3} e^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f^{3}}+\frac{2 a b \,d^{3} \left(-\left(f x +e \right)^{3} \cos \left(f x +e \right)+3 \left(f x +e \right)^{2} \sin \left(f x +e \right)-6 \sin \left(f x +e \right)+6 \left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{3}}+\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{a^{2} d^{3} e \left(f x +e \right)^{3}}{f^{3}}-\frac{3 a^{2} c \,d^{2} e \left(f x +e \right)^{2}}{f^{2}}+\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}-\frac{6 b^{2} c \,d^{2} e \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \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{6 a b \,d^{3} e^{2} \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{3}}+\frac{6 a b \,c^{2} d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}+\frac{2 a b \,d^{3} e^{3} \cos \left(f x +e \right)}{f^{3}}+\frac{3 b^{2} c \,d^{2} e^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f^{2}}-\frac{6 a b \,d^{3} e \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{3}}+\frac{6 a b c \,d^{2} \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}-\frac{3 b^{2} c^{2} d e \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}}{f}"," ",0,"1/f*(-2*a*b*c^3*cos(f*x+e)+1/f^3*b^2*d^3*((f*x+e)^3*(-1/2*sin(f*x+e)*cos(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*sin(f*x+e)*cos(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)+1/4*a^2/f^3*d^3*(f*x+e)^4-6/f^2*a*b*c*d^2*e^2*cos(f*x+e)+6/f*a*b*c^2*d*e*cos(f*x+e)-12/f^2*a*b*c*d^2*e*(sin(f*x+e)-(f*x+e)*cos(f*x+e))+a^2*c^3*(f*x+e)+b^2*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+3/2*a^2/f*c^2*d*(f*x+e)^2-a^2/f^3*d^3*e^3*(f*x+e)-1/f^3*b^2*d^3*e^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3/f^3*b^2*d^3*e*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/2*(f*x+e)*cos(f*x+e)^2+1/4*sin(f*x+e)*cos(f*x+e)+1/4*f*x+1/4*e-1/3*(f*x+e)^3)+3/f^3*b^2*d^3*e^2*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)+2/f^3*a*b*d^3*(-(f*x+e)^3*cos(f*x+e)+3*(f*x+e)^2*sin(f*x+e)-6*sin(f*x+e)+6*(f*x+e)*cos(f*x+e))+3/f^2*b^2*c*d^2*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/2*(f*x+e)*cos(f*x+e)^2+1/4*sin(f*x+e)*cos(f*x+e)+1/4*f*x+1/4*e-1/3*(f*x+e)^3)+3/f*b^2*c^2*d*((f*x+e)*(-1/2*sin(f*x+e)*cos(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^2*c*d^2*(f*x+e)^3+3/2*a^2/f^3*d^3*e^2*(f*x+e)^2-a^2/f^3*d^3*e*(f*x+e)^3-3*a^2/f^2*c*d^2*e*(f*x+e)^2+3*a^2/f^2*c*d^2*e^2*(f*x+e)-3*a^2/f*c^2*d*e*(f*x+e)+6/f^3*a*b*d^3*e^2*(sin(f*x+e)-(f*x+e)*cos(f*x+e))+6/f*a*b*c^2*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))+2/f^3*a*b*d^3*e^3*cos(f*x+e)+3/f^2*b^2*c*d^2*e^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-6/f^3*a*b*d^3*e*(-(f*x+e)^2*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))-6/f^2*b^2*c*d^2*e*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)+6/f^2*a*b*c*d^2*(-(f*x+e)^2*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))-3/f*b^2*c^2*d*e*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","B"
158,1,561,170,0.044000," ","int((d*x+c)^2*(a+b*sin(f*x+e))^2,x)","\frac{\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}}+\frac{2 a b \,d^{2} \left(-\left(f x +e \right)^{2} \cos \left(f x +e \right)+2 \cos \left(f x +e \right)+2 \left(f x +e \right) \sin \left(f x +e \right)\right)}{f^{2}}+\frac{4 a b c d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}-\frac{4 a b \,d^{2} e \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f^{2}}-2 a b \,c^{2} \cos \left(f x +e \right)+\frac{4 a b c d e \cos \left(f x +e \right)}{f}-\frac{2 a b \,d^{2} e^{2} \cos \left(f x +e \right)}{f^{2}}+\frac{b^{2} d^{2} \left(\left(f x +e \right)^{2} \left(-\frac{\sin \left(f x +e \right) \cos \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{\sin \left(f x +e \right) \cos \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 b^{2} c d \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \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 b^{2} d^{2} e \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \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}}+b^{2} c^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{2 b^{2} c d e \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}+\frac{b^{2} d^{2} e^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f^{2}}}{f}"," ",0,"1/f*(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)+2/f^2*a*b*d^2*(-(f*x+e)^2*cos(f*x+e)+2*cos(f*x+e)+2*(f*x+e)*sin(f*x+e))+4/f*a*b*c*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-4/f^2*a*b*d^2*e*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-2*a*b*c^2*cos(f*x+e)+4/f*a*b*c*d*e*cos(f*x+e)-2/f^2*a*b*d^2*e^2*cos(f*x+e)+1/f^2*b^2*d^2*((f*x+e)^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/2*(f*x+e)*cos(f*x+e)^2+1/4*sin(f*x+e)*cos(f*x+e)+1/4*f*x+1/4*e-1/3*(f*x+e)^3)+2/f*b^2*c*d*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)-2/f^2*b^2*d^2*e*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)+b^2*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2/f*b^2*c*d*e*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+1/f^2*b^2*d^2*e^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","B"
159,1,216,106,0.043000," ","int((d*x+c)*(a+b*sin(f*x+e))^2,x)","\frac{\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}+\frac{2 a b d \left(\sin \left(f x +e \right)-\left(f x +e \right) \cos \left(f x +e \right)\right)}{f}-2 a b c \cos \left(f x +e \right)+\frac{2 a b d e \cos \left(f x +e \right)}{f}+\frac{b^{2} d \left(\left(f x +e \right) \left(-\frac{\sin \left(f x +e \right) \cos \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}+b^{2} c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{b^{2} d e \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}}{f}"," ",0,"1/f*(1/2*a^2/f*d*(f*x+e)^2+a^2*c*(f*x+e)-a^2/f*d*e*(f*x+e)+2/f*a*b*d*(sin(f*x+e)-(f*x+e)*cos(f*x+e))-2*a*b*c*cos(f*x+e)+2/f*a*b*d*e*cos(f*x+e)+1/f*b^2*d*((f*x+e)*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/4*(f*x+e)^2+1/4*sin(f*x+e)^2)+b^2*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/f*b^2*d*e*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","B"
160,1,213,152,0.041000," ","int((a+b*sin(f*x+e))^2/(d*x+c),x)","\frac{a^{2} \ln \left(\left(f x +e \right) d +c f -d e \right)}{d}+\frac{2 a b \Si \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}-\frac{2 a b \Ci \left(f x +e +\frac{c f -d e}{d}\right) \sin \left(\frac{c f -d e}{d}\right)}{d}+\frac{b^{2} \ln \left(\left(f x +e \right) d +c f -d e \right)}{2 d}-\frac{b^{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{b^{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}"," ",0,"a^2*ln((f*x+e)*d+c*f-d*e)/d+2*a*b*Si(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d-2*a*b*Ci(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d+1/2*b^2*ln((f*x+e)*d+c*f-d*e)/d-1/2*b^2*Si(2*f*x+2*e+2*(c*f-d*e)/d)*sin(2*(c*f-d*e)/d)/d-1/2*b^2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d","A"
161,1,301,186,0.046000," ","int((a+b*sin(f*x+e))^2/(d*x+c)^2,x)","\frac{-\frac{a^{2} f^{2}}{\left(\left(f x +e \right) d +c f -d e \right) d}+2 f^{2} a b \left(-\frac{\sin \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) \sin \left(\frac{c f -d e}{d}\right)}{d}+\frac{\Ci \left(f x +e +\frac{c f -d e}{d}\right) \cos \left(\frac{c f -d e}{d}\right)}{d}}{d}\right)-\frac{f^{2} b^{2}}{2 \left(\left(f x +e \right) d +c f -d e \right) d}-\frac{f^{2} b^{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}}{f}"," ",0,"1/f*(-a^2*f^2/((f*x+e)*d+c*f-d*e)/d+2*f^2*a*b*(-sin(f*x+e)/((f*x+e)*d+c*f-d*e)/d+(Si(f*x+e+(c*f-d*e)/d)*sin((c*f-d*e)/d)/d+Ci(f*x+e+(c*f-d*e)/d)*cos((c*f-d*e)/d)/d)/d)-1/2*f^2*b^2/((f*x+e)*d+c*f-d*e)/d-1/4*f^2*b^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))","A"
162,1,374,241,0.045000," ","int((a+b*sin(f*x+e))^2/(d*x+c)^3,x)","\frac{-\frac{a^{2} f^{3}}{2 \left(\left(f x +e \right) d +c f -d e \right)^{2} d}+2 f^{3} a b \left(-\frac{\sin \left(f x +e \right)}{2 \left(\left(f x +e \right) d +c f -d e \right)^{2} d}+\frac{-\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}}{2 d}\right)-\frac{f^{3} b^{2}}{4 \left(\left(f x +e \right) d +c f -d e \right)^{2} d}-\frac{f^{3} b^{2} \left(-\frac{\cos \left(2 f x +2 e \right)}{\left(\left(f x +e \right) d +c f -d e \right)^{2} d}-\frac{-\frac{2 \sin \left(2 f x +2 e \right)}{\left(\left(f x +e \right) d +c f -d e \right) d}+\frac{\frac{4 \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)}{d}+\frac{4 \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)}{d}}{d}}{d}\right)}{4}}{f}"," ",0,"1/f*(-1/2*a^2*f^3/((f*x+e)*d+c*f-d*e)^2/d+2*f^3*a*b*(-1/2*sin(f*x+e)/((f*x+e)*d+c*f-d*e)^2/d+1/2*(-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)/d)-1/4*f^3*b^2/((f*x+e)*d+c*f-d*e)^2/d-1/4*f^3*b^2*(-cos(2*f*x+2*e)/((f*x+e)*d+c*f-d*e)^2/d-(-2*sin(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)*sin(2*(c*f-d*e)/d)/d+2*Ci(2*f*x+2*e+2*(c*f-d*e)/d)*cos(2*(c*f-d*e)/d)/d)/d)/d))","A"
163,0,0,435,0.760000," ","int((d*x+c)^3/(a+b*sin(f*x+e)),x)","\int \frac{\left(d x +c \right)^{3}}{a +b \sin \left(f x +e \right)}\, dx"," ",0,"int((d*x+c)^3/(a+b*sin(f*x+e)),x)","F"
164,0,0,321,0.477000," ","int((d*x+c)^2/(a+b*sin(f*x+e)),x)","\int \frac{\left(d x +c \right)^{2}}{a +b \sin \left(f x +e \right)}\, dx"," ",0,"int((d*x+c)^2/(a+b*sin(f*x+e)),x)","F"
165,1,501,204,0.129000," ","int((d*x+c)/(a+b*sin(f*x+e)),x)","\frac{2 i c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(f x +e \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{f \sqrt{-a^{2}+b^{2}}}+\frac{d \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{f \sqrt{-a^{2}+b^{2}}}+\frac{d \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) e}{f^{2} \sqrt{-a^{2}+b^{2}}}-\frac{d \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{f \sqrt{-a^{2}+b^{2}}}-\frac{d \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) e}{f^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i d \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{f^{2} \sqrt{-a^{2}+b^{2}}}+\frac{i d \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{f^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 i d e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(f x +e \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{f^{2} \sqrt{-a^{2}+b^{2}}}"," ",0,"2*I/f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(f*x+e))-2*a)/(-a^2+b^2)^(1/2))+1/f*d/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(f*x+e))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x+1/f^2*d/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(f*x+e))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*e-1/f*d/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(f*x+e))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-1/f^2*d/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(f*x+e))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*e-I/f^2*d/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(f*x+e))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))+I/f^2*d/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(f*x+e))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-2*I/f^2*d*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(f*x+e))-2*a)/(-a^2+b^2)^(1/2))","B"
166,0,0,22,0.097000," ","int(1/(d*x+c)/(a+b*sin(f*x+e)),x)","\int \frac{1}{\left(d x +c \right) \left(a +b \sin \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)/(a+b*sin(f*x+e)),x)","F"
167,0,0,22,0.105000," ","int(1/(d*x+c)^2/(a+b*sin(f*x+e)),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +b \sin \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(d*x+c)^2/(a+b*sin(f*x+e)),x)","F"
168,0,0,832,3.186000," ","int((d*x+c)^3/(a+b*sin(f*x+e))^2,x)","\int \frac{\left(d x +c \right)^{3}}{\left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*x+c)^3/(a+b*sin(f*x+e))^2,x)","F"
169,0,0,602,2.327000," ","int((d*x+c)^2/(a+b*sin(f*x+e))^2,x)","\int \frac{\left(d x +c \right)^{2}}{\left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*x+c)^2/(a+b*sin(f*x+e))^2,x)","F"
170,1,650,275,1.237000," ","int((d*x+c)/(a+b*sin(f*x+e))^2,x)","\frac{2 \left(d x +c \right) \left(i b +a \,{\mathrm e}^{i \left(f x +e \right)}\right)}{f \left(a^{2}-b^{2}\right) \left(b \,{\mathrm e}^{2 i \left(f x +e \right)}-b +2 i a \,{\mathrm e}^{i \left(f x +e \right)}\right)}-\frac{2 d \ln \left({\mathrm e}^{i \left(f x +e \right)}\right)}{\left(-a^{2}+b^{2}\right) f^{2}}+\frac{d \ln \left(i {\mathrm e}^{2 i \left(f x +e \right)} b -i b -2 a \,{\mathrm e}^{i \left(f x +e \right)}\right)}{\left(-a^{2}+b^{2}\right) f^{2}}+\frac{i d a \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{\left(-a^{2}+b^{2}\right)^{\frac{3}{2}} f^{2}}+\frac{d a \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{\left(-a^{2}+b^{2}\right)^{\frac{3}{2}} f}+\frac{d a \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) e}{\left(-a^{2}+b^{2}\right)^{\frac{3}{2}} f^{2}}+\frac{2 i a d e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(f x +e \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{\left(-a^{2}+b^{2}\right)^{\frac{3}{2}} f^{2}}-\frac{i d a \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{\left(-a^{2}+b^{2}\right)^{\frac{3}{2}} f^{2}}-\frac{d a \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{\left(-a^{2}+b^{2}\right)^{\frac{3}{2}} f}-\frac{d a \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(f x +e \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) e}{\left(-a^{2}+b^{2}\right)^{\frac{3}{2}} f^{2}}-\frac{2 i a c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(f x +e \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{\left(-a^{2}+b^{2}\right)^{\frac{3}{2}} f}"," ",0,"2*(d*x+c)*(I*b+a*exp(I*(f*x+e)))/f/(a^2-b^2)/(b*exp(2*I*(f*x+e))-b+2*I*a*exp(I*(f*x+e)))-2/(-a^2+b^2)/f^2*d*ln(exp(I*(f*x+e)))+1/(-a^2+b^2)/f^2*d*ln(I*exp(2*I*(f*x+e))*b-I*b-2*a*exp(I*(f*x+e)))+I/(-a^2+b^2)^(3/2)/f^2*d*a*dilog((I*a+b*exp(I*(f*x+e))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))+1/(-a^2+b^2)^(3/2)/f*d*a*ln((I*a+b*exp(I*(f*x+e))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+1/(-a^2+b^2)^(3/2)/f^2*d*a*ln((I*a+b*exp(I*(f*x+e))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*e+2*I/(-a^2+b^2)^(3/2)/f^2*a*d*e*arctan(1/2*(2*I*b*exp(I*(f*x+e))-2*a)/(-a^2+b^2)^(1/2))-I/(-a^2+b^2)^(3/2)/f^2*d*a*dilog((I*a+b*exp(I*(f*x+e))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-1/(-a^2+b^2)^(3/2)/f*d*a*ln((I*a+b*exp(I*(f*x+e))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x-1/(-a^2+b^2)^(3/2)/f^2*d*a*ln((I*a+b*exp(I*(f*x+e))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*e-2*I/(-a^2+b^2)^(3/2)/f*a*c*arctan(1/2*(2*I*b*exp(I*(f*x+e))-2*a)/(-a^2+b^2)^(1/2))","B"
171,0,0,22,4.382000," ","int(1/(d*x+c)/(a+b*sin(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right) \left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)/(a+b*sin(f*x+e))^2,x)","F"
172,0,0,22,8.140000," ","int(1/(d*x+c)^2/(a+b*sin(f*x+e))^2,x)","\int \frac{1}{\left(d x +c \right)^{2} \left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(d*x+c)^2/(a+b*sin(f*x+e))^2,x)","F"
173,0,0,22,0.395000," ","int((d*x+c)^m*(a+b*sin(f*x+e))^n,x)","\int \left(d x +c \right)^{m} \left(a +b \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((d*x+c)^m*(a+b*sin(f*x+e))^n,x)","F"
174,0,0,567,0.437000," ","int((d*x+c)^m*(a+b*sin(f*x+e))^3,x)","\int \left(d x +c \right)^{m} \left(a +b \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*x+c)^m*(a+b*sin(f*x+e))^3,x)","F"
175,0,0,302,0.385000," ","int((d*x+c)^m*(a+b*sin(f*x+e))^2,x)","\int \left(d x +c \right)^{m} \left(a +b \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*x+c)^m*(a+b*sin(f*x+e))^2,x)","F"
176,0,0,138,0.100000," ","int((d*x+c)^m*(a+b*sin(f*x+e)),x)","\int \left(d x +c \right)^{m} \left(a +b \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*x+c)^m*(a+b*sin(f*x+e)),x)","F"
177,0,0,22,0.116000," ","int((d*x+c)^m/(a+b*sin(f*x+e)),x)","\int \frac{\left(d x +c \right)^{m}}{a +b \sin \left(f x +e \right)}\, dx"," ",0,"int((d*x+c)^m/(a+b*sin(f*x+e)),x)","F"
178,0,0,22,0.365000," ","int((d*x+c)^m/(a+b*sin(f*x+e))^2,x)","\int \frac{\left(d x +c \right)^{m}}{\left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*x+c)^m/(a+b*sin(f*x+e))^2,x)","F"
179,1,526,145,0.266000," ","int((f*x+e)^3*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{f^{3} x^{4}}{4 a}+\frac{e \,f^{2} x^{3}}{a}+\frac{3 e^{2} f \,x^{2}}{2 a}+\frac{e^{3} x}{a}+\frac{2 f^{3} x^{3}+6 e \,f^{2} x^{2}+6 e^{2} f x +2 e^{3}}{d a \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}+\frac{12 i f^{3} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}+\frac{6 i f^{2} e \,c^{2}}{a \,d^{3}}-\frac{6 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{2}}{a \,d^{2}}-\frac{12 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{12 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}-\frac{12 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{6 i f^{2} e \,x^{2}}{a d}-\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a \,d^{2}}+\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{a \,d^{4}}+\frac{6 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e^{2}}{a \,d^{2}}-\frac{6 i f^{3} c^{2} x}{a \,d^{3}}+\frac{12 i f^{2} e \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{2 i f^{3} x^{3}}{a d}-\frac{12 f^{3} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}+\frac{6 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{4 i f^{3} c^{3}}{a \,d^{4}}-\frac{6 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{4}}+\frac{12 i f^{2} e c x}{a \,d^{2}}+\frac{12 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}"," ",0,"1/4/a*f^3*x^4+1/a*e*f^2*x^3+3/2/a*e^2*f*x^2+1/a*e^3*x+2*(f^3*x^3+3*e*f^2*x^2+3*e^2*f*x+e^3)/d/a/(exp(I*(d*x+c))+I)+6*I/a/d^3*f^2*e*c^2+6*I/a/d*f^2*e*x^2-6/a/d^2*f*ln(exp(I*(d*x+c))+I)*e^2-12/a/d^2*f^2*e*ln(1-I*exp(I*(d*x+c)))*x-12/a/d^3*f^2*e*ln(1-I*exp(I*(d*x+c)))*c-12/a/d^3*f^2*e*c*ln(exp(I*(d*x+c)))-6*I/a/d^3*f^3*c^2*x-6/a/d^2*f^3*ln(1-I*exp(I*(d*x+c)))*x^2+6/a/d^4*f^3*ln(1-I*exp(I*(d*x+c)))*c^2+6/a/d^2*f*ln(exp(I*(d*x+c)))*e^2+12*I/a/d^3*f^3*polylog(2,I*exp(I*(d*x+c)))*x+2*I/a/d*f^3*x^3-4*I/a/d^4*f^3*c^3-12*f^3*polylog(3,I*exp(I*(d*x+c)))/a/d^4+6/a/d^4*f^3*c^2*ln(exp(I*(d*x+c)))+12*I/a/d^3*f^2*e*polylog(2,I*exp(I*(d*x+c)))-6/a/d^4*f^3*c^2*ln(exp(I*(d*x+c))+I)+12*I/a/d^2*f^2*e*c*x+12/a/d^3*f^2*e*c*ln(exp(I*(d*x+c))+I)","B"
180,1,282,113,0.180000," ","int((f*x+e)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{f^{2} x^{3}}{3 a}+\frac{f e \,x^{2}}{a}+\frac{e^{2} x}{a}+\frac{2 f^{2} x^{2}+4 f e x +2 e^{2}}{d a \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}-\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e}{a \,d^{2}}+\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{a \,d^{2}}+\frac{2 i f^{2} x^{2}}{a d}+\frac{4 i f^{2} c x}{a \,d^{2}}+\frac{2 i f^{2} c^{2}}{a \,d^{3}}-\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}+\frac{4 i f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{4 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}-\frac{4 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}"," ",0,"1/3/a*f^2*x^3+1/a*f*e*x^2+1/a*e^2*x+2*(f^2*x^2+2*e*f*x+e^2)/d/a/(exp(I*(d*x+c))+I)-4/a/d^2*f*ln(exp(I*(d*x+c))+I)*e+4/a/d^2*f*ln(exp(I*(d*x+c)))*e+2*I/a/d*f^2*x^2+4*I/a/d^2*f^2*c*x+2*I/a/d^3*f^2*c^2-4/a/d^2*f^2*ln(1-I*exp(I*(d*x+c)))*x-4/a/d^3*f^2*ln(1-I*exp(I*(d*x+c)))*c+4*I*f^2*polylog(2,I*exp(I*(d*x+c)))/a/d^3+4/a/d^3*f^2*c*ln(exp(I*(d*x+c))+I)-4/a/d^3*f^2*c*ln(exp(I*(d*x+c)))","B"
181,1,446,62,0.141000," ","int((f*x+e)*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{2 e \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2 e}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{f x}{a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) d}+\frac{f x \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) d}+\frac{f \,x^{2}}{2 a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{f \,x^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{f \,x^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{f \,x^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{f x \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) d}-\frac{f x \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) d}+\frac{f \ln \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \,d^{2}}-\frac{2 f \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a \,d^{2}}"," ",0,"2/a*e/d*arctan(tan(1/2*d*x+1/2*c))+2/a*e/d/(tan(1/2*d*x+1/2*c)+1)+1/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x/d+1/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x/d*tan(1/2*d*x+1/2*c)^2+1/2/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x^2+1/2/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x^2*tan(1/2*d*x+1/2*c)+1/2/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x^2*tan(1/2*d*x+1/2*c)^2+1/2/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x^2*tan(1/2*d*x+1/2*c)^3-1/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x/d*tan(1/2*d*x+1/2*c)-1/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x/d*tan(1/2*d*x+1/2*c)^3+1/a*f/d^2*ln(1+tan(1/2*d*x+1/2*c)^2)-2/a*f/d^2*ln(tan(1/2*d*x+1/2*c)+1)","B"
182,1,41,28,0.065000," ","int(sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"2/a/d*arctan(tan(1/2*d*x+1/2*c))+2/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
183,0,0,28,0.276000," ","int(sin(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","\int \frac{\sin \left(d x +c \right)}{\left(f x +e \right) \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sin(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","F"
184,0,0,28,0.355000," ","int(sin(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\int \frac{\sin \left(d x +c \right)}{\left(f x +e \right)^{2} \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sin(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x)","F"
185,1,748,228,0.437000," ","int((f*x+e)^3*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{f^{3} x^{4}}{4 a}-\frac{e^{3} x}{a}-\frac{\left(f^{3} x^{3} d^{3}+3 d^{3} e \,f^{2} x^{2}+3 i d^{2} f^{3} x^{2}+3 d^{3} e^{2} f x +6 i d^{2} e \,f^{2} x +d^{3} e^{3}+3 i d^{2} e^{2} f -6 d \,f^{3} x -6 f^{2} e d -6 i f^{3}\right) {\mathrm e}^{i \left(d x +c \right)}}{2 a \,d^{4}}-\frac{\left(f^{3} x^{3} d^{3}+3 d^{3} e \,f^{2} x^{2}-3 i d^{2} f^{3} x^{2}+3 d^{3} e^{2} f x -6 i d^{2} e \,f^{2} x +d^{3} e^{3}-3 i d^{2} e^{2} f -6 d \,f^{3} x -6 f^{2} e d +6 i f^{3}\right) {\mathrm e}^{-i \left(d x +c \right)}}{2 a \,d^{4}}-\frac{2 \left(f^{3} x^{3}+3 e \,f^{2} x^{2}+3 e^{2} f x +e^{3}\right)}{d a \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}+\frac{12 f^{3} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{12 i f^{2} e c x}{a \,d^{2}}-\frac{e \,f^{2} x^{3}}{a}-\frac{3 e^{2} f \,x^{2}}{2 a}+\frac{6 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{2}}{a \,d^{2}}+\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a \,d^{2}}-\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{a \,d^{4}}-\frac{6 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e^{2}}{a \,d^{2}}-\frac{2 i f^{3} x^{3}}{a d}-\frac{6 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}+\frac{4 i f^{3} c^{3}}{a \,d^{4}}+\frac{6 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{4}}-\frac{12 i f^{3} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}-\frac{6 i f^{2} e \,c^{2}}{a \,d^{3}}+\frac{12 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{12 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}+\frac{6 i f^{3} c^{2} x}{a \,d^{3}}-\frac{12 i f^{2} e \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{12 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}+\frac{12 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{6 i f^{2} e \,x^{2}}{a d}"," ",0,"12/a/d^2*f^2*e*ln(1-I*exp(I*(d*x+c)))*x+12/a/d^3*f^2*e*ln(1-I*exp(I*(d*x+c)))*c+12/a/d^3*f^2*e*c*ln(exp(I*(d*x+c)))-12*I/a/d^2*e*f^2*c*x-2*I/a/d*f^3*x^3+4*I/a/d^4*f^3*c^3-1/4/a*f^3*x^4-1/a*e^3*x-2*(f^3*x^3+3*e*f^2*x^2+3*e^2*f*x+e^3)/d/a/(exp(I*(d*x+c))+I)-1/a*e*f^2*x^3-3/2/a*e^2*f*x^2-6/a/d^2*f*ln(exp(I*(d*x+c)))*e^2-6/a/d^4*f^3*c^2*ln(exp(I*(d*x+c)))+6/a/d^4*f^3*c^2*ln(exp(I*(d*x+c))+I)+6/a/d^2*f*ln(exp(I*(d*x+c))+I)*e^2-1/2*(f^3*x^3*d^3+3*I*d^2*f^3*x^2+3*d^3*e*f^2*x^2+6*I*d^2*e*f^2*x+3*d^3*e^2*f*x+3*I*d^2*e^2*f+d^3*e^3-6*d*f^3*x-6*I*f^3-6*f^2*e*d)/a/d^4*exp(I*(d*x+c))+6*I/a/d^3*f^3*c^2*x-12*I/a/d^3*f^3*polylog(2,I*exp(I*(d*x+c)))*x-6*I/a/d*e*f^2*x^2-6*I/a/d^3*e*f^2*c^2-12*I/a/d^3*e*f^2*polylog(2,I*exp(I*(d*x+c)))+6/a/d^2*f^3*ln(1-I*exp(I*(d*x+c)))*x^2-1/2*(f^3*x^3*d^3-3*I*d^2*f^3*x^2+3*d^3*e*f^2*x^2-6*I*d^2*e*f^2*x+3*d^3*e^2*f*x-3*I*d^2*e^2*f+d^3*e^3-6*d*f^3*x+6*I*f^3-6*f^2*e*d)/a/d^4*exp(-I*(d*x+c))+12*f^3*polylog(3,I*exp(I*(d*x+c)))/a/d^4-6/a/d^4*f^3*ln(1-I*exp(I*(d*x+c)))*c^2-12/a/d^3*f^2*e*c*ln(exp(I*(d*x+c))+I)","B"
186,1,408,172,0.562000," ","int((f*x+e)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{f^{2} x^{3}}{3 a}-\frac{f e \,x^{2}}{a}-\frac{e^{2} x}{a}-\frac{\left(f^{2} x^{2} d^{2}+2 d^{2} e f x +2 i d \,f^{2} x +d^{2} e^{2}+2 i d e f -2 f^{2}\right) {\mathrm e}^{i \left(d x +c \right)}}{2 d^{3} a}-\frac{\left(f^{2} x^{2} d^{2}+2 d^{2} e f x -2 i d \,f^{2} x +d^{2} e^{2}-2 i d e f -2 f^{2}\right) {\mathrm e}^{-i \left(d x +c \right)}}{2 d^{3} a}-\frac{2 \left(f^{2} x^{2}+2 f e x +e^{2}\right)}{d a \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}-\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{a \,d^{2}}+\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e}{a \,d^{2}}-\frac{4 i f^{2} c x}{a \,d^{2}}-\frac{4 i f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{2 i f^{2} c^{2}}{a \,d^{3}}+\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}-\frac{2 i f^{2} x^{2}}{a d}+\frac{4 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{4 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}"," ",0,"-1/3/a*f^2*x^3-1/a*f*e*x^2-1/a*e^2*x-1/2*(f^2*x^2*d^2+2*I*d*f^2*x+2*d^2*e*f*x+2*I*d*e*f+d^2*e^2-2*f^2)/d^3/a*exp(I*(d*x+c))-1/2*(f^2*x^2*d^2-2*I*d*f^2*x+2*d^2*e*f*x-2*I*d*e*f+d^2*e^2-2*f^2)/d^3/a*exp(-I*(d*x+c))-2*(f^2*x^2+2*e*f*x+e^2)/d/a/(exp(I*(d*x+c))+I)-4/a/d^2*f*ln(exp(I*(d*x+c)))*e+4/a/d^2*f*ln(exp(I*(d*x+c))+I)*e-4*I/a/d^2*f^2*c*x-4*I*f^2*polylog(2,I*exp(I*(d*x+c)))/a/d^3-2*I/a/d^3*f^2*c^2+4/a/d^2*f^2*ln(1-I*exp(I*(d*x+c)))*x+4/a/d^3*f^2*ln(1-I*exp(I*(d*x+c)))*c-2*I/a/d*f^2*x^2+4/a/d^3*f^2*c*ln(exp(I*(d*x+c)))-4/a/d^3*f^2*c*ln(exp(I*(d*x+c))+I)","B"
187,1,216,97,0.243000," ","int((f*x+e)*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{2 e}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{x f}{a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) d}+\frac{x f \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) d}+\frac{2 f \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a \,d^{2}}-\frac{f \ln \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \,d^{2}}-\frac{2 e}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 e \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{f \sin \left(d x +c \right)}{a \,d^{2}}-\frac{f \cos \left(d x +c \right) x}{a d}-\frac{f \,x^{2}}{2 a}+\frac{f \,c^{2}}{2 a \,d^{2}}"," ",0,"-2/a*e/d/(tan(1/2*d*x+1/2*c)+1)-1/a/(tan(1/2*d*x+1/2*c)+1)/d*x*f+1/a/(tan(1/2*d*x+1/2*c)+1)/d*x*f*tan(1/2*d*x+1/2*c)+2/a*f/d^2*ln(tan(1/2*d*x+1/2*c)+1)-1/a*f/d^2*ln(1+tan(1/2*d*x+1/2*c)^2)-2/a*e/d/(1+tan(1/2*d*x+1/2*c)^2)-2/a*e/d*arctan(tan(1/2*d*x+1/2*c))+f*sin(d*x+c)/a/d^2-1/a*f/d*cos(d*x+c)*x-1/2*f*x^2/a+1/2/a*f/d^2*c^2","B"
188,1,64,45,0.061000," ","int(sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)-2/a/d*arctan(tan(1/2*d*x+1/2*c))-2/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
189,0,0,30,0.579000," ","int(sin(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x)","\int \frac{\sin^{2}\left(d x +c \right)}{\left(f x +e \right) \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sin(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x)","F"
190,0,0,30,0.893000," ","int(sin(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\int \frac{\sin^{2}\left(d x +c \right)}{\left(f x +e \right)^{2} \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sin(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x)","F"
191,1,870,351,0.287000," ","int((f*x+e)^3*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{3 f^{3} x^{4}}{8 a}+\frac{3 e^{3} x}{2 a}+\frac{\left(f^{3} x^{3} d^{3}+3 d^{3} e \,f^{2} x^{2}+3 i d^{2} f^{3} x^{2}+3 d^{3} e^{2} f x +6 i d^{2} e \,f^{2} x +d^{3} e^{3}+3 i d^{2} e^{2} f -6 d \,f^{3} x -6 f^{2} e d -6 i f^{3}\right) {\mathrm e}^{i \left(d x +c \right)}}{2 a \,d^{4}}+\frac{\left(f^{3} x^{3} d^{3}+3 d^{3} e \,f^{2} x^{2}-3 i d^{2} f^{3} x^{2}+3 d^{3} e^{2} f x -6 i d^{2} e \,f^{2} x +d^{3} e^{3}-3 i d^{2} e^{2} f -6 d \,f^{3} x -6 f^{2} e d +6 i f^{3}\right) {\mathrm e}^{-i \left(d x +c \right)}}{2 a \,d^{4}}-\frac{12 f^{3} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{\left(2 f^{3} x^{3} d^{2}+6 d^{2} e \,f^{2} x^{2}+6 d^{2} e^{2} f x +2 d^{2} e^{3}-3 f^{3} x -3 f^{2} e \right) \sin \left(2 d x +2 c \right)}{8 d^{3} a}+\frac{12 i f^{2} e c x}{a \,d^{2}}+\frac{3 e \,f^{2} x^{3}}{2 a}+\frac{9 e^{2} f \,x^{2}}{4 a}-\frac{6 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{2}}{a \,d^{2}}-\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a \,d^{2}}+\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{a \,d^{4}}+\frac{6 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e^{2}}{a \,d^{2}}+\frac{2 i f^{3} x^{3}}{a d}+\frac{6 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{4 i f^{3} c^{3}}{a \,d^{4}}-\frac{6 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{4}}+\frac{2 f^{3} x^{3}+6 e \,f^{2} x^{2}+6 e^{2} f x +2 e^{3}}{d a \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}-\frac{3 f \left(2 f^{2} x^{2} d^{2}+4 d^{2} e f x +2 d^{2} e^{2}-f^{2}\right) \cos \left(2 d x +2 c \right)}{16 a \,d^{4}}+\frac{12 i f^{3} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}+\frac{6 i f^{2} e \,c^{2}}{a \,d^{3}}-\frac{12 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{12 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}-\frac{6 i f^{3} c^{2} x}{a \,d^{3}}+\frac{12 i f^{2} e \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{12 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}-\frac{12 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{6 i f^{2} e \,x^{2}}{a d}"," ",0,"-12/a/d^2*f^2*e*ln(1-I*exp(I*(d*x+c)))*x-12/a/d^3*f^2*e*ln(1-I*exp(I*(d*x+c)))*c-12/a/d^3*f^2*e*c*ln(exp(I*(d*x+c)))-6*I/a/d^3*f^3*c^2*x+12*I/a/d^3*f^2*e*polylog(2,I*exp(I*(d*x+c)))+6*I/a/d*f^2*e*x^2+6*I/a/d^3*f^2*e*c^2+3/8/a*f^3*x^4+3/2/a*e^3*x+2*(f^3*x^3+3*e*f^2*x^2+3*e^2*f*x+e^3)/d/a/(exp(I*(d*x+c))+I)-1/8/d^3*(2*d^2*f^3*x^3+6*d^2*e*f^2*x^2+6*d^2*e^2*f*x+2*d^2*e^3-3*f^3*x-3*e*f^2)/a*sin(2*d*x+2*c)+12*I/a/d^2*f^2*e*c*x+3/2/a*e*f^2*x^3+9/4/a*e^2*f*x^2+6/a/d^2*f*ln(exp(I*(d*x+c)))*e^2+6/a/d^4*f^3*c^2*ln(exp(I*(d*x+c)))-6/a/d^4*f^3*c^2*ln(exp(I*(d*x+c))+I)+2*I/a/d*f^3*x^3-4*I/a/d^4*f^3*c^3-6/a/d^2*f*ln(exp(I*(d*x+c))+I)*e^2+1/2*(f^3*x^3*d^3+3*I*d^2*f^3*x^2+3*d^3*e*f^2*x^2+6*I*d^2*e*f^2*x+3*d^3*e^2*f*x+3*I*d^2*e^2*f+d^3*e^3-6*d*f^3*x-6*I*f^3-6*f^2*e*d)/a/d^4*exp(I*(d*x+c))-3/16*f*(2*d^2*f^2*x^2+4*d^2*e*f*x+2*d^2*e^2-f^2)/a/d^4*cos(2*d*x+2*c)-6/a/d^2*f^3*ln(1-I*exp(I*(d*x+c)))*x^2+1/2*(f^3*x^3*d^3-3*I*d^2*f^3*x^2+3*d^3*e*f^2*x^2-6*I*d^2*e*f^2*x+3*d^3*e^2*f*x-3*I*d^2*e^2*f+d^3*e^3-6*d*f^3*x+6*I*f^3-6*f^2*e*d)/a/d^4*exp(-I*(d*x+c))-12*f^3*polylog(3,I*exp(I*(d*x+c)))/a/d^4+6/a/d^4*f^3*ln(1-I*exp(I*(d*x+c)))*c^2+12/a/d^3*f^2*e*c*ln(exp(I*(d*x+c))+I)+12*I/a/d^3*f^3*polylog(2,I*exp(I*(d*x+c)))*x","B"
192,1,481,254,0.711000," ","int((f*x+e)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{f^{2} x^{3}}{2 a}+\frac{3 f e \,x^{2}}{2 a}+\frac{3 e^{2} x}{2 a}+\frac{\left(f^{2} x^{2} d^{2}+2 d^{2} e f x +2 i d \,f^{2} x +d^{2} e^{2}+2 i d e f -2 f^{2}\right) {\mathrm e}^{i \left(d x +c \right)}}{2 d^{3} a}+\frac{\left(f^{2} x^{2} d^{2}+2 d^{2} e f x -2 i d \,f^{2} x +d^{2} e^{2}-2 i d e f -2 f^{2}\right) {\mathrm e}^{-i \left(d x +c \right)}}{2 d^{3} a}+\frac{2 f^{2} x^{2}+4 f e x +2 e^{2}}{d a \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}-\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e}{a \,d^{2}}+\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{a \,d^{2}}+\frac{4 i f^{2} c x}{a \,d^{2}}+\frac{4 i f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{2 i f^{2} c^{2}}{a \,d^{3}}-\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}+\frac{2 i f^{2} x^{2}}{a d}+\frac{4 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}-\frac{4 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{f \left(f x +e \right) \cos \left(2 d x +2 c \right)}{4 d^{2} a}-\frac{\left(2 f^{2} x^{2} d^{2}+4 d^{2} e f x +2 d^{2} e^{2}-f^{2}\right) \sin \left(2 d x +2 c \right)}{8 d^{3} a}"," ",0,"1/2/a*f^2*x^3+3/2/a*f*e*x^2+3/2/a*e^2*x+1/2*(f^2*x^2*d^2+2*I*d*f^2*x+2*d^2*e*f*x+2*I*d*e*f+d^2*e^2-2*f^2)/d^3/a*exp(I*(d*x+c))+1/2*(f^2*x^2*d^2-2*I*d*f^2*x+2*d^2*e*f*x-2*I*d*e*f+d^2*e^2-2*f^2)/d^3/a*exp(-I*(d*x+c))+2*(f^2*x^2+2*e*f*x+e^2)/d/a/(exp(I*(d*x+c))+I)-4/a/d^2*f*ln(exp(I*(d*x+c))+I)*e+4/a/d^2*f*ln(exp(I*(d*x+c)))*e+4*I/a/d^2*f^2*c*x+2*I/a/d^3*f^2*c^2+4*I*f^2*polylog(2,I*exp(I*(d*x+c)))/a/d^3-4/a/d^2*f^2*ln(1-I*exp(I*(d*x+c)))*x-4/a/d^3*f^2*ln(1-I*exp(I*(d*x+c)))*c+2*I/a/d*f^2*x^2+4/a/d^3*f^2*c*ln(exp(I*(d*x+c))+I)-4/a/d^3*f^2*c*ln(exp(I*(d*x+c)))-1/4/d^2*f*(f*x+e)/a*cos(2*d*x+2*c)-1/8*(2*d^2*f^2*x^2+4*d^2*e*f*x+2*d^2*e^2-f^2)/d^3/a*sin(2*d*x+2*c)","A"
193,1,662,138,0.289000," ","int((f*x+e)*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{3 e \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2 e}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{f \,x^{2}}{2 a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{f x}{a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) d}+\frac{f \,x^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{f \,x^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{f \,x^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{f x \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) d}+\frac{f x \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) d}-\frac{f x \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) d}-\frac{2 f \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a \,d^{2}}+\frac{f \ln \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \,d^{2}}+\frac{e \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 e \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{e \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 e}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{f \cos \left(d x +c \right) \sin \left(d x +c \right) x}{2 a d}+\frac{f \,x^{2}}{4 a}-\frac{f \,c^{2}}{4 a \,d^{2}}+\frac{f \left(\sin^{2}\left(d x +c \right)\right)}{4 a \,d^{2}}-\frac{f \sin \left(d x +c \right)}{a \,d^{2}}+\frac{f \cos \left(d x +c \right) x}{a d}"," ",0,"3/a*e/d*arctan(tan(1/2*d*x+1/2*c))+2/a*e/d/(tan(1/2*d*x+1/2*c)+1)+1/2/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x^2+1/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x/d+1/2/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x^2*tan(1/2*d*x+1/2*c)+1/2/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x^2*tan(1/2*d*x+1/2*c)^2+1/2/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x^2*tan(1/2*d*x+1/2*c)^3-1/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x/d*tan(1/2*d*x+1/2*c)+1/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x/d*tan(1/2*d*x+1/2*c)^2-1/a*f/(1+tan(1/2*d*x+1/2*c)^2)/(tan(1/2*d*x+1/2*c)+1)*x/d*tan(1/2*d*x+1/2*c)^3-2/a*f/d^2*ln(tan(1/2*d*x+1/2*c)+1)+1/a*f/d^2*ln(1+tan(1/2*d*x+1/2*c)^2)+1/a*e/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+2/a*e/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2-1/a*e/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+2/a*e/d/(1+tan(1/2*d*x+1/2*c)^2)^2-1/2/a*f/d*cos(d*x+c)*sin(d*x+c)*x+1/4*f*x^2/a-1/4/a*f/d^2*c^2+1/4*f*sin(d*x+c)^2/a/d^2-f*sin(d*x+c)/a/d^2+1/a*f/d*cos(d*x+c)*x","B"
194,1,163,71,0.064000," ","int(sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2+3/a/d*arctan(tan(1/2*d*x+1/2*c))+2/a/d/(tan(1/2*d*x+1/2*c)+1)","B"
195,0,0,30,1.049000," ","int(sin(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x)","\int \frac{\sin^{3}\left(d x +c \right)}{\left(f x +e \right) \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sin(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x)","F"
196,0,0,30,1.490000," ","int(sin(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\int \frac{\sin^{3}\left(d x +c \right)}{\left(f x +e \right)^{2} \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sin(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x)","F"
197,1,1151,317,0.410000," ","int((f*x+e)^3*csc(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{12 f^{3} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}+\frac{12 i f^{2} e c x}{a \,d^{2}}-\frac{6 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{2}}{a \,d^{2}}-\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a \,d^{2}}+\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{a \,d^{4}}+\frac{6 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e^{2}}{a \,d^{2}}+\frac{2 i f^{3} x^{3}}{a d}+\frac{6 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{4 i f^{3} c^{3}}{a \,d^{4}}-\frac{6 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{4}}+\frac{2 f^{3} x^{3}+6 e \,f^{2} x^{2}+6 e^{2} f x +2 e^{3}}{d a \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}+\frac{e^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a d}-\frac{e^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a d}+\frac{12 i f^{3} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}+\frac{6 i f^{2} e \,c^{2}}{a \,d^{3}}+\frac{6 i f^{3} \polylog \left(4, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}+\frac{6 e \,f^{2} \polylog \left(3, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{6 e \,f^{2} \polylog \left(3, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{6 f^{3} \polylog \left(3, {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}-\frac{6 f^{3} \polylog \left(3, -{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}-\frac{6 i f^{3} \polylog \left(4, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{f^{3} c^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{4}}-\frac{f^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x^{3}}{a d}+\frac{f^{3} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x^{3}}{a d}+\frac{f^{3} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c^{3}}{a \,d^{4}}+\frac{6 i e \,f^{2} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{6 i e \,f^{2} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{3 i e^{2} f \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}+\frac{3 i e^{2} f \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{3 i f^{3} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a \,d^{2}}+\frac{3 i f^{3} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a \,d^{2}}+\frac{3 e \,f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{3}}-\frac{3 e \,f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x^{2}}{a d}+\frac{3 e \,f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a d}+\frac{3 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) e^{2} f x}{a d}-\frac{3 \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) e^{2} f x}{a d}-\frac{3 e \,f^{2} c^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{3 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c \,e^{2} f}{a \,d^{2}}-\frac{3 e^{2} f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}-\frac{12 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{12 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}-\frac{6 i f^{3} c^{2} x}{a \,d^{3}}+\frac{12 i f^{2} e \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{12 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}-\frac{12 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{6 i f^{2} e \,x^{2}}{a d}"," ",0,"-12/a/d^2*f^2*e*ln(1-I*exp(I*(d*x+c)))*x-12/a/d^3*f^2*e*ln(1-I*exp(I*(d*x+c)))*c-12/a/d^3*f^2*e*c*ln(exp(I*(d*x+c)))-6*I/a/d^3*f^3*c^2*x+12*I/a/d^3*f^2*e*polylog(2,I*exp(I*(d*x+c)))+6*I/a/d*f^2*e*x^2+6*I/a/d^3*f^2*e*c^2+2*(f^3*x^3+3*e*f^2*x^2+3*e^2*f*x+e^3)/d/a/(exp(I*(d*x+c))+I)+12*I/a/d^2*f^2*e*c*x+6/a/d^2*f*ln(exp(I*(d*x+c)))*e^2+6/a/d^4*f^3*c^2*ln(exp(I*(d*x+c)))-6/a/d^4*f^3*c^2*ln(exp(I*(d*x+c))+I)+2*I/a/d*f^3*x^3-4*I/a/d^4*f^3*c^3-6/a/d^2*f*ln(exp(I*(d*x+c))+I)*e^2+1/a/d*e^3*ln(exp(I*(d*x+c))-1)-1/a/d*e^3*ln(exp(I*(d*x+c))+1)-6/a/d^2*f^3*ln(1-I*exp(I*(d*x+c)))*x^2-12*f^3*polylog(3,I*exp(I*(d*x+c)))/a/d^4+6*I*f^3*polylog(4,exp(I*(d*x+c)))/a/d^4-1/a/d^4*f^3*c^3*ln(exp(I*(d*x+c))-1)+6/a/d^3*e*f^2*polylog(3,exp(I*(d*x+c)))-6/a/d^3*e*f^2*polylog(3,-exp(I*(d*x+c)))+6/a/d^3*f^3*polylog(3,exp(I*(d*x+c)))*x-6/a/d^3*f^3*polylog(3,-exp(I*(d*x+c)))*x-6*I*f^3*polylog(4,-exp(I*(d*x+c)))/a/d^4+6/a/d^4*f^3*ln(1-I*exp(I*(d*x+c)))*c^2-1/a/d*f^3*ln(exp(I*(d*x+c))+1)*x^3+1/a/d*f^3*ln(1-exp(I*(d*x+c)))*x^3+1/a/d^4*f^3*ln(1-exp(I*(d*x+c)))*c^3+3/a/d^3*e*f^2*c^2*ln(exp(I*(d*x+c))-1)-3*I/a/d^2*e^2*f*polylog(2,exp(I*(d*x+c)))+3*I/a/d^2*e^2*f*polylog(2,-exp(I*(d*x+c)))-3*I/a/d^2*f^3*polylog(2,exp(I*(d*x+c)))*x^2+3*I/a/d^2*f^3*polylog(2,-exp(I*(d*x+c)))*x^2+12/a/d^3*f^2*e*c*ln(exp(I*(d*x+c))+I)+12*I/a/d^3*f^3*polylog(2,I*exp(I*(d*x+c)))*x+6*I/a/d^2*e*f^2*polylog(2,-exp(I*(d*x+c)))*x-6*I/a/d^2*e*f^2*polylog(2,exp(I*(d*x+c)))*x-3/a/d*e*f^2*ln(exp(I*(d*x+c))+1)*x^2+3/a/d*e*f^2*ln(1-exp(I*(d*x+c)))*x^2+3/a/d*ln(1-exp(I*(d*x+c)))*e^2*f*x-3/a/d*ln(exp(I*(d*x+c))+1)*e^2*f*x-3/a/d^3*e*f^2*c^2*ln(1-exp(I*(d*x+c)))+3/a/d^2*ln(1-exp(I*(d*x+c)))*c*e^2*f-3/a/d^2*e^2*f*c*ln(exp(I*(d*x+c))-1)","B"
198,1,643,223,0.236000," ","int((f*x+e)^2*csc(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{a \,d^{3}}-\frac{f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x^{2}}{a d}+\frac{f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{3}}+\frac{f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a d}-\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e}{a \,d^{2}}+\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{a \,d^{2}}+\frac{2 i f^{2} x^{2}}{a d}+\frac{2 i f^{2} c^{2}}{a \,d^{3}}-\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}-\frac{e^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a d}+\frac{e^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a d}-\frac{2 f^{2} \polylog \left(3, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{2 f^{2} \polylog \left(3, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{4 i f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{4 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}-\frac{4 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{2 i f^{2} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{2 e f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}+\frac{2 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) e f x}{a d}-\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) e f x}{a d}+\frac{2 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c e f}{a \,d^{2}}-\frac{2 i e f \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}+\frac{2 i e f \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{2 i f^{2} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{2 f^{2} x^{2}+4 f e x +2 e^{2}}{d a \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}+\frac{4 i f^{2} c x}{a \,d^{2}}"," ",0,"-1/a/d*e^2*ln(exp(I*(d*x+c))+1)+1/a/d*e^2*ln(exp(I*(d*x+c))-1)-4/a/d^2*f*ln(exp(I*(d*x+c))+I)*e+4/a/d^2*f*ln(exp(I*(d*x+c)))*e-4/a/d^2*f^2*ln(1-I*exp(I*(d*x+c)))*x-4/a/d^3*f^2*ln(1-I*exp(I*(d*x+c)))*c+4/a/d^3*f^2*c*ln(exp(I*(d*x+c))+I)-4/a/d^3*f^2*c*ln(exp(I*(d*x+c)))+2*I/a/d*f^2*x^2+2*I/a/d^3*f^2*c^2-2/a/d^2*e*f*c*ln(exp(I*(d*x+c))-1)+2/a/d*ln(1-exp(I*(d*x+c)))*e*f*x-2/a/d*ln(exp(I*(d*x+c))+1)*e*f*x+2/a/d^2*ln(1-exp(I*(d*x+c)))*c*e*f-1/a/d^3*f^2*ln(1-exp(I*(d*x+c)))*c^2-1/a/d*f^2*ln(exp(I*(d*x+c))+1)*x^2+1/a/d^3*f^2*c^2*ln(exp(I*(d*x+c))-1)-2*I/a/d^2*e*f*polylog(2,exp(I*(d*x+c)))+2*I/a/d^2*e*f*polylog(2,-exp(I*(d*x+c)))-2*I/a/d^2*f^2*polylog(2,exp(I*(d*x+c)))*x+2*I/a/d^2*f^2*polylog(2,-exp(I*(d*x+c)))*x+2*(f^2*x^2+2*e*f*x+e^2)/d/a/(exp(I*(d*x+c))+I)+4*I/a/d^2*f^2*c*x+1/a/d*f^2*ln(1-exp(I*(d*x+c)))*x^2-2*f^2*polylog(3,-exp(I*(d*x+c)))/a/d^3+2*f^2*polylog(3,exp(I*(d*x+c)))/a/d^3+4*I*f^2*polylog(2,I*exp(I*(d*x+c)))/a/d^3","B"
199,1,245,114,0.243000," ","int((f*x+e)*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{2 f x +2 e}{d a \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}-\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a d}+\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a d}-\frac{f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}-\frac{i f \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}+\frac{i f \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{2 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{2}}+\frac{2 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) f x}{a d}+\frac{\ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) f x}{a d}+\frac{\ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c f}{a \,d^{2}}"," ",0,"2*(f*x+e)/d/a/(exp(I*(d*x+c))+I)-1/a/d*e*ln(exp(I*(d*x+c))+1)+1/a/d*e*ln(exp(I*(d*x+c))-1)-1/a/d^2*f*c*ln(exp(I*(d*x+c))-1)-I*f*polylog(2,exp(I*(d*x+c)))/a/d^2+I*f*polylog(2,-exp(I*(d*x+c)))/a/d^2-2/a/d^2*f*ln(exp(I*(d*x+c))+I)+2/a/d^2*f*ln(exp(I*(d*x+c)))-1/a/d*ln(exp(I*(d*x+c))+1)*f*x+1/a/d*ln(1-exp(I*(d*x+c)))*f*x+1/a/d^2*ln(1-exp(I*(d*x+c)))*c*f","B"
200,1,40,38,0.086000," ","int(csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/a/d*ln(tan(1/2*d*x+1/2*c))+2/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
201,0,0,28,5.110000," ","int(csc(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","\int \frac{\csc \left(d x +c \right)}{\left(f x +e \right) \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(csc(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","F"
202,0,0,28,10.398000," ","int(csc(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\int \frac{\csc \left(d x +c \right)}{\left(f x +e \right)^{2} \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(csc(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x)","F"
203,1,1705,419,0.446000," ","int((f*x+e)^3*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{2 \left(-2 f^{3} x^{3}+i {\mathrm e}^{i \left(d x +c \right)} f^{3} x^{3}-6 e \,f^{2} x^{2}+3 i {\mathrm e}^{i \left(d x +c \right)} e \,f^{2} x^{2}-6 e^{2} f x +3 i {\mathrm e}^{i \left(d x +c \right)} e^{2} f x -2 e^{3}+i {\mathrm e}^{i \left(d x +c \right)} e^{3}+f^{3} x^{3} {\mathrm e}^{2 i \left(d x +c \right)}+3 e \,f^{2} x^{2} {\mathrm e}^{2 i \left(d x +c \right)}+3 e^{2} f x \,{\mathrm e}^{2 i \left(d x +c \right)}+e^{3} {\mathrm e}^{2 i \left(d x +c \right)}\right)}{\left({\mathrm e}^{2 i \left(d x +c \right)}-1\right) \left({\mathrm e}^{i \left(d x +c \right)}+i\right) d a}-\frac{6 i f^{3} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}-\frac{6 i e \,f^{2} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{12 f^{3} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{24 i f^{2} e c x}{a \,d^{2}}+\frac{6 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{2}}{a \,d^{2}}+\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a \,d^{2}}-\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{a \,d^{4}}-\frac{12 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e^{2}}{a \,d^{2}}-\frac{4 i f^{3} x^{3}}{a d}-\frac{12 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}+\frac{8 i f^{3} c^{3}}{a \,d^{4}}+\frac{6 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{4}}-\frac{e^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a d}+\frac{e^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a d}-\frac{12 i f^{3} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}-\frac{12 i f^{2} e \,c^{2}}{a \,d^{3}}+\frac{6 f^{3} \polylog \left(3, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}+\frac{6 f^{3} \polylog \left(3, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{6 i f^{3} \polylog \left(4, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{6 e \,f^{2} \polylog \left(3, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{6 e \,f^{2} \polylog \left(3, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{6 f^{3} \polylog \left(3, {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}+\frac{6 f^{3} \polylog \left(3, -{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}+\frac{6 i f^{3} \polylog \left(4, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}+\frac{f^{3} c^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{4}}+\frac{f^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x^{3}}{a d}-\frac{f^{3} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x^{3}}{a d}-\frac{f^{3} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c^{3}}{a \,d^{4}}-\frac{6 i e \,f^{2} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{6 i e \,f^{2} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{3 i e^{2} f \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{3 i e^{2} f \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}+\frac{3 i f^{3} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a \,d^{2}}-\frac{3 i f^{3} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a \,d^{2}}-\frac{3 e \,f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{3}}+\frac{3 e \,f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x^{2}}{a d}-\frac{3 e \,f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a d}-\frac{3 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) e^{2} f x}{a d}+\frac{3 \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) e^{2} f x}{a d}+\frac{3 e \,f^{2} c^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{3 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c \,e^{2} f}{a \,d^{2}}+\frac{3 e^{2} f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}+\frac{12 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{12 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}+\frac{3 f^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x^{2}}{a \,d^{2}}+\frac{3 f^{3} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a \,d^{2}}-\frac{3 f^{3} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{a \,d^{4}}+\frac{3 e^{2} f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a \,d^{2}}+\frac{3 e^{2} f \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}+\frac{3 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{4}}+\frac{12 i f^{3} c^{2} x}{a \,d^{3}}-\frac{12 i f^{2} e \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{12 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}+\frac{24 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{6 e \,f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{3}}-\frac{6 i e \,f^{2} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{6 i f^{3} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}+\frac{6 e \,f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{6 e \,f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}+\frac{6 e \,f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x}{a \,d^{2}}-\frac{12 i f^{2} e \,x^{2}}{a d}"," ",0,"12/a/d^2*f^2*e*ln(1-I*exp(I*(d*x+c)))*x+12/a/d^3*f^2*e*ln(1-I*exp(I*(d*x+c)))*c+24/a/d^3*f^2*e*c*ln(exp(I*(d*x+c)))-6/a/d^3*e*f^2*c*ln(exp(I*(d*x+c))-1)-6*I/a/d^2*e*f^2*polylog(2,-exp(I*(d*x+c)))*x+6*I/a/d^2*e*f^2*polylog(2,exp(I*(d*x+c)))*x-24*I/a/d^2*e*f^2*c*x-6*I/a/d^3*e*f^2*polylog(2,-exp(I*(d*x+c)))-3*I/a/d^2*e^2*f*polylog(2,-exp(I*(d*x+c)))+3*I/a/d^2*e^2*f*polylog(2,exp(I*(d*x+c)))-6*I/a/d^3*f^3*polylog(2,-exp(I*(d*x+c)))*x-6*I/a/d^3*f^3*polylog(2,exp(I*(d*x+c)))*x-12*I/a/d^3*e*f^2*c^2-3*I/a/d^2*f^3*polylog(2,-exp(I*(d*x+c)))*x^2+3*I/a/d^2*f^3*polylog(2,exp(I*(d*x+c)))*x^2+3/a/d^2*f^3*ln(exp(I*(d*x+c))+1)*x^2+3/a/d^2*f^3*ln(1-exp(I*(d*x+c)))*x^2-3/a/d^4*f^3*ln(1-exp(I*(d*x+c)))*c^2+3/a/d^2*e^2*f*ln(exp(I*(d*x+c))+1)+3/a/d^2*e^2*f*ln(exp(I*(d*x+c))-1)+3/a/d^4*f^3*c^2*ln(exp(I*(d*x+c))-1)+8*I/a/d^4*f^3*c^3-4*I/a/d*f^3*x^3-12/a/d^2*f*ln(exp(I*(d*x+c)))*e^2-12/a/d^4*f^3*c^2*ln(exp(I*(d*x+c)))+6/a/d^4*f^3*c^2*ln(exp(I*(d*x+c))+I)+6/a/d^2*f*ln(exp(I*(d*x+c))+I)*e^2-1/a/d*e^3*ln(exp(I*(d*x+c))-1)+1/a/d*e^3*ln(exp(I*(d*x+c))+1)-12*I/a/d^3*f^3*polylog(2,I*exp(I*(d*x+c)))*x-12*I/a/d^3*e*f^2*polylog(2,I*exp(I*(d*x+c)))+6/a/d^2*f^3*ln(1-I*exp(I*(d*x+c)))*x^2+6/a/d^2*e*f^2*ln(1-exp(I*(d*x+c)))*x+6/a/d^3*e*f^2*ln(1-exp(I*(d*x+c)))*c+6/a/d^2*e*f^2*ln(exp(I*(d*x+c))+1)*x+12*I/a/d^3*f^3*c^2*x-12*I/a/d*e*f^2*x^2-6*I/a/d^3*e*f^2*polylog(2,exp(I*(d*x+c)))+6*f^3*polylog(3,-exp(I*(d*x+c)))/a/d^4+6*f^3*polylog(3,exp(I*(d*x+c)))/a/d^4+12*f^3*polylog(3,I*exp(I*(d*x+c)))/a/d^4+6*I*f^3*polylog(4,-exp(I*(d*x+c)))/a/d^4-6*I*f^3*polylog(4,exp(I*(d*x+c)))/a/d^4+1/a/d^4*f^3*c^3*ln(exp(I*(d*x+c))-1)-6/a/d^3*e*f^2*polylog(3,exp(I*(d*x+c)))+6/a/d^3*e*f^2*polylog(3,-exp(I*(d*x+c)))-6/a/d^3*f^3*polylog(3,exp(I*(d*x+c)))*x+6/a/d^3*f^3*polylog(3,-exp(I*(d*x+c)))*x-6/a/d^4*f^3*ln(1-I*exp(I*(d*x+c)))*c^2+1/a/d*f^3*ln(exp(I*(d*x+c))+1)*x^3-1/a/d*f^3*ln(1-exp(I*(d*x+c)))*x^3-1/a/d^4*f^3*ln(1-exp(I*(d*x+c)))*c^3-3/a/d^3*e*f^2*c^2*ln(exp(I*(d*x+c))-1)-12/a/d^3*f^2*e*c*ln(exp(I*(d*x+c))+I)-2*(-2*f^3*x^3+I*exp(I*(d*x+c))*f^3*x^3-6*e*f^2*x^2+3*I*exp(I*(d*x+c))*e*f^2*x^2-6*e^2*f*x+3*I*exp(I*(d*x+c))*e^2*f*x-2*e^3+I*exp(I*(d*x+c))*e^3+f^3*x^3*exp(2*I*(d*x+c))+3*e*f^2*x^2*exp(2*I*(d*x+c))+3*e^2*f*x*exp(2*I*(d*x+c))+e^3*exp(2*I*(d*x+c)))/(exp(2*I*(d*x+c))-1)/(exp(I*(d*x+c))+I)/d/a+3/a/d*e*f^2*ln(exp(I*(d*x+c))+1)*x^2-3/a/d*e*f^2*ln(1-exp(I*(d*x+c)))*x^2-3/a/d*ln(1-exp(I*(d*x+c)))*e^2*f*x+3/a/d*ln(exp(I*(d*x+c))+1)*e^2*f*x+3/a/d^3*e*f^2*c^2*ln(1-exp(I*(d*x+c)))-3/a/d^2*ln(1-exp(I*(d*x+c)))*c*e^2*f+3/a/d^2*e^2*f*c*ln(exp(I*(d*x+c))-1)","B"
204,1,942,296,0.285000," ","int((f*x+e)^2*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{a \,d^{3}}+\frac{f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x^{2}}{a d}-\frac{f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{3}}-\frac{f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{a d}+\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e}{a \,d^{2}}-\frac{8 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{a \,d^{2}}-\frac{4 i f^{2} x^{2}}{a d}-\frac{4 i f^{2} c^{2}}{a \,d^{3}}+\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}-\frac{2 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{3}}+\frac{2 e f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a \,d^{2}}+\frac{2 e f \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}+\frac{2 f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{2 f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}+\frac{2 f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x}{a \,d^{2}}-\frac{2 i f^{2} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{2 i f^{2} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{e^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a d}-\frac{e^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a d}+\frac{2 f^{2} \polylog \left(3, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{2 f^{2} \polylog \left(3, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{4 i f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{4 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}+\frac{8 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{2 i f^{2} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{2 e f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}-\frac{2 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) e f x}{a d}+\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) e f x}{a d}-\frac{2 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c e f}{a \,d^{2}}+\frac{2 i e f \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{2 i e f \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}+\frac{2 i f^{2} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{8 i f^{2} c x}{a \,d^{2}}-\frac{2 \left(-2 f^{2} x^{2}+i {\mathrm e}^{i \left(d x +c \right)} f^{2} x^{2}-4 f e x +2 i {\mathrm e}^{i \left(d x +c \right)} e f x -2 e^{2}+i {\mathrm e}^{i \left(d x +c \right)} e^{2}+f^{2} x^{2} {\mathrm e}^{2 i \left(d x +c \right)}+2 e f x \,{\mathrm e}^{2 i \left(d x +c \right)}+e^{2} {\mathrm e}^{2 i \left(d x +c \right)}\right)}{\left({\mathrm e}^{2 i \left(d x +c \right)}-1\right) \left({\mathrm e}^{i \left(d x +c \right)}+i\right) d a}"," ",0,"-2/a/d^3*f^2*c*ln(exp(I*(d*x+c))-1)+2/a/d^2*e*f*ln(exp(I*(d*x+c))+1)+2/a/d^2*e*f*ln(exp(I*(d*x+c))-1)+2/a/d^2*f^2*ln(1-exp(I*(d*x+c)))*x+2/a/d^3*f^2*ln(1-exp(I*(d*x+c)))*c+2/a/d^2*f^2*ln(exp(I*(d*x+c))+1)*x+1/a/d*e^2*ln(exp(I*(d*x+c))+1)-1/a/d*e^2*ln(exp(I*(d*x+c))-1)+4/a/d^2*f*ln(exp(I*(d*x+c))+I)*e-8/a/d^2*f*ln(exp(I*(d*x+c)))*e+4/a/d^2*f^2*ln(1-I*exp(I*(d*x+c)))*x+4/a/d^3*f^2*ln(1-I*exp(I*(d*x+c)))*c-4/a/d^3*f^2*c*ln(exp(I*(d*x+c))+I)+8/a/d^3*f^2*c*ln(exp(I*(d*x+c)))-2*I/a/d^3*f^2*polylog(2,-exp(I*(d*x+c)))-4*I/a/d*f^2*x^2-4*I/a/d^3*f^2*c^2+2/a/d^2*e*f*c*ln(exp(I*(d*x+c))-1)-2/a/d*ln(1-exp(I*(d*x+c)))*e*f*x+2/a/d*ln(exp(I*(d*x+c))+1)*e*f*x-2/a/d^2*ln(1-exp(I*(d*x+c)))*c*e*f+1/a/d^3*f^2*ln(1-exp(I*(d*x+c)))*c^2+1/a/d*f^2*ln(exp(I*(d*x+c))+1)*x^2-1/a/d^3*f^2*c^2*ln(exp(I*(d*x+c))-1)-1/a/d*f^2*ln(1-exp(I*(d*x+c)))*x^2-8*I/a/d^2*f^2*c*x-2*I/a/d^2*f^2*polylog(2,-exp(I*(d*x+c)))*x+2*I/a/d^2*e*f*polylog(2,exp(I*(d*x+c)))-2*I/a/d^2*e*f*polylog(2,-exp(I*(d*x+c)))+2*I/a/d^2*f^2*polylog(2,exp(I*(d*x+c)))*x-2*(-2*f^2*x^2+I*exp(I*(d*x+c))*f^2*x^2-4*f*e*x+2*I*exp(I*(d*x+c))*e*f*x-2*e^2+I*exp(I*(d*x+c))*e^2+f^2*x^2*exp(2*I*(d*x+c))+2*e*f*x*exp(2*I*(d*x+c))+e^2*exp(2*I*(d*x+c)))/(exp(2*I*(d*x+c))-1)/(exp(I*(d*x+c))+I)/d/a-2*I*f^2*polylog(2,exp(I*(d*x+c)))/a/d^3+2*f^2*polylog(3,-exp(I*(d*x+c)))/a/d^3-2*f^2*polylog(3,exp(I*(d*x+c)))/a/d^3-4*I*f^2*polylog(2,I*exp(I*(d*x+c)))/a/d^3","B"
205,1,351,149,0.303000," ","int((f*x+e)*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{2 \left(-2 f x +i {\mathrm e}^{i \left(d x +c \right)} f x -2 e +i {\mathrm e}^{i \left(d x +c \right)} e +f x \,{\mathrm e}^{2 i \left(d x +c \right)}+e \,{\mathrm e}^{2 i \left(d x +c \right)}\right)}{\left({\mathrm e}^{2 i \left(d x +c \right)}-1\right) \left({\mathrm e}^{i \left(d x +c \right)}+i\right) d a}+\frac{i f \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{i f \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}+\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a d}-\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a d}+\frac{f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}+\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) f x}{a d}-\frac{\ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) f x}{a d}-\frac{\ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c f}{a \,d^{2}}+\frac{2 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{2}}-\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}+\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a \,d^{2}}+\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}"," ",0,"-2*(-2*f*x+I*exp(I*(d*x+c))*f*x-2*e+I*exp(I*(d*x+c))*e+f*x*exp(2*I*(d*x+c))+e*exp(2*I*(d*x+c)))/(exp(2*I*(d*x+c))-1)/(exp(I*(d*x+c))+I)/d/a+I*f*polylog(2,exp(I*(d*x+c)))/a/d^2-I*f*polylog(2,-exp(I*(d*x+c)))/a/d^2+1/a/d*e*ln(exp(I*(d*x+c))+1)-1/a/d*e*ln(exp(I*(d*x+c))-1)+1/a/d^2*f*c*ln(exp(I*(d*x+c))-1)+1/a/d*ln(exp(I*(d*x+c))+1)*f*x-1/a/d*ln(1-exp(I*(d*x+c)))*f*x-1/a/d^2*ln(1-exp(I*(d*x+c)))*c*f+2/a/d^2*f*ln(exp(I*(d*x+c))+I)-4/a/d^2*f*ln(exp(I*(d*x+c)))+1/a/d^2*f*ln(exp(I*(d*x+c))+1)+1/a/d^2*f*ln(exp(I*(d*x+c))-1)","B"
206,1,77,51,0.095000," ","int(csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-1/2/a/d/tan(1/2*d*x+1/2*c)-1/a/d*ln(tan(1/2*d*x+1/2*c))-2/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
207,0,0,30,4.754000," ","int(csc(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x)","\int \frac{\csc^{2}\left(d x +c \right)}{\left(f x +e \right) \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(csc(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x)","F"
208,0,0,30,7.478000," ","int(csc(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\int \frac{\csc^{2}\left(d x +c \right)}{\left(f x +e \right)^{2} \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(csc(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x)","F"
209,1,2257,540,0.445000," ","int((f*x+e)^3*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-12/a/d^2*f^2*e*ln(1-I*exp(I*(d*x+c)))*x-12/a/d^3*f^2*e*ln(1-I*exp(I*(d*x+c)))*c-24/a/d^3*f^2*e*c*ln(exp(I*(d*x+c)))+9*I/a/d^2*polylog(2,-exp(I*(d*x+c)))*e*f^2*x-9*I/a/d^2*polylog(2,exp(I*(d*x+c)))*e*f^2*x+24*I/a/d^2*c*e*f^2*x+12*I/a/d^3*f^2*e*polylog(2,I*exp(I*(d*x+c)))+6/a/d^3*e*f^2*c*ln(exp(I*(d*x+c))-1)+(-3*I*f^3*x^2*exp(4*I*(d*x+c))-3*I*e^2*f*exp(4*I*(d*x+c))-5*d*f^3*x^3*exp(2*I*(d*x+c))+3*I*e^2*f*exp(2*I*(d*x+c))+3*I*f^3*x^2*exp(2*I*(d*x+c))-I*d*e^3*exp(I*(d*x+c))+4*d*f^3*x^3+12*d*e*f^2*x^2+12*d*e^2*f*x-3*f^3*x^2*exp(I*(d*x+c))-3*exp(I*(d*x+c))*e^2*f+4*d*e^3-3*I*d*e*f^2*x^2*exp(I*(d*x+c))-3*I*d*e^2*f*x*exp(I*(d*x+c))-5*d*e^3*exp(2*I*(d*x+c))+3*d*e^3*exp(4*I*(d*x+c))+3*f^3*x^2*exp(3*I*(d*x+c))+3*e^2*f*exp(3*I*(d*x+c))+6*e*f^2*x*exp(3*I*(d*x+c))+3*d*f^3*x^3*exp(4*I*(d*x+c))+3*I*d*e^3*exp(3*I*(d*x+c))-6*e*f^2*x*exp(I*(d*x+c))-15*d*e^2*f*x*exp(2*I*(d*x+c))+6*I*e*f^2*x*exp(2*I*(d*x+c))+9*d*e*f^2*x^2*exp(4*I*(d*x+c))+9*d*e^2*f*x*exp(4*I*(d*x+c))+3*I*d*f^3*x^3*exp(3*I*(d*x+c))-I*d*f^3*x^3*exp(I*(d*x+c))-15*d*e*f^2*x^2*exp(2*I*(d*x+c))+9*I*d*e*f^2*x^2*exp(3*I*(d*x+c))+9*I*d*e^2*f*x*exp(3*I*(d*x+c))-6*I*e*f^2*x*exp(4*I*(d*x+c)))/(exp(2*I*(d*x+c))-1)^2/d^2/(exp(I*(d*x+c))+I)/a-3/a/d^2*f^3*ln(exp(I*(d*x+c))+1)*x^2-3/a/d^2*f^3*ln(1-exp(I*(d*x+c)))*x^2+3/a/d^4*f^3*ln(1-exp(I*(d*x+c)))*c^2-3/a/d^2*e^2*f*ln(exp(I*(d*x+c))+1)-3/a/d^2*e^2*f*ln(exp(I*(d*x+c))-1)-3/a/d^4*f^3*c^2*ln(exp(I*(d*x+c))-1)+12/a/d^2*f*ln(exp(I*(d*x+c)))*e^2+12/a/d^4*f^3*c^2*ln(exp(I*(d*x+c)))-6/a/d^4*f^3*c^2*ln(exp(I*(d*x+c))+I)-6/a/d^2*f*ln(exp(I*(d*x+c))+I)*e^2+3/2/a/d*e^3*ln(exp(I*(d*x+c))-1)-3/2/a/d*e^3*ln(exp(I*(d*x+c))+1)-3/a/d^3*f^3*ln(exp(I*(d*x+c))+1)*x+3/a/d^3*f^3*ln(1-exp(I*(d*x+c)))*x+3/a/d^4*f^3*ln(1-exp(I*(d*x+c)))*c+4*I/a/d*f^3*x^3-8*I/a/d^4*f^3*c^3-6/a/d^2*f^3*ln(1-I*exp(I*(d*x+c)))*x^2+3/a/d^3*e*f^2*ln(exp(I*(d*x+c))-1)-3/a/d^3*e*f^2*ln(exp(I*(d*x+c))+1)-3/a/d^4*f^3*c*ln(exp(I*(d*x+c))-1)-6/a/d^2*e*f^2*ln(1-exp(I*(d*x+c)))*x-6/a/d^3*e*f^2*ln(1-exp(I*(d*x+c)))*c-6/a/d^2*e*f^2*ln(exp(I*(d*x+c))+1)*x-6*f^3*polylog(3,-exp(I*(d*x+c)))/a/d^4-6*f^3*polylog(3,exp(I*(d*x+c)))/a/d^4-12*f^3*polylog(3,I*exp(I*(d*x+c)))/a/d^4+9*I*f^3*polylog(4,exp(I*(d*x+c)))/a/d^4+3*I*f^3*polylog(2,-exp(I*(d*x+c)))/a/d^4-3*I*f^3*polylog(2,exp(I*(d*x+c)))/a/d^4-9*I*f^3*polylog(4,-exp(I*(d*x+c)))/a/d^4-3/2/a/d^4*f^3*c^3*ln(exp(I*(d*x+c))-1)+9/a/d^3*e*f^2*polylog(3,exp(I*(d*x+c)))-9/a/d^3*e*f^2*polylog(3,-exp(I*(d*x+c)))+9/a/d^3*f^3*polylog(3,exp(I*(d*x+c)))*x-9/a/d^3*f^3*polylog(3,-exp(I*(d*x+c)))*x+6/a/d^4*f^3*ln(1-I*exp(I*(d*x+c)))*c^2-3/2/a/d*f^3*ln(exp(I*(d*x+c))+1)*x^3+3/2/a/d*f^3*ln(1-exp(I*(d*x+c)))*x^3+3/2/a/d^4*f^3*ln(1-exp(I*(d*x+c)))*c^3+9/2/a/d^3*e*f^2*c^2*ln(exp(I*(d*x+c))-1)+12/a/d^3*f^2*e*c*ln(exp(I*(d*x+c))+I)+12*I/a/d^3*f^3*polylog(2,I*exp(I*(d*x+c)))*x-9/2/a/d*e*f^2*ln(exp(I*(d*x+c))+1)*x^2+9/2/a/d*e*f^2*ln(1-exp(I*(d*x+c)))*x^2+9/2/a/d*ln(1-exp(I*(d*x+c)))*e^2*f*x-9/2/a/d*ln(exp(I*(d*x+c))+1)*e^2*f*x-9/2/a/d^3*e*f^2*c^2*ln(1-exp(I*(d*x+c)))+9/2/a/d^2*ln(1-exp(I*(d*x+c)))*c*e^2*f-9/2/a/d^2*e^2*f*c*ln(exp(I*(d*x+c))-1)+12*I/a/d*e*f^2*x^2-9/2*I/a/d^2*e^2*f*polylog(2,exp(I*(d*x+c)))+9/2*I/a/d^2*e^2*f*polylog(2,-exp(I*(d*x+c)))-12*I/a/d^3*f^3*c^2*x+12*I/a/d^3*c^2*e*f^2+6*I/a/d^3*e*f^2*polylog(2,exp(I*(d*x+c)))+6*I/a/d^3*e*f^2*polylog(2,-exp(I*(d*x+c)))-9/2*I/a/d^2*f^3*polylog(2,exp(I*(d*x+c)))*x^2+9/2*I/a/d^2*f^3*polylog(2,-exp(I*(d*x+c)))*x^2+6*I/a/d^3*f^3*polylog(2,-exp(I*(d*x+c)))*x+6*I/a/d^3*f^3*polylog(2,exp(I*(d*x+c)))*x","B"
210,1,1215,359,0.375000," ","int((f*x+e)^2*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{d^{3} a}+\frac{f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{d^{3} a}-\frac{3 f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{2 a \,d^{3}}-\frac{3 f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x^{2}}{2 a d}+\frac{3 f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{2 a \,d^{3}}+\frac{3 f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{2 a d}-\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e}{a \,d^{2}}+\frac{8 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{a \,d^{2}}+\frac{4 i f^{2} x^{2}}{a d}+\frac{4 i f^{2} c^{2}}{a \,d^{3}}-\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{4 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}+\frac{2 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{3}}-\frac{2 e f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a \,d^{2}}-\frac{2 e f \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}-\frac{2 f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{2 f^{2} \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}-\frac{2 f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x}{a \,d^{2}}+\frac{2 i f^{2} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{2 i f^{2} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{3 e^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{2 a d}+\frac{3 e^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{2 a d}-\frac{3 f^{2} \polylog \left(3, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{3 f^{2} \polylog \left(3, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{4 i f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{4 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}-\frac{8 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{3 i f^{2} \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}-\frac{3 e f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}+\frac{3 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) e f x}{a d}-\frac{3 \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) e f x}{a d}+\frac{3 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c e f}{a \,d^{2}}-\frac{3 i e f \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}+\frac{3 i e f \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{3 i f^{2} \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{8 i f^{2} c x}{a \,d^{2}}+\frac{3 d \,f^{2} x^{2} {\mathrm e}^{4 i \left(d x +c \right)}+6 d e f x \,{\mathrm e}^{4 i \left(d x +c \right)}+3 d \,e^{2} {\mathrm e}^{4 i \left(d x +c \right)}-5 d \,f^{2} x^{2} {\mathrm e}^{2 i \left(d x +c \right)}-i d \,e^{2} {\mathrm e}^{i \left(d x +c \right)}-10 d e f x \,{\mathrm e}^{2 i \left(d x +c \right)}+2 f^{2} x \,{\mathrm e}^{3 i \left(d x +c \right)}+2 i e f \,{\mathrm e}^{2 i \left(d x +c \right)}+6 i d e f x \,{\mathrm e}^{3 i \left(d x +c \right)}-5 d \,e^{2} {\mathrm e}^{2 i \left(d x +c \right)}+4 d \,f^{2} x^{2}+2 e f \,{\mathrm e}^{3 i \left(d x +c \right)}+3 i d \,e^{2} {\mathrm e}^{3 i \left(d x +c \right)}-i d \,f^{2} x^{2} {\mathrm e}^{i \left(d x +c \right)}-2 i d e f x \,{\mathrm e}^{i \left(d x +c \right)}+8 d e f x -2 f^{2} x \,{\mathrm e}^{i \left(d x +c \right)}-2 i e f \,{\mathrm e}^{4 i \left(d x +c \right)}+3 i d \,f^{2} x^{2} {\mathrm e}^{3 i \left(d x +c \right)}+4 d \,e^{2}-2 \,{\mathrm e}^{i \left(d x +c \right)} e f -2 i f^{2} x \,{\mathrm e}^{4 i \left(d x +c \right)}+2 i f^{2} x \,{\mathrm e}^{2 i \left(d x +c \right)}}{\left({\mathrm e}^{2 i \left(d x +c \right)}-1\right)^{2} d^{2} \left({\mathrm e}^{i \left(d x +c \right)}+i\right) a}"," ",0,"-1/d^3/a*f^2*ln(exp(I*(d*x+c))+1)+1/d^3/a*f^2*ln(exp(I*(d*x+c))-1)+2/a/d^3*f^2*c*ln(exp(I*(d*x+c))-1)-2/a/d^2*e*f*ln(exp(I*(d*x+c))+1)-2/a/d^2*e*f*ln(exp(I*(d*x+c))-1)-2/a/d^2*f^2*ln(1-exp(I*(d*x+c)))*x-2/a/d^3*f^2*ln(1-exp(I*(d*x+c)))*c-2/a/d^2*f^2*ln(exp(I*(d*x+c))+1)*x-3/2/a/d*e^2*ln(exp(I*(d*x+c))+1)+3/2/a/d*e^2*ln(exp(I*(d*x+c))-1)-4/a/d^2*f*ln(exp(I*(d*x+c))+I)*e+8/a/d^2*f*ln(exp(I*(d*x+c)))*e-4/a/d^2*f^2*ln(1-I*exp(I*(d*x+c)))*x-4/a/d^3*f^2*ln(1-I*exp(I*(d*x+c)))*c+4/a/d^3*f^2*c*ln(exp(I*(d*x+c))+I)-8/a/d^3*f^2*c*ln(exp(I*(d*x+c)))-3/a/d^2*e*f*c*ln(exp(I*(d*x+c))-1)+3/a/d*ln(1-exp(I*(d*x+c)))*e*f*x-3/a/d*ln(exp(I*(d*x+c))+1)*e*f*x+3/a/d^2*ln(1-exp(I*(d*x+c)))*c*e*f-3/2/a/d^3*f^2*ln(1-exp(I*(d*x+c)))*c^2-3/2/a/d*f^2*ln(exp(I*(d*x+c))+1)*x^2+3/2/a/d^3*f^2*c^2*ln(exp(I*(d*x+c))-1)+3/2/a/d*f^2*ln(1-exp(I*(d*x+c)))*x^2+2*I*f^2*polylog(2,-exp(I*(d*x+c)))/a/d^3+4*I/d/a*f^2*x^2+4*I/d^3/a*c^2*f^2+2*I/d^3/a*f^2*polylog(2,exp(I*(d*x+c)))-3*f^2*polylog(3,-exp(I*(d*x+c)))/a/d^3+3*f^2*polylog(3,exp(I*(d*x+c)))/a/d^3+4*I*f^2*polylog(2,I*exp(I*(d*x+c)))/a/d^3+3*I/d^2/a*polylog(2,-exp(I*(d*x+c)))*f^2*x-3*I/d^2/a*polylog(2,exp(I*(d*x+c)))*f^2*x+8*I/d^2/a*c*f^2*x-3*I/d^2/a*e*f*polylog(2,exp(I*(d*x+c)))+3*I/d^2/a*e*f*polylog(2,-exp(I*(d*x+c)))+(3*d*f^2*x^2*exp(4*I*(d*x+c))+6*d*e*f*x*exp(4*I*(d*x+c))+3*d*e^2*exp(4*I*(d*x+c))-5*d*f^2*x^2*exp(2*I*(d*x+c))-I*d*e^2*exp(I*(d*x+c))-10*d*e*f*x*exp(2*I*(d*x+c))+2*f^2*x*exp(3*I*(d*x+c))+2*I*e*f*exp(2*I*(d*x+c))+6*I*d*e*f*x*exp(3*I*(d*x+c))-5*d*e^2*exp(2*I*(d*x+c))+4*d*f^2*x^2+2*e*f*exp(3*I*(d*x+c))+3*I*d*e^2*exp(3*I*(d*x+c))-I*d*f^2*x^2*exp(I*(d*x+c))-2*I*d*e*f*x*exp(I*(d*x+c))+8*d*e*f*x-2*f^2*x*exp(I*(d*x+c))-2*I*e*f*exp(4*I*(d*x+c))+3*I*d*f^2*x^2*exp(3*I*(d*x+c))+4*d*e^2-2*exp(I*(d*x+c))*e*f-2*I*f^2*x*exp(4*I*(d*x+c))+2*I*f^2*x*exp(2*I*(d*x+c)))/(exp(2*I*(d*x+c))-1)^2/d^2/(exp(I*(d*x+c))+I)/a","B"
211,1,468,188,0.392000," ","int((f*x+e)*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{3 d f x \,{\mathrm e}^{4 i \left(d x +c \right)}+3 d e \,{\mathrm e}^{4 i \left(d x +c \right)}-5 d f x \,{\mathrm e}^{2 i \left(d x +c \right)}+3 i d f x \,{\mathrm e}^{3 i \left(d x +c \right)}-5 d e \,{\mathrm e}^{2 i \left(d x +c \right)}+f \,{\mathrm e}^{3 i \left(d x +c \right)}+3 i d e \,{\mathrm e}^{3 i \left(d x +c \right)}-i f \,{\mathrm e}^{4 i \left(d x +c \right)}+4 d f x -i d f x \,{\mathrm e}^{i \left(d x +c \right)}+4 d e -{\mathrm e}^{i \left(d x +c \right)} f -i d e \,{\mathrm e}^{i \left(d x +c \right)}+i f \,{\mathrm e}^{2 i \left(d x +c \right)}}{\left({\mathrm e}^{2 i \left(d x +c \right)}-1\right)^{2} d^{2} \left({\mathrm e}^{i \left(d x +c \right)}+i\right) a}-\frac{3 i f \polylog \left(2, {\mathrm e}^{i \left(d x +c \right)}\right)}{2 a \,d^{2}}+\frac{3 i f \polylog \left(2, -{\mathrm e}^{i \left(d x +c \right)}\right)}{2 a \,d^{2}}-\frac{3 e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{2 a d}+\frac{3 e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{2 a d}-\frac{3 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{2 a \,d^{2}}-\frac{3 \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) f x}{2 a d}+\frac{3 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) f x}{2 a d}+\frac{3 \ln \left(1-{\mathrm e}^{i \left(d x +c \right)}\right) c f}{2 a \,d^{2}}-\frac{2 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{2}}+\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a \,d^{2}}-\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}"," ",0,"(3*d*f*x*exp(4*I*(d*x+c))+3*d*e*exp(4*I*(d*x+c))-5*d*f*x*exp(2*I*(d*x+c))+3*I*d*f*x*exp(3*I*(d*x+c))-5*d*e*exp(2*I*(d*x+c))+f*exp(3*I*(d*x+c))+3*I*d*e*exp(3*I*(d*x+c))-I*f*exp(4*I*(d*x+c))+4*d*f*x-I*d*f*x*exp(I*(d*x+c))+4*d*e-exp(I*(d*x+c))*f-I*d*e*exp(I*(d*x+c))+I*f*exp(2*I*(d*x+c)))/(exp(2*I*(d*x+c))-1)^2/d^2/(exp(I*(d*x+c))+I)/a-3/2*I*f*polylog(2,exp(I*(d*x+c)))/a/d^2+3/2*I*f*polylog(2,-exp(I*(d*x+c)))/a/d^2-3/2/a/d*e*ln(exp(I*(d*x+c))+1)+3/2/a/d*e*ln(exp(I*(d*x+c))-1)-3/2/a/d^2*f*c*ln(exp(I*(d*x+c))-1)-3/2/a/d*ln(exp(I*(d*x+c))+1)*f*x+3/2/a/d*ln(1-exp(I*(d*x+c)))*f*x+3/2/a/d^2*ln(1-exp(I*(d*x+c)))*c*f-2/a/d^2*f*ln(exp(I*(d*x+c))+I)+4/a/d^2*f*ln(exp(I*(d*x+c)))-1/a/d^2*f*ln(exp(I*(d*x+c))+1)-1/a/d^2*f*ln(exp(I*(d*x+c))-1)","B"
212,1,115,78,0.114000," ","int(csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}+\frac{2}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/a/d*tan(1/2*d*x+1/2*c)-1/8/a/d/tan(1/2*d*x+1/2*c)^2+1/2/a/d/tan(1/2*d*x+1/2*c)+3/2/a/d*ln(tan(1/2*d*x+1/2*c))+2/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
213,0,0,30,10.852000," ","int(csc(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x)","\int \frac{\csc^{3}\left(d x +c \right)}{\left(f x +e \right) \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(csc(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x)","F"
214,0,0,30,12.504000," ","int(csc(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\int \frac{\csc^{3}\left(d x +c \right)}{\left(f x +e \right)^{2} \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(csc(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x)","F"
215,0,0,30,0.512000," ","int((f*x+e)^m*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \left(\sin^{2}\left(d x +c \right)\right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","F"
216,0,0,28,0.198000," ","int((f*x+e)^m*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \sin \left(d x +c \right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*sin(d*x+c)/(a+a*sin(d*x+c)),x)","F"
217,0,0,22,0.134000," ","int((f*x+e)^m/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m}}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m/(a+a*sin(d*x+c)),x)","F"
218,0,0,28,0.143000," ","int((f*x+e)^m*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \csc \left(d x +c \right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*csc(d*x+c)/(a+a*sin(d*x+c)),x)","F"
219,0,0,30,0.172000," ","int((f*x+e)^m*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \left(\csc^{2}\left(d x +c \right)\right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","F"
220,0,0,482,1.409000," ","int((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \sin \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x)","F"
221,0,0,360,1.102000," ","int((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \sin \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x)","F"
222,1,548,235,0.197000," ","int((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{f \,x^{2}}{2 b}+\frac{e x}{b}-\frac{2 i a e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d b \sqrt{-a^{2}+b^{2}}}-\frac{a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d b \sqrt{-a^{2}+b^{2}}}-\frac{a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b \sqrt{-a^{2}+b^{2}}}+\frac{a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d b \sqrt{-a^{2}+b^{2}}}+\frac{a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b \sqrt{-a^{2}+b^{2}}}+\frac{i a f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b \sqrt{-a^{2}+b^{2}}}-\frac{i a f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b \sqrt{-a^{2}+b^{2}}}+\frac{2 i a f c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b \sqrt{-a^{2}+b^{2}}}"," ",0,"1/2*f*x^2/b+e*x/b-2*I/d/b*a*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-1/d/b*a*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x-1/d^2/b*a*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+1/d/b*a*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+1/d^2/b*a*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+I/d^2/b*a*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))-I/d^2/b*a*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+2*I/d^2/b*a*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))","B"
223,1,70,52,0.006000," ","int(sin(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}-\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}"," ",0,"2/d/b*arctan(tan(1/2*d*x+1/2*c))-2/d/b*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
224,0,0,581,1.529000," ","int((f*x+e)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \left(\sin^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
225,0,0,431,1.555000," ","int((f*x+e)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \left(\sin^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
226,1,625,279,0.521000," ","int((f*x+e)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{a f \,x^{2}}{2 b^{2}}-\frac{a e x}{b^{2}}-\frac{\left(d f x +d e +i f \right) {\mathrm e}^{i \left(d x +c \right)}}{2 d^{2} b}-\frac{\left(d f x +d e -i f \right) {\mathrm e}^{-i \left(d x +c \right)}}{2 d^{2} b}+\frac{2 i a^{2} e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d \sqrt{-a^{2}+b^{2}}}+\frac{a^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{b^{2} d \sqrt{-a^{2}+b^{2}}}+\frac{a^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{a^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{b^{2} d \sqrt{-a^{2}+b^{2}}}-\frac{a^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i a^{2} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{i a^{2} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 i a^{2} f c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}"," ",0,"-1/2*a*f*x^2/b^2-a*e*x/b^2-1/2*(d*f*x+I*f+d*e)/d^2/b*exp(I*(d*x+c))-1/2*(d*f*x-I*f+d*e)/d^2/b*exp(-I*(d*x+c))+2*I*a^2/b^2/d*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+a^2/b^2/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x+a^2/b^2/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c-a^2/b^2/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-a^2/b^2/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-I*a^2/b^2/d^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))+I*a^2/b^2/d^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-2*I*a^2/b^2/d^2*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))","B"
227,1,96,70,0.062000," ","int(sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{2}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-2/d/b/(1+tan(1/2*d*x+1/2*c)^2)-2/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))+2/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2","A"
228,0,0,726,0.335000," ","int((f*x+e)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \left(\sin^{3}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","F"
229,0,0,534,0.648000," ","int((f*x+e)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \left(\sin^{3}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","F"
230,1,686,342,0.754000," ","int((f*x+e)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{a^{2} f \,x^{2}}{2 b^{3}}+\frac{f \,x^{2}}{4 b}+\frac{a^{2} e x}{b^{3}}+\frac{e x}{2 b}+\frac{a \left(d f x +d e +i f \right) {\mathrm e}^{i \left(d x +c \right)}}{2 b^{2} d^{2}}+\frac{a \left(d f x +d e -i f \right) {\mathrm e}^{-i \left(d x +c \right)}}{2 b^{2} d^{2}}+\frac{2 i a^{3} f c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{3} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{a^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{b^{3} d \sqrt{-a^{2}+b^{2}}}-\frac{a^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{b^{3} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{a^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{b^{3} d \sqrt{-a^{2}+b^{2}}}+\frac{a^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{b^{3} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{i a^{3} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{b^{3} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i a^{3} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{b^{3} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 i a^{3} e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{3} d \sqrt{-a^{2}+b^{2}}}-\frac{f \cos \left(2 d x +2 c \right)}{8 d^{2} b}-\frac{\left(f x +e \right) \sin \left(2 d x +2 c \right)}{4 d b}"," ",0,"1/2*a^2*f*x^2/b^3+1/4*f*x^2/b+a^2*e*x/b^3+1/2*e*x/b+1/2*a*(d*f*x+I*f+d*e)/b^2/d^2*exp(I*(d*x+c))+1/2*a*(d*f*x-I*f+d*e)/b^2/d^2*exp(-I*(d*x+c))-I*a^3/b^3/d^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-a^3/b^3/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x-a^3/b^3/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+a^3/b^3/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+a^3/b^3/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+2*I*a^3/b^3/d^2*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+I*a^3/b^3/d^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))-2*I*a^3/b^3/d*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-1/8*f/d^2/b*cos(2*d*x+2*c)-1/4*(f*x+e)/d/b*sin(2*d*x+2*c)","B"
231,1,216,98,0.063000," ","int(sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*a+2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2+1/d/b*arctan(tan(1/2*d*x+1/2*c))-2/d*a^3/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
232,0,0,654,1.583000," ","int((f*x+e)^3*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \csc \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*csc(d*x+c)/(a+b*sin(d*x+c)),x)","F"
233,0,0,470,0.992000," ","int((f*x+e)^2*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \csc \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*csc(d*x+c)/(a+b*sin(d*x+c)),x)","F"
234,1,660,287,0.253000," ","int((f*x+e)*csc(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{2 i e b \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d a \sqrt{-a^{2}+b^{2}}}-\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a d}-\frac{f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}+\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a d}-\frac{f b \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d a \sqrt{-a^{2}+b^{2}}}-\frac{f b \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} a \sqrt{-a^{2}+b^{2}}}+\frac{f b \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d a \sqrt{-a^{2}+b^{2}}}+\frac{f b \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} a \sqrt{-a^{2}+b^{2}}}+\frac{i f b \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \sqrt{-a^{2}+b^{2}}}-\frac{i f b \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \sqrt{-a^{2}+b^{2}}}-\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) f x}{a d}+\frac{i f \dilog \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{d^{2} a}+\frac{i f \dilog \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}+\frac{2 i f c b \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \sqrt{-a^{2}+b^{2}}}"," ",0,"-2*I/d*e/a*b/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-1/a/d*e*ln(exp(I*(d*x+c))+1)-1/a/d^2*f*c*ln(exp(I*(d*x+c))-1)+1/a/d*e*ln(exp(I*(d*x+c))-1)-1/d*f*b/a/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x-1/d^2*f*b/a/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+1/d*f*b/a/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+1/d^2*f*b/a/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+I/d^2*f*b/a/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))-I/d^2*f*b/a/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-1/a/d*ln(exp(I*(d*x+c))+1)*f*x+I/d^2*f/a*dilog(exp(I*(d*x+c))+1)+I/d^2*f*dilog(exp(I*(d*x+c)))/a+2*I/d^2*f*c/a*b/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))","B"
235,1,69,62,0.003000," ","int(csc(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}"," ",0,"1/a/d*ln(tan(1/2*d*x+1/2*c))-2/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
236,0,0,794,4.656000," ","int((f*x+e)^3*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \left(\csc^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
237,0,0,575,3.593000," ","int((f*x+e)^2*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \left(\csc^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
238,1,766,332,0.292000," ","int((f*x+e)*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{i b f \dilog \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a^{2} d^{2}}-\frac{2 i b^{2} f c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i b^{2} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{b f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x}{a^{2} d}-\frac{2 i \left(f x +e \right)}{d a \left({\mathrm e}^{2 i \left(d x +c \right)}-1\right)}+\frac{2 i b^{2} e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d \sqrt{-a^{2}+b^{2}}}+\frac{b^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{a^{2} d \sqrt{-a^{2}+b^{2}}}+\frac{b^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{a^{2} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{i b^{2} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{b e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a^{2} d}-\frac{b e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a^{2} d}+\frac{b f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a^{2} d^{2}}-\frac{2 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{b^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{a^{2} d \sqrt{-a^{2}+b^{2}}}-\frac{b^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{a^{2} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i b f \dilog \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a^{2} d^{2}}+\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a \,d^{2}}+\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}"," ",0,"-I/a^2/d^2*b*f*dilog(exp(I*(d*x+c)))-2*I/a^2/d^2*b^2*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-I/a^2/d^2*b*f*dilog(exp(I*(d*x+c))+1)+1/a^2/d*b*f*ln(exp(I*(d*x+c))+1)*x-2*I*(f*x+e)/d/a/(exp(2*I*(d*x+c))-1)-I/a^2/d^2*b^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))+1/a^2/d*b^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x+1/a^2/d^2*b^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+I/a^2/d^2*b^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+1/a^2/d*b*e*ln(exp(I*(d*x+c))+1)-1/a^2/d*b*e*ln(exp(I*(d*x+c))-1)+1/a^2/d^2*b*f*c*ln(exp(I*(d*x+c))-1)-2/a/d^2*f*ln(exp(I*(d*x+c)))-1/a^2/d*b^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-1/a^2/d^2*b^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+2*I/a^2/d*b^2*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+1/a/d^2*f*ln(exp(I*(d*x+c))+1)+1/a/d^2*f*ln(exp(I*(d*x+c))-1)","B"
239,1,109,78,0.003000," ","int(csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-1/2/a/d/tan(1/2*d*x+1/2*c)-1/d/a^2*b*ln(tan(1/2*d*x+1/2*c))+2/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
240,0,0,30,0.452000," ","int((f*x+e)^m*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \left(\sin^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
241,0,0,28,0.187000," ","int((f*x+e)^m*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \sin \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*sin(d*x+c)/(a+b*sin(d*x+c)),x)","F"
242,0,0,22,0.083000," ","int((f*x+e)^m/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m}}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m/(a+b*sin(d*x+c)),x)","F"
243,0,0,28,0.120000," ","int((f*x+e)^m*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \csc \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*csc(d*x+c)/(a+b*sin(d*x+c)),x)","F"
244,0,0,30,0.158000," ","int((f*x+e)^m*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \left(\csc^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
245,1,750,514,1.451000," ","int((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c))^2,x)","\frac{2 i a \left(f x +e \right) \left(b -i a \,{\mathrm e}^{i \left(d x +c \right)}\right)}{b \left(-a^{2}+b^{2}\right) d \left(b \,{\mathrm e}^{2 i \left(d x +c \right)}-b +2 i a \,{\mathrm e}^{i \left(d x +c \right)}\right)}+\frac{a f \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{b \,d^{2} \left(a^{2}-b^{2}\right)}-\frac{2 a f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{b \,d^{2} \left(a^{2}-b^{2}\right)}+\frac{2 i b c f \arctan \left(\frac{2 i 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) \sqrt{-a^{2}+b^{2}}}-\frac{2 i b e \arctan \left(\frac{2 i 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) \sqrt{-a^{2}+b^{2}}}+\frac{i b f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}}-\frac{i b f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}}+\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}}+\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}}-\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}}-\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}}"," ",0,"2*I*a*(f*x+e)*(b-I*a*exp(I*(d*x+c)))/b/(-a^2+b^2)/d/(b*exp(2*I*(d*x+c))-b+2*I*a*exp(I*(d*x+c)))+1/b/d^2/(a^2-b^2)*a*f*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-2/b/d^2/(a^2-b^2)*a*f*ln(exp(I*(d*x+c)))+2*I*b/d^2/(a^2-b^2)*c*f/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-2*I*b/d/(a^2-b^2)*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+I*b/d^2/(a^2-b^2)*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))-I*b/d^2/(a^2-b^2)*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+b/d/(a^2-b^2)*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+b/d^2/(a^2-b^2)*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-b/d/(a^2-b^2)*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x-b/d^2/(a^2-b^2)*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c","A"
246,0,0,991,2.784000," ","int((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x)","\int \frac{\left(f x +e \right)^{2} \sin \left(d x +c \right)}{\left(a +b \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x)","F"
247,0,0,1359,3.010000," ","int((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c))^2,x)","\int \frac{\left(f x +e \right)^{3} \sin \left(d x +c \right)}{\left(a +b \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c))^2,x)","F"
248,1,1084,667,2.645000," ","int((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c))^3,x)","\frac{i \left(4 i b \,a^{3} d e \,{\mathrm e}^{i \left(d x +c \right)}-3 i b^{3} a d f x \,{\mathrm e}^{3 i \left(d x +c \right)}-3 i b^{3} a d e \,{\mathrm e}^{3 i \left(d x +c \right)}+5 i b^{3} a d f x \,{\mathrm e}^{i \left(d x +c \right)}+2 a^{4} d f x \,{\mathrm e}^{2 i \left(d x +c \right)}+5 b^{2} d f x \,{\mathrm e}^{2 i \left(d x +c \right)} a^{2}+2 b^{4} d f x \,{\mathrm e}^{2 i \left(d x +c \right)}+4 i b \,a^{3} d f x \,{\mathrm e}^{i \left(d x +c \right)}+5 i b^{3} a d e \,{\mathrm e}^{i \left(d x +c \right)}-2 i b^{2} f \,{\mathrm e}^{2 i \left(d x +c \right)} a^{2}+2 i a^{4} f \,{\mathrm e}^{2 i \left(d x +c \right)}+2 a^{4} d e \,{\mathrm e}^{2 i \left(d x +c \right)}+b \,a^{3} f \,{\mathrm e}^{3 i \left(d x +c \right)}+5 b^{2} d e \,{\mathrm e}^{2 i \left(d x +c \right)} a^{2}-b^{3} a f \,{\mathrm e}^{3 i \left(d x +c \right)}+2 b^{4} d e \,{\mathrm e}^{2 i \left(d x +c \right)}-a^{2} b^{2} d f x -2 b^{4} d f x -b \,a^{3} f \,{\mathrm e}^{i \left(d x +c \right)}-a^{2} b^{2} d e +b^{3} a f \,{\mathrm e}^{i \left(d x +c \right)}-2 b^{4} d e \right)}{\left(i b +2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \,{\mathrm e}^{2 i \left(d x +c \right)}\right)^{2} \left(a^{2}-b^{2}\right)^{2} d^{2} b}+\frac{a^{2} f \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{2 b \,d^{2} \left(-a^{2}+b^{2}\right)^{2}}-\frac{a^{2} f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{b \,d^{2} \left(-a^{2}+b^{2}\right)^{2}}+\frac{b f \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d^{2} \left(-a^{2}+b^{2}\right)^{2}}-\frac{2 b f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} \left(-a^{2}+b^{2}\right)^{2}}-\frac{3 i b a e \arctan \left(\frac{2 i 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{5}{2}}}+\frac{3 b a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{2 d \left(-a^{2}+b^{2}\right)^{\frac{5}{2}}}+\frac{3 b a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{2 d^{2} \left(-a^{2}+b^{2}\right)^{\frac{5}{2}}}+\frac{3 i b a f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{2 d^{2} \left(-a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{3 i b a f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{2 d^{2} \left(-a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{3 b a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{2 d \left(-a^{2}+b^{2}\right)^{\frac{5}{2}}}-\frac{3 b a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{2 d^{2} \left(-a^{2}+b^{2}\right)^{\frac{5}{2}}}+\frac{3 i b a f c \arctan \left(\frac{2 i 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{5}{2}}}"," ",0,"I*(4*I*b*a^3*d*e*exp(I*(d*x+c))-3*I*b^3*a*d*f*x*exp(3*I*(d*x+c))-3*I*b^3*a*d*e*exp(3*I*(d*x+c))+5*I*b^3*a*d*f*x*exp(I*(d*x+c))+2*a^4*d*f*x*exp(2*I*(d*x+c))+5*b^2*d*f*x*exp(2*I*(d*x+c))*a^2+2*b^4*d*f*x*exp(2*I*(d*x+c))+4*I*b*a^3*d*f*x*exp(I*(d*x+c))+5*I*b^3*a*d*e*exp(I*(d*x+c))-2*I*b^2*f*exp(2*I*(d*x+c))*a^2+2*I*a^4*f*exp(2*I*(d*x+c))+2*a^4*d*e*exp(2*I*(d*x+c))+b*a^3*f*exp(3*I*(d*x+c))+5*b^2*d*e*exp(2*I*(d*x+c))*a^2-b^3*a*f*exp(3*I*(d*x+c))+2*b^4*d*e*exp(2*I*(d*x+c))-a^2*b^2*d*f*x-2*b^4*d*f*x-b*a^3*f*exp(I*(d*x+c))-a^2*b^2*d*e+b^3*a*f*exp(I*(d*x+c))-2*b^4*d*e)/(I*b+2*a*exp(I*(d*x+c))-I*b*exp(2*I*(d*x+c)))^2/(a^2-b^2)^2/d^2/b+1/2/b/d^2/(-a^2+b^2)^2*a^2*f*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-1/b/d^2/(-a^2+b^2)^2*a^2*f*ln(exp(I*(d*x+c)))+b/d^2/(-a^2+b^2)^2*f*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-2*b/d^2/(-a^2+b^2)^2*f*ln(exp(I*(d*x+c)))-3*I*b/d/(-a^2+b^2)^(5/2)*a*e*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+3/2*b/d/(-a^2+b^2)^(5/2)*a*f*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+3/2*b/d^2/(-a^2+b^2)^(5/2)*a*f*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+3/2*I*b/d^2/(-a^2+b^2)^(5/2)*a*f*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))-3/2*I*b/d^2/(-a^2+b^2)^(5/2)*a*f*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-3/2*b/d/(-a^2+b^2)^(5/2)*a*f*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x-3/2*b/d^2/(-a^2+b^2)^(5/2)*a*f*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+3*I*b/d^2/(-a^2+b^2)^(5/2)*a*f*c*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))","A"
249,0,0,1427,5.178000," ","int((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x)","\int \frac{\left(f x +e \right)^{2} \sin \left(d x +c \right)}{\left(a +b \sin \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x)","F"
250,0,0,2104,3.663000," ","int((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c))^3,x)","\int \frac{\left(f x +e \right)^{3} \sin \left(d x +c \right)}{\left(a +b \sin \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c))^3,x)","F"
251,1,679,134,0.273000," ","int((f*x+e)^3*cos(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{i e^{3} x}{a}-\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e^{3}}{d a}+\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{3}}{d a}-\frac{i f^{3} x^{4}}{4 a}-\frac{6 i e^{2} f c x}{d a}+\frac{6 i c^{2} e \,f^{2} x}{d^{2} a}-\frac{12 i e \,f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{d^{2} a}-\frac{6 e \,f^{2} c^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right)}{d^{3} a}-\frac{6 e^{2} f c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{d^{2} a}+\frac{6 e \,f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{d^{3} a}+\frac{6 e^{2} f c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}-\frac{6 e \,f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{3} a}+\frac{6 e^{2} f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{d a}+\frac{6 e^{2} f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{d^{2} a}+\frac{6 e \,f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{d a}+\frac{2 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{3}}{d a}+\frac{2 f^{3} c^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right)}{d^{4} a}+\frac{2 f^{3} c^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{4} a}-\frac{2 f^{3} c^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{d^{4} a}-\frac{3 i f^{3} c^{4}}{2 d^{4} a}-\frac{i e \,f^{2} x^{3}}{a}-\frac{3 i e^{2} f \,x^{2}}{2 a}+\frac{12 f^{3} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{d^{3} a}+\frac{12 e \,f^{2} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{d^{3} a}+\frac{12 i f^{3} \polylog \left(4, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}+\frac{4 i c^{3} e \,f^{2}}{d^{3} a}-\frac{3 i e^{2} f \,c^{2}}{d^{2} a}-\frac{2 i f^{3} c^{3} x}{d^{3} a}-\frac{6 i f^{3} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{d^{2} a}-\frac{6 i e^{2} f \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}"," ",0,"I/a*e^3*x+2/d/a*f^3*ln(1-I*exp(I*(d*x+c)))*x^3-6/d^3/a*e*f^2*c^2*ln(1-I*exp(I*(d*x+c)))-6/d^2/a*e^2*f*c*ln(exp(I*(d*x+c))+I)+6/d^3/a*e*f^2*c^2*ln(exp(I*(d*x+c))+I)+6/d^2/a*e^2*f*c*ln(exp(I*(d*x+c)))-6/d^3/a*e*f^2*c^2*ln(exp(I*(d*x+c)))+6/d/a*e^2*f*ln(1-I*exp(I*(d*x+c)))*x+6/d^2/a*e^2*f*ln(1-I*exp(I*(d*x+c)))*c-2/d/a*ln(exp(I*(d*x+c)))*e^3+2/d/a*ln(exp(I*(d*x+c))+I)*e^3-1/4*I/a*f^3*x^4+6/d/a*e*f^2*ln(1-I*exp(I*(d*x+c)))*x^2-12*I/d^2/a*e*f^2*polylog(2,I*exp(I*(d*x+c)))*x-6*I/d/a*e^2*f*c*x+6*I/d^2/a*c^2*e*f^2*x-6*I/d^2/a*f^3*polylog(2,I*exp(I*(d*x+c)))*x^2+4*I/d^3/a*c^3*e*f^2-3*I/d^2/a*e^2*f*c^2-6*I/d^2/a*e^2*f*polylog(2,I*exp(I*(d*x+c)))-2*I/d^3/a*f^3*c^3*x+2/d^4/a*f^3*c^3*ln(1-I*exp(I*(d*x+c)))+12/d^3/a*f^3*polylog(3,I*exp(I*(d*x+c)))*x+2/d^4/a*f^3*c^3*ln(exp(I*(d*x+c)))-2/d^4/a*f^3*c^3*ln(exp(I*(d*x+c))+I)+12/d^3/a*e*f^2*polylog(3,I*exp(I*(d*x+c)))-3/2*I/d^4/a*f^3*c^4-I/a*e*f^2*x^3-3/2*I/a*e^2*f*x^2+12*I*f^3*polylog(4,I*exp(I*(d*x+c)))/a/d^4","B"
252,1,421,101,0.216000," ","int((f*x+e)^2*cos(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{i e^{2} x}{a}+\frac{2 i f^{2} c^{2} x}{d^{2} a}-\frac{i f e \,x^{2}}{a}+\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{2}}{d a}-\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e^{2}}{d a}+\frac{4 f e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{d a}+\frac{4 f e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{d^{2} a}-\frac{4 f e c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{d^{2} a}-\frac{4 i f e \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}+\frac{2 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{d a}-\frac{2 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{d^{3} a}+\frac{4 i f^{2} c^{3}}{3 d^{3} a}-\frac{4 i f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{d^{2} a}-\frac{2 i e f \,c^{2}}{d^{2} a}+\frac{4 f e c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}-\frac{2 f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{3} a}+\frac{2 f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{d^{3} a}-\frac{i f^{2} x^{3}}{3 a}-\frac{4 i e f c x}{d a}+\frac{4 f^{2} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}"," ",0,"I/a*e^2*x+2*I/d^2/a*f^2*c^2*x-4*I/d^2/a*f*e*polylog(2,I*exp(I*(d*x+c)))+2/d/a*ln(exp(I*(d*x+c))+I)*e^2-2/d/a*ln(exp(I*(d*x+c)))*e^2+4/d/a*f*e*ln(1-I*exp(I*(d*x+c)))*x+4/d^2/a*f*e*ln(1-I*exp(I*(d*x+c)))*c-4/d^2/a*f*e*c*ln(exp(I*(d*x+c))+I)-I/a*f*e*x^2+2/d/a*f^2*ln(1-I*exp(I*(d*x+c)))*x^2-2/d^3/a*f^2*ln(1-I*exp(I*(d*x+c)))*c^2+4/3*I/d^3/a*f^2*c^3-2*I/d^2/a*e*f*c^2-1/3*I/a*f^2*x^3+4/d^2/a*f*e*c*ln(exp(I*(d*x+c)))-2/d^3/a*f^2*c^2*ln(exp(I*(d*x+c)))+2/d^3/a*f^2*c^2*ln(exp(I*(d*x+c))+I)-4*I/d^2/a*f^2*polylog(2,I*exp(I*(d*x+c)))*x-4*I/d/a*e*f*c*x+4*f^2*polylog(3,I*exp(I*(d*x+c)))/a/d^3","B"
253,1,203,69,0.229000," ","int((f*x+e)*cos(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{i f \,x^{2}}{2 a}+\frac{i e x}{a}+\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e}{d a}-\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{d a}-\frac{2 i f c x}{d a}-\frac{i f \,c^{2}}{d^{2} a}+\frac{2 f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{d a}+\frac{2 f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{d^{2} a}-\frac{2 i f \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}-\frac{2 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{d^{2} a}+\frac{2 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}"," ",0,"-1/2*I/a*f*x^2+I/a*e*x+2/d/a*ln(exp(I*(d*x+c))+I)*e-2/d/a*ln(exp(I*(d*x+c)))*e-2*I/d/a*f*c*x-I/d^2/a*f*c^2+2/d/a*f*ln(1-I*exp(I*(d*x+c)))*x+2/d^2/a*f*ln(1-I*exp(I*(d*x+c)))*c-2*I*f*polylog(2,I*exp(I*(d*x+c)))/a/d^2-2/d^2/a*f*c*ln(exp(I*(d*x+c))+I)+2/d^2/a*f*c*ln(exp(I*(d*x+c)))","B"
254,1,19,16,0.049000," ","int(cos(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\ln \left(a +a \sin \left(d x +c \right)\right)}{d a}"," ",0,"1/d*ln(a+a*sin(d*x+c))/a","A"
255,0,0,28,0.263000," ","int(cos(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","\int \frac{\cos \left(d x +c \right)}{\left(f x +e \right) \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(cos(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","F"
256,0,0,28,0.301000," ","int(cos(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\int \frac{\cos \left(d x +c \right)}{\left(f x +e \right)^{2} \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(cos(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x)","F"
257,1,436,97,0.125000," ","int((f*x+e)^3*cos(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{f^{3} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)-3 c \,f^{3} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)+3 f^{2} e d \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)+3 c^{2} f^{3} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-6 c d e \,f^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+3 d^{2} e^{2} f \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+c^{3} f^{3} \cos \left(d x +c \right)-3 c^{2} d e \,f^{2} \cos \left(d x +c \right)+3 c \,d^{2} e^{2} f \cos \left(d x +c \right)-d^{3} e^{3} \cos \left(d x +c \right)-\frac{f^{3} \left(d x +c \right)^{4}}{4}+c \,f^{3} \left(d x +c \right)^{3}-f^{2} e d \left(d x +c \right)^{3}-\frac{3 c^{2} f^{3} \left(d x +c \right)^{2}}{2}+3 c d e \,f^{2} \left(d x +c \right)^{2}-\frac{3 d^{2} e^{2} f \left(d x +c \right)^{2}}{2}+c^{3} f^{3} \left(d x +c \right)-3 c^{2} d e \,f^{2} \left(d x +c \right)+3 c \,d^{2} e^{2} f \left(d x +c \right)-d^{3} e^{3} \left(d x +c \right)}{d^{4} a}"," ",0,"-1/d^4/a*(f^3*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-3*c*f^3*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+3*f^2*e*d*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+3*c^2*f^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-6*c*d*e*f^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+3*d^2*e^2*f*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+c^3*f^3*cos(d*x+c)-3*c^2*d*e*f^2*cos(d*x+c)+3*c*d^2*e^2*f*cos(d*x+c)-d^3*e^3*cos(d*x+c)-1/4*f^3*(d*x+c)^4+c*f^3*(d*x+c)^3-f^2*e*d*(d*x+c)^3-3/2*c^2*f^3*(d*x+c)^2+3*c*d*e*f^2*(d*x+c)^2-3/2*d^2*e^2*f*(d*x+c)^2+c^3*f^3*(d*x+c)-3*c^2*d*e*f^2*(d*x+c)+3*c*d^2*e^2*f*(d*x+c)-d^3*e^3*(d*x+c))","B"
258,1,215,73,0.122000," ","int((f*x+e)^2*cos(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{f^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)-2 c \,f^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+2 d e f \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-c^{2} f^{2} \cos \left(d x +c \right)+2 c d e f \cos \left(d x +c \right)-d^{2} e^{2} \cos \left(d x +c \right)-\frac{f^{2} \left(d x +c \right)^{3}}{3}+c \,f^{2} \left(d x +c \right)^{2}-d e f \left(d x +c \right)^{2}-c^{2} f^{2} \left(d x +c \right)+2 c d e f \left(d x +c \right)-d^{2} e^{2} \left(d x +c \right)}{d^{3} a}"," ",0,"-1/d^3/a*(f^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-2*c*f^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+2*d*e*f*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-c^2*f^2*cos(d*x+c)+2*c*d*e*f*cos(d*x+c)-d^2*e^2*cos(d*x+c)-1/3*f^2*(d*x+c)^3+c*f^2*(d*x+c)^2-d*e*f*(d*x+c)^2-c^2*f^2*(d*x+c)+2*c*d*e*f*(d*x+c)-d^2*e^2*(d*x+c))","B"
259,1,78,49,0.116000," ","int((f*x+e)*cos(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{f \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+c f \cos \left(d x +c \right)-d e \cos \left(d x +c \right)-\frac{f \left(d x +c \right)^{2}}{2}+c f \left(d x +c \right)-d e \left(d x +c \right)}{d^{2} a}"," ",0,"-1/d^2/a*(f*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+c*f*cos(d*x+c)-d*e*cos(d*x+c)-1/2*f*(d*x+c)^2+c*f*(d*x+c)-d*e*(d*x+c))","A"
260,1,43,19,0.105000," ","int(cos(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"2/a/d/(1+tan(1/2*d*x+1/2*c)^2)+2/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
261,1,102,72,0.112000," ","int(cos(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x)","-\frac{\Si \left(d x +c +\frac{-c f +d e}{f}\right) \cos \left(\frac{-c f +d e}{f}\right)}{a f}+\frac{\Ci \left(d x +c +\frac{-c f +d e}{f}\right) \sin \left(\frac{-c f +d e}{f}\right)}{a f}+\frac{\ln \left(\left(d x +c \right) f -c f +d e \right)}{a f}"," ",0,"-1/a*Si(d*x+c+(-c*f+d*e)/f)*cos((-c*f+d*e)/f)/f+1/a*Ci(d*x+c+(-c*f+d*e)/f)*sin((-c*f+d*e)/f)/f+1/a*ln((d*x+c)*f-c*f+d*e)/f","A"
262,1,132,95,0.113000," ","int(cos(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\frac{d \left(\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) f -c f +d e \right) f}-\frac{\frac{\Si \left(d x +c +\frac{-c f +d e}{f}\right) \sin \left(\frac{-c f +d e}{f}\right)}{f}+\frac{\Ci \left(d x +c +\frac{-c f +d e}{f}\right) \cos \left(\frac{-c f +d e}{f}\right)}{f}}{f}-\frac{1}{\left(\left(d x +c \right) f -c f +d e \right) f}\right)}{a}"," ",0,"d/a*(sin(d*x+c)/((d*x+c)*f-c*f+d*e)/f-(Si(d*x+c+(-c*f+d*e)/f)*sin((-c*f+d*e)/f)/f+Ci(d*x+c+(-c*f+d*e)/f)*cos((-c*f+d*e)/f)/f)/f-1/((d*x+c)*f-c*f+d*e)/f)","A"
263,1,737,207,0.124000," ","int((f*x+e)^3*cos(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{f^{3} \left(-\frac{\left(d x +c \right)^{3} \left(\cos^{2}\left(d x +c \right)\right)}{2}+\frac{3 \left(d x +c \right)^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{2}+\frac{3 \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{4}-\frac{3 \cos \left(d x +c \right) \sin \left(d x +c \right)}{8}-\frac{3 d x}{8}-\frac{3 c}{8}-\frac{\left(d x +c \right)^{3}}{2}\right)-3 c \,f^{3} \left(-\frac{\left(d x +c \right)^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2}+\left(d x +c \right) \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-\frac{\left(d x +c \right)^{2}}{4}-\frac{\left(\sin^{2}\left(d x +c \right)\right)}{4}\right)+3 f^{2} e d \left(-\frac{\left(d x +c \right)^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2}+\left(d x +c \right) \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-\frac{\left(d x +c \right)^{2}}{4}-\frac{\left(\sin^{2}\left(d x +c \right)\right)}{4}\right)+3 c^{2} f^{3} \left(-\frac{\left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{2}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{4}+\frac{d x}{4}+\frac{c}{4}\right)-6 c d e \,f^{2} \left(-\frac{\left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{2}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{4}+\frac{d x}{4}+\frac{c}{4}\right)+3 d^{2} e^{2} f \left(-\frac{\left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{2}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{4}+\frac{d x}{4}+\frac{c}{4}\right)+\frac{c^{3} f^{3} \left(\cos^{2}\left(d x +c \right)\right)}{2}-\frac{3 c^{2} d e \,f^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2}+\frac{3 c \,d^{2} e^{2} f \left(\cos^{2}\left(d x +c \right)\right)}{2}-\frac{d^{3} e^{3} \left(\cos^{2}\left(d x +c \right)\right)}{2}-f^{3} \left(\left(d x +c \right)^{3} \sin \left(d x +c \right)+3 \left(d x +c \right)^{2} \cos \left(d x +c \right)-6 \cos \left(d x +c \right)-6 \left(d x +c \right) \sin \left(d x +c \right)\right)+3 c \,f^{3} \left(\left(d x +c \right)^{2} \sin \left(d x +c \right)-2 \sin \left(d x +c \right)+2 \left(d x +c \right) \cos \left(d x +c \right)\right)-3 f^{2} e d \left(\left(d x +c \right)^{2} \sin \left(d x +c \right)-2 \sin \left(d x +c \right)+2 \left(d x +c \right) \cos \left(d x +c \right)\right)-3 c^{2} f^{3} \left(\cos \left(d x +c \right)+\left(d x +c \right) \sin \left(d x +c \right)\right)+6 c d e \,f^{2} \left(\cos \left(d x +c \right)+\left(d x +c \right) \sin \left(d x +c \right)\right)-3 d^{2} e^{2} f \left(\cos \left(d x +c \right)+\left(d x +c \right) \sin \left(d x +c \right)\right)+\sin \left(d x +c \right) c^{3} f^{3}-3 \sin \left(d x +c \right) c^{2} d e \,f^{2}+3 \sin \left(d x +c \right) c \,d^{2} e^{2} f -\sin \left(d x +c \right) d^{3} e^{3}}{d^{4} a}"," ",0,"-1/d^4/a*(f^3*(-1/2*(d*x+c)^3*cos(d*x+c)^2+3/2*(d*x+c)^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+3/4*(d*x+c)*cos(d*x+c)^2-3/8*cos(d*x+c)*sin(d*x+c)-3/8*d*x-3/8*c-1/2*(d*x+c)^3)-3*c*f^3*(-1/2*(d*x+c)^2*cos(d*x+c)^2+(d*x+c)*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-1/4*(d*x+c)^2-1/4*sin(d*x+c)^2)+3*f^2*e*d*(-1/2*(d*x+c)^2*cos(d*x+c)^2+(d*x+c)*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-1/4*(d*x+c)^2-1/4*sin(d*x+c)^2)+3*c^2*f^3*(-1/2*(d*x+c)*cos(d*x+c)^2+1/4*cos(d*x+c)*sin(d*x+c)+1/4*d*x+1/4*c)-6*c*d*e*f^2*(-1/2*(d*x+c)*cos(d*x+c)^2+1/4*cos(d*x+c)*sin(d*x+c)+1/4*d*x+1/4*c)+3*d^2*e^2*f*(-1/2*(d*x+c)*cos(d*x+c)^2+1/4*cos(d*x+c)*sin(d*x+c)+1/4*d*x+1/4*c)+1/2*c^3*f^3*cos(d*x+c)^2-3/2*c^2*d*e*f^2*cos(d*x+c)^2+3/2*c*d^2*e^2*f*cos(d*x+c)^2-1/2*d^3*e^3*cos(d*x+c)^2-f^3*((d*x+c)^3*sin(d*x+c)+3*(d*x+c)^2*cos(d*x+c)-6*cos(d*x+c)-6*(d*x+c)*sin(d*x+c))+3*c*f^3*((d*x+c)^2*sin(d*x+c)-2*sin(d*x+c)+2*(d*x+c)*cos(d*x+c))-3*f^2*e*d*((d*x+c)^2*sin(d*x+c)-2*sin(d*x+c)+2*(d*x+c)*cos(d*x+c))-3*c^2*f^3*(cos(d*x+c)+(d*x+c)*sin(d*x+c))+6*c*d*e*f^2*(cos(d*x+c)+(d*x+c)*sin(d*x+c))-3*d^2*e^2*f*(cos(d*x+c)+(d*x+c)*sin(d*x+c))+sin(d*x+c)*c^3*f^3-3*sin(d*x+c)*c^2*d*e*f^2+3*sin(d*x+c)*c*d^2*e^2*f-sin(d*x+c)*d^3*e^3)","B"
264,1,339,151,0.113000," ","int((f*x+e)^2*cos(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{f^{2} \left(-\frac{\left(d x +c \right)^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2}+\left(d x +c \right) \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-\frac{\left(d x +c \right)^{2}}{4}-\frac{\left(\sin^{2}\left(d x +c \right)\right)}{4}\right)-2 c \,f^{2} \left(-\frac{\left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{2}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{4}+\frac{d x}{4}+\frac{c}{4}\right)+2 d e f \left(-\frac{\left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{2}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{4}+\frac{d x}{4}+\frac{c}{4}\right)-\frac{c^{2} f^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2}+c d e f \left(\cos^{2}\left(d x +c \right)\right)-\frac{d^{2} e^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2}-f^{2} \left(\left(d x +c \right)^{2} \sin \left(d x +c \right)-2 \sin \left(d x +c \right)+2 \left(d x +c \right) \cos \left(d x +c \right)\right)+2 c \,f^{2} \left(\cos \left(d x +c \right)+\left(d x +c \right) \sin \left(d x +c \right)\right)-2 d e f \left(\cos \left(d x +c \right)+\left(d x +c \right) \sin \left(d x +c \right)\right)-\sin \left(d x +c \right) c^{2} f^{2}+2 \sin \left(d x +c \right) c d e f -\sin \left(d x +c \right) d^{2} e^{2}}{d^{3} a}"," ",0,"-1/d^3/a*(f^2*(-1/2*(d*x+c)^2*cos(d*x+c)^2+(d*x+c)*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-1/4*(d*x+c)^2-1/4*sin(d*x+c)^2)-2*c*f^2*(-1/2*(d*x+c)*cos(d*x+c)^2+1/4*cos(d*x+c)*sin(d*x+c)+1/4*d*x+1/4*c)+2*d*e*f*(-1/2*(d*x+c)*cos(d*x+c)^2+1/4*cos(d*x+c)*sin(d*x+c)+1/4*d*x+1/4*c)-1/2*c^2*f^2*cos(d*x+c)^2+c*d*e*f*cos(d*x+c)^2-1/2*d^2*e^2*cos(d*x+c)^2-f^2*((d*x+c)^2*sin(d*x+c)-2*sin(d*x+c)+2*(d*x+c)*cos(d*x+c))+2*c*f^2*(cos(d*x+c)+(d*x+c)*sin(d*x+c))-2*d*e*f*(cos(d*x+c)+(d*x+c)*sin(d*x+c))-sin(d*x+c)*c^2*f^2+2*sin(d*x+c)*c*d*e*f-sin(d*x+c)*d^2*e^2)","B"
265,1,114,85,0.109000," ","int((f*x+e)*cos(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{f \left(-\frac{\left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{2}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{4}+\frac{d x}{4}+\frac{c}{4}\right)+\frac{c f \left(\cos^{2}\left(d x +c \right)\right)}{2}-\frac{\left(\cos^{2}\left(d x +c \right)\right) d e}{2}-f \left(\cos \left(d x +c \right)+\left(d x +c \right) \sin \left(d x +c \right)\right)+\sin \left(d x +c \right) c f -\sin \left(d x +c \right) d e}{d^{2} a}"," ",0,"-1/d^2/a*(f*(-1/2*(d*x+c)*cos(d*x+c)^2+1/4*cos(d*x+c)*sin(d*x+c)+1/4*d*x+1/4*c)+1/2*c*f*cos(d*x+c)^2-1/2*cos(d*x+c)^2*d*e-f*(cos(d*x+c)+(d*x+c)*sin(d*x+c))+sin(d*x+c)*c*f-sin(d*x+c)*d*e)","A"
266,1,28,30,0.051000," ","int(cos(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{\frac{\left(\sin^{2}\left(d x +c \right)\right)}{2}-\sin \left(d x +c \right)}{a d}"," ",0,"-1/a/d*(1/2*sin(d*x+c)^2-sin(d*x+c))","A"
267,1,161,124,0.106000," ","int(cos(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x)","-\frac{\frac{\Si \left(2 d x +2 c +\frac{-2 c f +2 d e}{f}\right) \cos \left(\frac{-2 c f +2 d e}{f}\right)}{2 f}-\frac{\Ci \left(2 d x +2 c +\frac{-2 c f +2 d e}{f}\right) \sin \left(\frac{-2 c f +2 d e}{f}\right)}{2 f}-\frac{\Si \left(d x +c +\frac{-c f +d e}{f}\right) \sin \left(\frac{-c f +d e}{f}\right)}{f}-\frac{\Ci \left(d x +c +\frac{-c f +d e}{f}\right) \cos \left(\frac{-c f +d e}{f}\right)}{f}}{a}"," ",0,"-1/a*(1/2*Si(2*d*x+2*c+2*(-c*f+d*e)/f)*cos(2*(-c*f+d*e)/f)/f-1/2*Ci(2*d*x+2*c+2*(-c*f+d*e)/f)*sin(2*(-c*f+d*e)/f)/f-Si(d*x+c+(-c*f+d*e)/f)*sin((-c*f+d*e)/f)/f-Ci(d*x+c+(-c*f+d*e)/f)*cos((-c*f+d*e)/f)/f)","A"
268,1,230,173,0.109000," ","int(cos(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x)","-\frac{d \left(-\frac{\sin \left(2 d x +2 c \right)}{2 \left(\left(d x +c \right) f -c f +d e \right) f}+\frac{\frac{2 \Si \left(2 d x +2 c +\frac{-2 c f +2 d e}{f}\right) \sin \left(\frac{-2 c f +2 d e}{f}\right)}{f}+\frac{2 \Ci \left(2 d x +2 c +\frac{-2 c f +2 d e}{f}\right) \cos \left(\frac{-2 c f +2 d e}{f}\right)}{f}}{2 f}+\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) f -c f +d e \right) f}+\frac{\frac{\Si \left(d x +c +\frac{-c f +d e}{f}\right) \cos \left(\frac{-c f +d e}{f}\right)}{f}-\frac{\Ci \left(d x +c +\frac{-c f +d e}{f}\right) \sin \left(\frac{-c f +d e}{f}\right)}{f}}{f}\right)}{a}"," ",0,"-d/a*(-1/2*sin(2*d*x+2*c)/((d*x+c)*f-c*f+d*e)/f+1/2*(2*Si(2*d*x+2*c+2*(-c*f+d*e)/f)*sin(2*(-c*f+d*e)/f)/f+2*Ci(2*d*x+2*c+2*(-c*f+d*e)/f)*cos(2*(-c*f+d*e)/f)/f)/f+cos(d*x+c)/((d*x+c)*f-c*f+d*e)/f+(Si(d*x+c+(-c*f+d*e)/f)*cos((-c*f+d*e)/f)/f-Ci(d*x+c+(-c*f+d*e)/f)*sin((-c*f+d*e)/f)/f)/f)","A"
269,1,1265,444,0.422000," ","int((f*x+e)^3*sec(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{3 i e^{2} f \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{2 a \,d^{2}}+\frac{3 i f^{3} \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{2 a \,d^{2}}+\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{3}}{2 d a}+\frac{3 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2} e \,f^{2}}{2 a \,d^{3}}-\frac{3 i e \,f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{d^{2} a}-\frac{3 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) e \,f^{2} x^{2}}{2 a d}-\frac{e^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 a d}-\frac{3 e \,f^{2} c^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right)}{2 d^{3} a}-\frac{3 e^{2} f c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{2 d^{2} a}+\frac{3 e \,f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{2 d^{3} a}+\frac{3 e^{2} f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{2 d a}+\frac{3 e^{2} f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{2 d^{2} a}+\frac{3 e \,f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{2 d a}-\frac{i \left(d \,f^{3} x^{3} {\mathrm e}^{i \left(d x +c \right)}+3 d e \,f^{2} x^{2} {\mathrm e}^{i \left(d x +c \right)}+3 d \,e^{2} f x \,{\mathrm e}^{i \left(d x +c \right)}+d \,e^{3} {\mathrm e}^{i \left(d x +c \right)}+3 f^{3} x^{2}-3 i f^{3} x^{2} {\mathrm e}^{i \left(d x +c \right)}+6 e \,f^{2} x -6 i e \,f^{2} x \,{\mathrm e}^{i \left(d x +c \right)}+3 e^{2} f -3 i e^{2} f \,{\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} \left({\mathrm e}^{i \left(d x +c \right)}+i\right)^{2} a}-\frac{f^{3} \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) x^{3}}{2 a d}-\frac{f^{3} \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c^{3}}{2 a \,d^{4}}-\frac{3 i f^{3} x^{2}}{a \,d^{2}}+\frac{f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{3}}{2 d a}+\frac{f^{3} c^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right)}{2 d^{4} a}-\frac{f^{3} c^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{2 d^{4} a}+\frac{3 f^{3} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{d^{3} a}+\frac{3 e \,f^{2} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{d^{3} a}+\frac{3 i f^{3} \polylog \left(4, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{3 i f^{3} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{2 d^{2} a}-\frac{3 i e^{2} f \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{2 d^{2} a}+\frac{3 i \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right) e \,f^{2} x}{a \,d^{2}}-\frac{3 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c \,e^{2} f}{2 a \,d^{2}}-\frac{6 i f^{3} c x}{a \,d^{3}}-\frac{3 e \,f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 a \,d^{3}}-\frac{6 e \,f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{6 e \,f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}+\frac{6 f^{3} c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{6 f^{3} c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{4}}+\frac{f^{3} c^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 a \,d^{4}}+\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}+\frac{6 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{4}}-\frac{3 f^{3} \polylog \left(3, -i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}-\frac{6 i f^{3} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{3 i f^{3} \polylog \left(4, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{3 e \,f^{2} \polylog \left(3, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{3 i c^{2} f^{3}}{a \,d^{4}}+\frac{3 e^{2} f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 a \,d^{2}}-\frac{3 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) e^{2} f x}{2 a d}"," ",0,"-I*(d*f^3*x^3*exp(I*(d*x+c))+3*d*e*f^2*x^2*exp(I*(d*x+c))+3*d*e^2*f*x*exp(I*(d*x+c))+d*e^3*exp(I*(d*x+c))+3*f^3*x^2-3*I*f^3*x^2*exp(I*(d*x+c))+6*e*f^2*x-6*I*e*f^2*x*exp(I*(d*x+c))+3*e^2*f-3*I*e^2*f*exp(I*(d*x+c)))/d^2/(exp(I*(d*x+c))+I)^2/a+3/2/a/d^3*ln(1+I*exp(I*(d*x+c)))*c^2*e*f^2-3/2/a/d*ln(1+I*exp(I*(d*x+c)))*e*f^2*x^2+3/2*I/a/d^2*e^2*f*polylog(2,-I*exp(I*(d*x+c)))+3/2*I/a/d^2*f^3*polylog(2,-I*exp(I*(d*x+c)))*x^2+1/2/d/a*f^3*ln(1-I*exp(I*(d*x+c)))*x^3-3/2/d^3/a*e*f^2*c^2*ln(1-I*exp(I*(d*x+c)))-3/2/d^2/a*e^2*f*c*ln(exp(I*(d*x+c))+I)+3/2/d^3/a*e*f^2*c^2*ln(exp(I*(d*x+c))+I)+3/2/d/a*e^2*f*ln(1-I*exp(I*(d*x+c)))*x+3/2/d^2/a*e^2*f*ln(1-I*exp(I*(d*x+c)))*c+1/2/d/a*ln(exp(I*(d*x+c))+I)*e^3+3/2/d/a*e*f^2*ln(1-I*exp(I*(d*x+c)))*x^2+3/2/a/d^2*e^2*f*c*ln(exp(I*(d*x+c))-I)-3/2/a/d*ln(1+I*exp(I*(d*x+c)))*e^2*f*x-3/2/a/d^2*ln(1+I*exp(I*(d*x+c)))*c*e^2*f-3/2*I/a/d^2*f^3*polylog(2,I*exp(I*(d*x+c)))*x^2-6*I/a/d^3*f^3*c*x-3/2*I/a/d^2*e^2*f*polylog(2,I*exp(I*(d*x+c)))-1/2/a/d*e^3*ln(exp(I*(d*x+c))-I)+1/2/d^4/a*f^3*c^3*ln(1-I*exp(I*(d*x+c)))+3/d^3/a*f^3*polylog(3,I*exp(I*(d*x+c)))*x-1/2/d^4/a*f^3*c^3*ln(exp(I*(d*x+c))+I)+3/d^3/a*e*f^2*polylog(3,I*exp(I*(d*x+c)))-3/2/a/d^3*e*f^2*c^2*ln(exp(I*(d*x+c))-I)-1/2/a/d*f^3*ln(1+I*exp(I*(d*x+c)))*x^3-1/2/a/d^4*f^3*ln(1+I*exp(I*(d*x+c)))*c^3-3/a/d^3*f^3*polylog(3,-I*exp(I*(d*x+c)))*x-3*I/a/d^2*f^3*x^2-6*I/a/d^4*f^3*polylog(2,I*exp(I*(d*x+c)))-3*I/a/d^4*c^2*f^3+3*I*f^3*polylog(4,I*exp(I*(d*x+c)))/a/d^4-3*I*f^3*polylog(4,-I*exp(I*(d*x+c)))/a/d^4-3*I/a/d^2*polylog(2,I*exp(I*(d*x+c)))*e*f^2*x+3*I/a/d^2*polylog(2,-I*exp(I*(d*x+c)))*e*f^2*x-6/a/d^3*e*f^2*ln(exp(I*(d*x+c)))+6/a/d^3*e*f^2*ln(exp(I*(d*x+c))+I)-3/a/d^3*e*f^2*polylog(3,-I*exp(I*(d*x+c)))+6/a/d^4*f^3*c*ln(exp(I*(d*x+c)))-6/a/d^4*f^3*c*ln(exp(I*(d*x+c))+I)+1/2/a/d^4*f^3*c^3*ln(exp(I*(d*x+c))-I)+6/a/d^3*f^3*ln(1-I*exp(I*(d*x+c)))*x+6/a/d^4*f^3*ln(1-I*exp(I*(d*x+c)))*c","B"
270,1,677,257,0.310000," ","int((f*x+e)^2*sec(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{i \left(d \,f^{2} x^{2} {\mathrm e}^{i \left(d x +c \right)}+2 d e f x \,{\mathrm e}^{i \left(d x +c \right)}+d \,e^{2} {\mathrm e}^{i \left(d x +c \right)}+2 f^{2} x -2 i f^{2} x \,{\mathrm e}^{i \left(d x +c \right)}+2 e f -2 i e f \,{\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} \left({\mathrm e}^{i \left(d x +c \right)}+i\right)^{2} a}+\frac{2 f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{d^{3} a}-\frac{2 f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{3} a}-\frac{e^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 d a}+\frac{f e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{d a}+\frac{f e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{d^{2} a}-\frac{f e c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{d^{2} a}+\frac{f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{2 d a}-\frac{f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{2 d^{3} a}+\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{2}}{2 d a}+\frac{\ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2} f^{2}}{2 d^{3} a}-\frac{f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 d^{3} a}-\frac{\ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) f^{2} x^{2}}{2 d a}+\frac{i \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right) f^{2} x}{d^{2} a}+\frac{i e f \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}-\frac{\ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) e f x}{d a}-\frac{\ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c e f}{d^{2} a}+\frac{e f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{d^{2} a}-\frac{i f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{d^{2} a}-\frac{i f e \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}+\frac{f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{2 d^{3} a}-\frac{f^{2} \polylog \left(3, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{f^{2} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}"," ",0,"-I*(d*f^2*x^2*exp(I*(d*x+c))+2*d*e*f*x*exp(I*(d*x+c))+d*e^2*exp(I*(d*x+c))+2*f^2*x-2*I*f^2*x*exp(I*(d*x+c))+2*e*f-2*I*e*f*exp(I*(d*x+c)))/d^2/(exp(I*(d*x+c))+I)^2/a+2/d^3/a*f^2*ln(exp(I*(d*x+c))+I)-2/d^3/a*f^2*ln(exp(I*(d*x+c)))-1/2/d/a*e^2*ln(exp(I*(d*x+c))-I)+1/d/a*f*e*ln(1-I*exp(I*(d*x+c)))*x+1/d^2/a*f*e*ln(1-I*exp(I*(d*x+c)))*c-1/d^2/a*f*e*c*ln(exp(I*(d*x+c))+I)+1/2/d/a*f^2*ln(1-I*exp(I*(d*x+c)))*x^2-1/2/d^3/a*f^2*ln(1-I*exp(I*(d*x+c)))*c^2+1/2/d/a*ln(exp(I*(d*x+c))+I)*e^2+1/2/d^3/a*ln(1+I*exp(I*(d*x+c)))*c^2*f^2-1/2/d^3/a*f^2*c^2*ln(exp(I*(d*x+c))-I)-1/2/d/a*ln(1+I*exp(I*(d*x+c)))*f^2*x^2-I/d^2/a*e*f*polylog(2,I*exp(I*(d*x+c)))-I/d^2/a*polylog(2,I*exp(I*(d*x+c)))*f^2*x-1/d/a*ln(1+I*exp(I*(d*x+c)))*e*f*x-1/d^2/a*ln(1+I*exp(I*(d*x+c)))*c*e*f+1/d^2/a*e*f*c*ln(exp(I*(d*x+c))-I)+I/d^2/a*polylog(2,-I*exp(I*(d*x+c)))*f^2*x+I/d^2/a*e*f*polylog(2,-I*exp(I*(d*x+c)))+1/2/d^3/a*f^2*c^2*ln(exp(I*(d*x+c))+I)-f^2*polylog(3,-I*exp(I*(d*x+c)))/a/d^3+f^2*polylog(3,I*exp(I*(d*x+c)))/a/d^3","B"
271,1,303,149,0.337000," ","int((f*x+e)*sec(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{i \left(d f x \,{\mathrm e}^{i \left(d x +c \right)}+d e \,{\mathrm e}^{i \left(d x +c \right)}+f -i f \,{\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} \left({\mathrm e}^{i \left(d x +c \right)}+i\right)^{2} a}-\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 a d}+\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e}{2 d a}-\frac{f \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) x}{2 a d}-\frac{f \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c}{2 a \,d^{2}}+\frac{i f \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{2 a \,d^{2}}+\frac{f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{2 d a}+\frac{f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{2 d^{2} a}-\frac{i f \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{2 a \,d^{2}}+\frac{f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 a \,d^{2}}-\frac{f c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{2 d^{2} a}"," ",0,"-I*(d*f*x*exp(I*(d*x+c))+d*e*exp(I*(d*x+c))+f-I*f*exp(I*(d*x+c)))/d^2/(exp(I*(d*x+c))+I)^2/a-1/2/a/d*e*ln(exp(I*(d*x+c))-I)+1/2/d/a*ln(exp(I*(d*x+c))+I)*e-1/2/a/d*f*ln(1+I*exp(I*(d*x+c)))*x-1/2/a/d^2*f*ln(1+I*exp(I*(d*x+c)))*c+1/2*I*f*polylog(2,-I*exp(I*(d*x+c)))/a/d^2+1/2/d/a*f*ln(1-I*exp(I*(d*x+c)))*x+1/2/d^2/a*f*ln(1-I*exp(I*(d*x+c)))*c-1/2*I*f*polylog(2,I*exp(I*(d*x+c)))/a/d^2+1/2/a/d^2*f*c*ln(exp(I*(d*x+c))-I)-1/2/d^2/a*f*c*ln(exp(I*(d*x+c))+I)","B"
272,1,54,33,0.108000," ","int(sec(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{4 a d}-\frac{1}{2 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{4 a d}"," ",0,"-1/4/a/d*ln(sin(d*x+c)-1)-1/2/a/d/(1+sin(d*x+c))+1/4*ln(1+sin(d*x+c))/a/d","A"
273,0,0,28,2.256000," ","int(sec(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","\int \frac{\sec \left(d x +c \right)}{\left(f x +e \right) \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sec(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x)","F"
274,0,0,28,4.023000," ","int(sec(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\int \frac{\sec \left(d x +c \right)}{\left(f x +e \right)^{2} \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sec(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x)","F"
275,1,1124,438,0.518000," ","int((f*x+e)^3*sec(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{3 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 a \,d^{4}}+\frac{3 e^{2} f \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 a \,d^{2}}+\frac{5 f^{3} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{8 i f^{2} e c x}{a \,d^{2}}+\frac{5 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{2}}{2 a \,d^{2}}+\frac{5 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{2 a \,d^{2}}-\frac{5 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{2 a \,d^{4}}-\frac{4 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e^{2}}{a \,d^{2}}-\frac{4 i f^{3} x^{3}}{3 a d}-\frac{4 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}+\frac{8 i f^{3} c^{3}}{3 a \,d^{4}}+\frac{5 f^{3} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{2 a \,d^{4}}-\frac{5 i f^{3} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{3}}-\frac{4 i f^{2} e \,c^{2}}{a \,d^{3}}-\frac{3 i e \,f^{2} \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{3 i \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right) f^{3} x}{a \,d^{3}}+\frac{3 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) e \,f^{2} x}{a \,d^{2}}+\frac{3 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c e \,f^{2}}{a \,d^{3}}-\frac{3 e \,f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{a \,d^{3}}+\frac{3 f^{3} \polylog \left(3, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{2 f^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}+\frac{2 f^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{4}}+\frac{5 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{5 f^{2} e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}+\frac{4 i f^{3} c^{2} x}{a \,d^{3}}-\frac{5 i f^{2} e \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{5 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{a \,d^{3}}+\frac{8 f^{2} e c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{4 i f^{2} e \,x^{2}}{a d}+\frac{3 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) f^{3} x^{2}}{2 a \,d^{2}}-\frac{3 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2} f^{3}}{2 a \,d^{4}}-\frac{24 d^{2} e \,f^{2} x^{2} {\mathrm e}^{i \left(d x +c \right)}+24 d^{2} e^{2} f x \,{\mathrm e}^{i \left(d x +c \right)}+6 i d e \,f^{2} x \,{\mathrm e}^{3 i \left(d x +c \right)}+12 i d^{2} e^{2} f x +3 i d \,e^{2} f \,{\mathrm e}^{3 i \left(d x +c \right)}+6 i f^{3} x +3 i d \,f^{3} x^{2} {\mathrm e}^{i \left(d x +c \right)}+3 i d \,f^{3} x^{2} {\mathrm e}^{3 i \left(d x +c \right)}+4 i d^{2} e^{3}+6 i e \,f^{2}+12 i d^{2} e \,f^{2} x^{2}+4 i d^{2} f^{3} x^{3}+8 d^{2} e^{3} {\mathrm e}^{i \left(d x +c \right)}+6 i e \,f^{2} {\mathrm e}^{2 i \left(d x +c \right)}+6 f^{3} x \,{\mathrm e}^{i \left(d x +c \right)}+6 e \,f^{2} {\mathrm e}^{i \left(d x +c \right)}+6 f^{3} x \,{\mathrm e}^{3 i \left(d x +c \right)}+6 e \,f^{2} {\mathrm e}^{3 i \left(d x +c \right)}+8 d^{2} f^{3} x^{3} {\mathrm e}^{i \left(d x +c \right)}+6 i f^{3} x \,{\mathrm e}^{2 i \left(d x +c \right)}+6 i d e \,f^{2} x \,{\mathrm e}^{i \left(d x +c \right)}+3 i d \,e^{2} f \,{\mathrm e}^{i \left(d x +c \right)}}{3 \left({\mathrm e}^{i \left(d x +c \right)}-i\right) \left({\mathrm e}^{i \left(d x +c \right)}+i\right)^{3} d^{3} a}"," ",0,"5/a/d^2*f^2*e*ln(1-I*exp(I*(d*x+c)))*x+5/a/d^3*f^2*e*ln(1-I*exp(I*(d*x+c)))*c+8/a/d^3*f^2*e*c*ln(exp(I*(d*x+c)))+3/2/a/d^4*f^3*c^2*ln(exp(I*(d*x+c))-I)+3/2/a/d^2*e^2*f*ln(exp(I*(d*x+c))-I)+8/3*I/a/d^4*c^3*f^3-4/3*I/a/d*f^3*x^3-4/a/d^2*f*ln(exp(I*(d*x+c)))*e^2-4/a/d^4*f^3*c^2*ln(exp(I*(d*x+c)))+5/2/a/d^4*f^3*c^2*ln(exp(I*(d*x+c))+I)+5/2/a/d^2*f*ln(exp(I*(d*x+c))+I)*e^2-1/3*(24*d^2*e*f^2*x^2*exp(I*(d*x+c))+24*d^2*e^2*f*x*exp(I*(d*x+c))+6*I*d*e*f^2*x*exp(3*I*(d*x+c))+12*I*d^2*e^2*f*x+3*I*d*e^2*f*exp(3*I*(d*x+c))+6*I*f^3*x+3*I*d*f^3*x^2*exp(I*(d*x+c))+3*I*d*f^3*x^2*exp(3*I*(d*x+c))+4*I*d^2*e^3+6*I*e*f^2+12*I*d^2*e*f^2*x^2+4*I*d^2*f^3*x^3+8*d^2*e^3*exp(I*(d*x+c))+6*I*e*f^2*exp(2*I*(d*x+c))+6*f^3*x*exp(I*(d*x+c))+6*e*f^2*exp(I*(d*x+c))+6*f^3*x*exp(3*I*(d*x+c))+6*e*f^2*exp(3*I*(d*x+c))+8*d^2*f^3*x^3*exp(I*(d*x+c))+6*I*f^3*x*exp(2*I*(d*x+c))+6*I*d*e*f^2*x*exp(I*(d*x+c))+3*I*d*e^2*f*exp(I*(d*x+c)))/(exp(I*(d*x+c))-I)/(exp(I*(d*x+c))+I)^3/d^3/a+5/2/a/d^2*f^3*ln(1-I*exp(I*(d*x+c)))*x^2+4*I/a/d^3*c^2*f^3*x-3*I/a/d^3*e*f^2*polylog(2,-I*exp(I*(d*x+c)))-5*I/a/d^3*e*f^2*polylog(2,I*exp(I*(d*x+c)))-3*I/a/d^3*polylog(2,-I*exp(I*(d*x+c)))*f^3*x-4*I/a/d^3*c^2*e*f^2+3/2/a/d^2*ln(1+I*exp(I*(d*x+c)))*f^3*x^2+3/a/d^2*ln(1+I*exp(I*(d*x+c)))*e*f^2*x+3/a/d^3*ln(1+I*exp(I*(d*x+c)))*c*e*f^2-3/a/d^3*e*f^2*c*ln(exp(I*(d*x+c))-I)-5*I/a/d^3*polylog(2,I*exp(I*(d*x+c)))*f^3*x-4*I/a/d*e*f^2*x^2-8*I/a/d^2*c*e*f^2*x+3*f^3*polylog(3,-I*exp(I*(d*x+c)))/a/d^4+5*f^3*polylog(3,I*exp(I*(d*x+c)))/a/d^4-2/a/d^4*f^3*ln(exp(I*(d*x+c)))+2/a/d^4*f^3*ln(exp(I*(d*x+c))+I)-5/2/a/d^4*f^3*ln(1-I*exp(I*(d*x+c)))*c^2-5/a/d^3*f^2*e*c*ln(exp(I*(d*x+c))+I)-3/2/a/d^4*ln(1+I*exp(I*(d*x+c)))*c^2*f^3","B"
276,1,573,300,0.385000," ","int((f*x+e)^2*sec(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{2 \left(4 d^{2} e^{2} {\mathrm e}^{i \left(d x +c \right)}+2 i d^{2} e^{2}+f^{2} {\mathrm e}^{3 i \left(d x +c \right)}+i f^{2} {\mathrm e}^{2 i \left(d x +c \right)}+i f^{2}+4 d^{2} f^{2} x^{2} {\mathrm e}^{i \left(d x +c \right)}+2 i d^{2} f^{2} x^{2}+f^{2} {\mathrm e}^{i \left(d x +c \right)}+8 d^{2} e f x \,{\mathrm e}^{i \left(d x +c \right)}+i d \,f^{2} x \,{\mathrm e}^{i \left(d x +c \right)}+i d e f \,{\mathrm e}^{i \left(d x +c \right)}+i d \,f^{2} x \,{\mathrm e}^{3 i \left(d x +c \right)}+i d e f \,{\mathrm e}^{3 i \left(d x +c \right)}+4 i d^{2} e f x \right)}{3 \left({\mathrm e}^{i \left(d x +c \right)}-i\right) \left({\mathrm e}^{i \left(d x +c \right)}+i\right)^{3} d^{3} a}+\frac{e f \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{a \,d^{2}}+\frac{5 f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e}{3 a \,d^{2}}-\frac{8 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{3 a \,d^{2}}-\frac{f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{a \,d^{3}}-\frac{5 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{3 a \,d^{3}}+\frac{8 f^{2} c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{3 a \,d^{3}}-\frac{5 i f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{3 a \,d^{3}}-\frac{i f^{2} \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}-\frac{4 i f^{2} c^{2}}{3 a \,d^{3}}+\frac{f^{2} \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) x}{a \,d^{2}}+\frac{f^{2} \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c}{a \,d^{3}}-\frac{8 i f^{2} c x}{3 a \,d^{2}}+\frac{5 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{3 a \,d^{2}}+\frac{5 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{3 a \,d^{3}}-\frac{4 i f^{2} x^{2}}{3 a d}"," ",0,"-2/3*(4*d^2*e^2*exp(I*(d*x+c))+2*I*d^2*e^2+f^2*exp(3*I*(d*x+c))+I*f^2*exp(2*I*(d*x+c))+I*f^2+4*d^2*f^2*x^2*exp(I*(d*x+c))+2*I*d^2*f^2*x^2+f^2*exp(I*(d*x+c))+8*d^2*e*f*x*exp(I*(d*x+c))+I*d*f^2*x*exp(I*(d*x+c))+I*d*e*f*exp(I*(d*x+c))+I*d*f^2*x*exp(3*I*(d*x+c))+I*d*e*f*exp(3*I*(d*x+c))+4*I*d^2*e*f*x)/(exp(I*(d*x+c))-I)/(exp(I*(d*x+c))+I)^3/d^3/a+1/a/d^2*e*f*ln(exp(I*(d*x+c))-I)+5/3/a/d^2*f*ln(exp(I*(d*x+c))+I)*e-8/3/a/d^2*f*ln(exp(I*(d*x+c)))*e-1/a/d^3*f^2*c*ln(exp(I*(d*x+c))-I)-5/3/a/d^3*f^2*c*ln(exp(I*(d*x+c))+I)+8/3/a/d^3*f^2*c*ln(exp(I*(d*x+c)))-4/3*I/a/d^3*f^2*c^2-I/a/d^3*f^2*polylog(2,-I*exp(I*(d*x+c)))-8/3*I/a/d^2*f^2*c*x+1/a/d^2*f^2*ln(1+I*exp(I*(d*x+c)))*x+1/a/d^3*f^2*ln(1+I*exp(I*(d*x+c)))*c-5/3*I/a/d^3*f^2*polylog(2,I*exp(I*(d*x+c)))+5/3/a/d^2*f^2*ln(1-I*exp(I*(d*x+c)))*x+5/3/a/d^3*f^2*ln(1-I*exp(I*(d*x+c)))*c-4/3*I/a/d*f^2*x^2","A"
277,1,466,138,0.308000," ","int((f*x+e)*sec(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{e}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 e}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{e}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3 e}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{f x}{3 a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) d}-\frac{4 f x \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{3 a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) d}-\frac{2 f x \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) d}-\frac{4 f x \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) d}+\frac{f x \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) d}-\frac{f \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{3 a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) d^{2}}+\frac{f \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) d^{2}}+\frac{f \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a \,d^{2}}+\frac{5 f \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{6 a \,d^{2}}-\frac{2 f \ln \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a \,d^{2}}"," ",0,"-1/2/a*e/d/(tan(1/2*d*x+1/2*c)-1)-2/3/a*e/d/(tan(1/2*d*x+1/2*c)+1)^3+1/a*e/d/(tan(1/2*d*x+1/2*c)+1)^2-3/2/a*e/d/(tan(1/2*d*x+1/2*c)+1)+1/3/a*f/(tan(1/2*d*x+1/2*c)+1)^3/(tan(1/2*d*x+1/2*c)-1)*x/d-4/3/a*f/(tan(1/2*d*x+1/2*c)+1)^3/(tan(1/2*d*x+1/2*c)-1)*x/d*tan(1/2*d*x+1/2*c)-2/a*f/(tan(1/2*d*x+1/2*c)+1)^3/(tan(1/2*d*x+1/2*c)-1)*x/d*tan(1/2*d*x+1/2*c)^2-4/3/a*f/(tan(1/2*d*x+1/2*c)+1)^3/(tan(1/2*d*x+1/2*c)-1)*x/d*tan(1/2*d*x+1/2*c)^3+1/3/a*f/(tan(1/2*d*x+1/2*c)+1)^3/(tan(1/2*d*x+1/2*c)-1)*x/d*tan(1/2*d*x+1/2*c)^4-1/3/a*f/(tan(1/2*d*x+1/2*c)+1)^3/(tan(1/2*d*x+1/2*c)-1)/d^2*tan(1/2*d*x+1/2*c)+1/3/a*f/(tan(1/2*d*x+1/2*c)+1)^3/(tan(1/2*d*x+1/2*c)-1)/d^2*tan(1/2*d*x+1/2*c)^3+1/2/a*f/d^2*ln(tan(1/2*d*x+1/2*c)-1)+5/6/a*f/d^2*ln(tan(1/2*d*x+1/2*c)+1)-2/3/a*f/d^2*ln(1+tan(1/2*d*x+1/2*c)^2)","B"
278,1,70,38,0.125000," ","int(sec(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d a}"," ",0,"2/d/a*(-1/4/(tan(1/2*d*x+1/2*c)-1)-1/3/(tan(1/2*d*x+1/2*c)+1)^3+1/2/(tan(1/2*d*x+1/2*c)+1)^2-3/4/(tan(1/2*d*x+1/2*c)+1))","A"
279,0,0,30,3.898000," ","int(sec(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(f x +e \right) \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sec(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x)","F"
280,0,0,30,6.602000," ","int(sec(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(f x +e \right)^{2} \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sec(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x)","F"
281,1,2161,612,0.649000," ","int((f*x+e)^3*sec(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{9 i e^{2} f \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{8 a \,d^{2}}+\frac{9 i f^{3} \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{8 a \,d^{2}}+\frac{3 \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{3}}{8 d a}-\frac{3 f^{3} \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) x}{2 a \,d^{3}}-\frac{3 f^{3} \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c}{2 a \,d^{4}}-\frac{3 e \,f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 a \,d^{3}}+\frac{3 f^{3} c \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 a \,d^{4}}+\frac{3 i f^{3} \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{2 a \,d^{4}}+\frac{9 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2} e \,f^{2}}{8 a \,d^{3}}-\frac{9 i e \,f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{4 d^{2} a}-\frac{9 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) e \,f^{2} x^{2}}{8 a d}-\frac{3 e^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{8 a d}-\frac{9 e \,f^{2} c^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right)}{8 d^{3} a}-\frac{9 e^{2} f c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{8 d^{2} a}+\frac{9 e \,f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{8 d^{3} a}+\frac{9 e^{2} f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{8 d a}+\frac{9 e^{2} f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{8 d^{2} a}+\frac{9 e \,f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{8 d a}-\frac{3 f^{3} \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) x^{3}}{8 a d}-\frac{3 f^{3} \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c^{3}}{8 a \,d^{4}}-\frac{i f^{3} x^{2}}{a \,d^{2}}+\frac{3 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{3}}{8 d a}+\frac{3 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d^{3} f^{3} x^{3} {\mathrm e}^{2 i \left(d x +c \right)}-8 i d^{2} f^{3} x^{2} {\mathrm e}^{3 i \left(d x +c \right)}-8 i d^{2} e^{2} f \,{\mathrm e}^{3 i \left(d x +c \right)}+6 i d^{3} f^{3} x^{3} {\mathrm e}^{4 i \left(d x +c \right)}+9 d^{3} e \,f^{2} x^{2} {\mathrm e}^{5 i \left(d x +c \right)}-9 i d^{2} f^{3} x^{2} {\mathrm e}^{5 i \left(d x +c \right)}-9 i d^{2} e^{2} f \,{\mathrm e}^{5 i \left(d x +c \right)}+9 d^{3} e^{2} f x \,{\mathrm e}^{5 i \left(d x +c \right)}+6 d^{3} e \,f^{2} x^{2} {\mathrm e}^{3 i \left(d x +c \right)}+6 d^{3} e^{2} f x \,{\mathrm e}^{3 i \left(d x +c \right)}+44 d^{2} e \,f^{2} x \,{\mathrm e}^{2 i \left(d x +c \right)}+8 d^{2} e \,f^{2} x -4 i f^{3} {\mathrm e}^{3 i \left(d x +c \right)}+2 d^{3} e^{3} {\mathrm e}^{3 i \left(d x +c \right)}-2 i f^{3} {\mathrm e}^{5 i \left(d x +c \right)}+3 d^{3} e^{3} {\mathrm e}^{i \left(d x +c \right)}-2 i f^{3} {\mathrm e}^{i \left(d x +c \right)}+3 d^{3} e^{3} {\mathrm e}^{5 i \left(d x +c \right)}+2 f^{3} {\mathrm e}^{4 i \left(d x +c \right)}+4 f^{3} {\mathrm e}^{2 i \left(d x +c \right)}+2 i d^{2} e \,f^{2} x \,{\mathrm e}^{i \left(d x +c \right)}-18 i d^{3} e \,f^{2} x^{2} {\mathrm e}^{2 i \left(d x +c \right)}-18 i d^{3} e^{2} f x \,{\mathrm e}^{2 i \left(d x +c \right)}-16 i d^{2} e \,f^{2} x \,{\mathrm e}^{3 i \left(d x +c \right)}+18 i d^{3} e \,f^{2} x^{2} {\mathrm e}^{4 i \left(d x +c \right)}+18 i d^{3} e^{2} f x \,{\mathrm e}^{4 i \left(d x +c \right)}-18 i d^{2} e \,f^{2} x \,{\mathrm e}^{5 i \left(d x +c \right)}+2 d \,f^{3} x \,{\mathrm e}^{i \left(d x +c \right)}+2 d e \,f^{2} {\mathrm e}^{i \left(d x +c \right)}+22 d^{2} e^{2} f \,{\mathrm e}^{2 i \left(d x +c \right)}+22 d^{2} f^{3} x^{2} {\mathrm e}^{2 i \left(d x +c \right)}+4 d \,f^{3} x \,{\mathrm e}^{3 i \left(d x +c \right)}+4 d e \,f^{2} {\mathrm e}^{3 i \left(d x +c \right)}+6 i d^{3} e^{3} {\mathrm e}^{4 i \left(d x +c \right)}-6 i d^{3} e^{3} {\mathrm e}^{2 i \left(d x +c \right)}+3 d^{3} f^{3} x^{3} {\mathrm e}^{5 i \left(d x +c \right)}+2 d \,f^{3} x \,{\mathrm e}^{5 i \left(d x +c \right)}+2 d e \,f^{2} {\mathrm e}^{5 i \left(d x +c \right)}+18 d^{2} e^{2} f \,{\mathrm e}^{4 i \left(d x +c \right)}+18 d^{2} f^{3} x^{2} {\mathrm e}^{4 i \left(d x +c \right)}+2 d^{3} f^{3} x^{3} {\mathrm e}^{3 i \left(d x +c \right)}+3 d^{3} f^{3} x^{3} {\mathrm e}^{i \left(d x +c \right)}\right)}{4 \left({\mathrm e}^{i \left(d x +c \right)}+i\right)^{4} d^{4} \left({\mathrm e}^{i \left(d x +c \right)}-i\right)^{2} a}+\frac{9 i \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right) e \,f^{2} x}{4 a \,d^{2}}-\frac{9 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c \,e^{2} f}{8 a \,d^{2}}-\frac{2 i f^{3} c x}{a \,d^{3}}-\frac{9 e \,f^{2} c^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{8 a \,d^{3}}-\frac{2 e \,f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{3}}+\frac{7 e \,f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{2 a \,d^{3}}+\frac{2 f^{3} c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{4}}-\frac{7 f^{3} c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{2 a \,d^{4}}+\frac{3 f^{3} c^{3} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{8 a \,d^{4}}+\frac{7 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{2 a \,d^{3}}+\frac{7 f^{3} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{2 a \,d^{4}}-\frac{9 f^{3} \polylog \left(3, -i {\mathrm e}^{i \left(d x +c \right)}\right) x}{4 a \,d^{3}}-\frac{7 i f^{3} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{2 a \,d^{4}}-\frac{9 i f^{3} \polylog \left(4, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{4 a \,d^{4}}-\frac{9 e \,f^{2} \polylog \left(3, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{4 a \,d^{3}}-\frac{i c^{2} f^{3}}{a \,d^{4}}+\frac{9 e^{2} f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{8 a \,d^{2}}-\frac{9 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) e^{2} f x}{8 a d}"," ",0,"9/4*I/a/d^2*polylog(2,-I*exp(I*(d*x+c)))*e*f^2*x-9/4*I/a/d^2*polylog(2,I*exp(I*(d*x+c)))*e*f^2*x-3/2/a/d^3*f^3*ln(1+I*exp(I*(d*x+c)))*x-3/2/a/d^4*f^3*ln(1+I*exp(I*(d*x+c)))*c-3/2/a/d^3*e*f^2*ln(exp(I*(d*x+c))-I)+9/8/a/d^3*ln(1+I*exp(I*(d*x+c)))*c^2*e*f^2-9/8/a/d*ln(1+I*exp(I*(d*x+c)))*e*f^2*x^2-1/4*I*(-4*I*f^3*exp(3*I*(d*x+c))+2*d^3*e^3*exp(3*I*(d*x+c))-2*I*f^3*exp(5*I*(d*x+c))+3*d^3*e^3*exp(I*(d*x+c))-2*I*f^3*exp(I*(d*x+c))+2*f^3+4*d^2*e^2*f+3*d^3*e^3*exp(5*I*(d*x+c))+4*d^2*f^3*x^2+2*f^3*exp(4*I*(d*x+c))+2*I*d^2*e*f^2*x*exp(I*(d*x+c))-18*I*d^3*e*f^2*x^2*exp(2*I*(d*x+c))-18*I*d^3*e^2*f*x*exp(2*I*(d*x+c))+4*f^3*exp(2*I*(d*x+c))+I*d^2*f^3*x^2*exp(I*(d*x+c))+I*d^2*e^2*f*exp(I*(d*x+c))+9*d^3*e*f^2*x^2*exp(I*(d*x+c))+9*d^3*e^2*f*x*exp(I*(d*x+c))+8*d^2*e*f^2*x+36*d^2*e*f^2*x*exp(4*I*(d*x+c))-6*I*d^3*f^3*x^3*exp(2*I*(d*x+c))-8*I*d^2*f^3*x^2*exp(3*I*(d*x+c))-8*I*d^2*e^2*f*exp(3*I*(d*x+c))+6*I*d^3*f^3*x^3*exp(4*I*(d*x+c))-16*I*d^2*e*f^2*x*exp(3*I*(d*x+c))+18*I*d^3*e*f^2*x^2*exp(4*I*(d*x+c))+18*I*d^3*e^2*f*x*exp(4*I*(d*x+c))-18*I*d^2*e*f^2*x*exp(5*I*(d*x+c))+9*d^3*e*f^2*x^2*exp(5*I*(d*x+c))+22*d^2*e^2*f*exp(2*I*(d*x+c))+22*d^2*f^3*x^2*exp(2*I*(d*x+c))+4*d*f^3*x*exp(3*I*(d*x+c))+4*d*e*f^2*exp(3*I*(d*x+c))+6*I*d^3*e^3*exp(4*I*(d*x+c))-6*I*d^3*e^3*exp(2*I*(d*x+c))+3*d^3*f^3*x^3*exp(5*I*(d*x+c))+2*d*f^3*x*exp(5*I*(d*x+c))+2*d*e*f^2*exp(5*I*(d*x+c))+18*d^2*e^2*f*exp(4*I*(d*x+c))+18*d^2*f^3*x^2*exp(4*I*(d*x+c))+2*d^3*f^3*x^3*exp(3*I*(d*x+c))-9*I*d^2*f^3*x^2*exp(5*I*(d*x+c))-9*I*d^2*e^2*f*exp(5*I*(d*x+c))+3*d^3*f^3*x^3*exp(I*(d*x+c))+2*d*f^3*x*exp(I*(d*x+c))+2*d*e*f^2*exp(I*(d*x+c))+9*d^3*e^2*f*x*exp(5*I*(d*x+c))+6*d^3*e*f^2*x^2*exp(3*I*(d*x+c))+6*d^3*e^2*f*x*exp(3*I*(d*x+c))+44*d^2*e*f^2*x*exp(2*I*(d*x+c)))/(exp(I*(d*x+c))+I)^4/d^4/(exp(I*(d*x+c))-I)^2/a+3/2/a/d^4*f^3*c*ln(exp(I*(d*x+c))-I)-I/a/d^2*f^3*x^2-I/a/d^4*c^2*f^3+3/2*I/a/d^4*f^3*polylog(2,-I*exp(I*(d*x+c)))-7/2*I/a/d^4*f^3*polylog(2,I*exp(I*(d*x+c)))+3/8/d/a*f^3*ln(1-I*exp(I*(d*x+c)))*x^3-9/8/d^3/a*e*f^2*c^2*ln(1-I*exp(I*(d*x+c)))-9/8/d^2/a*e^2*f*c*ln(exp(I*(d*x+c))+I)+9/8/d^3/a*e*f^2*c^2*ln(exp(I*(d*x+c))+I)+9/8/d/a*e^2*f*ln(1-I*exp(I*(d*x+c)))*x+9/8/d^2/a*e^2*f*ln(1-I*exp(I*(d*x+c)))*c+3/8/d/a*ln(exp(I*(d*x+c))+I)*e^3+9/8/d/a*e*f^2*ln(1-I*exp(I*(d*x+c)))*x^2+9/8/a/d^2*e^2*f*c*ln(exp(I*(d*x+c))-I)-9/8/a/d*ln(1+I*exp(I*(d*x+c)))*e^2*f*x-9/8/a/d^2*ln(1+I*exp(I*(d*x+c)))*c*e^2*f-3/8/a/d*e^3*ln(exp(I*(d*x+c))-I)+3/8/d^4/a*f^3*c^3*ln(1-I*exp(I*(d*x+c)))+9/4/d^3/a*f^3*polylog(3,I*exp(I*(d*x+c)))*x-3/8/d^4/a*f^3*c^3*ln(exp(I*(d*x+c))+I)+9/4/d^3/a*e*f^2*polylog(3,I*exp(I*(d*x+c)))-9/8/a/d^3*e*f^2*c^2*ln(exp(I*(d*x+c))-I)-3/8/a/d*f^3*ln(1+I*exp(I*(d*x+c)))*x^3-3/8/a/d^4*f^3*ln(1+I*exp(I*(d*x+c)))*c^3-9/4/a/d^3*f^3*polylog(3,-I*exp(I*(d*x+c)))*x+9/4*I*f^3*polylog(4,I*exp(I*(d*x+c)))/a/d^4-9/4*I*f^3*polylog(4,-I*exp(I*(d*x+c)))/a/d^4+9/8*I/a/d^2*e^2*f*polylog(2,-I*exp(I*(d*x+c)))-9/8*I/a/d^2*e^2*f*polylog(2,I*exp(I*(d*x+c)))-2*I/a/d^3*f^3*c*x-9/8*I/a/d^2*f^3*polylog(2,I*exp(I*(d*x+c)))*x^2+9/8*I/a/d^2*f^3*polylog(2,-I*exp(I*(d*x+c)))*x^2-2/a/d^3*e*f^2*ln(exp(I*(d*x+c)))+7/2/a/d^3*e*f^2*ln(exp(I*(d*x+c))+I)-9/4/a/d^3*e*f^2*polylog(3,-I*exp(I*(d*x+c)))+2/a/d^4*f^3*c*ln(exp(I*(d*x+c)))-7/2/a/d^4*f^3*c*ln(exp(I*(d*x+c))+I)+3/8/a/d^4*f^3*c^3*ln(exp(I*(d*x+c))-I)+7/2/a/d^3*f^3*ln(1-I*exp(I*(d*x+c)))*x+7/2/a/d^4*f^3*ln(1-I*exp(I*(d*x+c)))*c","B"
282,1,1119,382,0.622000," ","int((f*x+e)^2*sec(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{3 i f^{2} \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right) x}{4 d^{2} a}+\frac{7 f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{6 d^{3} a}-\frac{2 f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{3 d^{3} a}-\frac{3 e^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{8 d a}+\frac{3 f e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{4 d a}+\frac{3 f e \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{4 d^{2} a}-\frac{3 f e c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{4 d^{2} a}+\frac{3 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x^{2}}{8 d a}-\frac{3 f^{2} \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2}}{8 d^{3} a}+\frac{3 \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e^{2}}{8 d a}+\frac{3 \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c^{2} f^{2}}{8 d^{3} 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e}^{3 i \left(d x +c \right)}+2 f^{2} {\mathrm e}^{i \left(d x +c \right)}+8 d e f +18 d^{2} e f x \,{\mathrm e}^{i \left(d x +c \right)}+9 d^{2} e^{2} {\mathrm e}^{i \left(d x +c \right)}+18 d^{2} e f x \,{\mathrm e}^{5 i \left(d x +c \right)}+12 d^{2} e f x \,{\mathrm e}^{3 i \left(d x +c \right)}-18 i d \,f^{2} x \,{\mathrm e}^{5 i \left(d x +c \right)}-18 i d e f \,{\mathrm e}^{5 i \left(d x +c \right)}+18 i d^{2} f^{2} x^{2} {\mathrm e}^{4 i \left(d x +c \right)}-18 i d^{2} f^{2} x^{2} {\mathrm e}^{2 i \left(d x +c \right)}+2 f^{2} {\mathrm e}^{5 i \left(d x +c \right)}+8 d \,f^{2} x +9 d^{2} e^{2} {\mathrm e}^{5 i \left(d x +c \right)}+6 d^{2} e^{2} {\mathrm e}^{3 i \left(d x +c \right)}-36 i d^{2} e f x \,{\mathrm e}^{2 i \left(d x +c \right)}+36 i d^{2} e f x \,{\mathrm e}^{4 i \left(d x +c \right)}+6 d^{2} f^{2} x^{2} {\mathrm e}^{3 i \left(d x +c \right)}+36 d \,f^{2} x \,{\mathrm e}^{4 i \left(d x +c \right)}+36 d e f \,{\mathrm e}^{4 i \left(d x +c \right)}+9 d^{2} f^{2} x^{2} {\mathrm e}^{5 i \left(d x +c \right)}-18 i d^{2} e^{2} {\mathrm e}^{2 i \left(d x +c \right)}+18 i d^{2} e^{2} {\mathrm e}^{4 i \left(d x +c \right)}+44 d \,f^{2} x \,{\mathrm e}^{2 i \left(d x +c \right)}+44 d e f \,{\mathrm e}^{2 i \left(d x +c \right)}\right)}{12 \left({\mathrm e}^{i \left(d x +c \right)}+i\right)^{4} d^{3} \left({\mathrm e}^{i \left(d x +c \right)}-i\right)^{2} a}-\frac{3 i f e \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{4 d^{2} a}-\frac{3 f^{2} \polylog \left(3, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{4 a \,d^{3}}+\frac{3 f^{2} \polylog \left(3, i {\mathrm e}^{i \left(d x +c \right)}\right)}{4 a \,d^{3}}-\frac{f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{2 d^{3} a}"," ",0,"3/4*I/d^2/a*e*f*polylog(2,-I*exp(I*(d*x+c)))+7/6/d^3/a*f^2*ln(exp(I*(d*x+c))+I)-2/3/d^3/a*f^2*ln(exp(I*(d*x+c)))-3/8/d/a*e^2*ln(exp(I*(d*x+c))-I)+3/4/d/a*f*e*ln(1-I*exp(I*(d*x+c)))*x+3/4/d^2/a*f*e*ln(1-I*exp(I*(d*x+c)))*c-3/4/d^2/a*f*e*c*ln(exp(I*(d*x+c))+I)+3/8/d/a*f^2*ln(1-I*exp(I*(d*x+c)))*x^2-3/8/d^3/a*f^2*ln(1-I*exp(I*(d*x+c)))*c^2+3/8/d/a*ln(exp(I*(d*x+c))+I)*e^2+3/8/d^3/a*ln(1+I*exp(I*(d*x+c)))*c^2*f^2-3/8/d^3/a*f^2*c^2*ln(exp(I*(d*x+c))-I)-3/8/d/a*ln(1+I*exp(I*(d*x+c)))*f^2*x^2-3/4/d/a*ln(1+I*exp(I*(d*x+c)))*e*f*x-3/4/d^2/a*ln(1+I*exp(I*(d*x+c)))*c*e*f+3/4/d^2/a*e*f*c*ln(exp(I*(d*x+c))-I)+3/8/d^3/a*f^2*c^2*ln(exp(I*(d*x+c))+I)+3/4*I/d^2/a*polylog(2,-I*exp(I*(d*x+c)))*f^2*x-3/4*I/d^2/a*polylog(2,I*exp(I*(d*x+c)))*f^2*x-3/4*I/d^2/a*e*f*polylog(2,I*exp(I*(d*x+c)))-1/12*I*(2*f^2*exp(5*I*(d*x+c))-16*I*d*f^2*x*exp(3*I*(d*x+c))-16*I*d*e*f*exp(3*I*(d*x+c))+18*d^2*e*f*x*exp(5*I*(d*x+c))+4*f^2*exp(3*I*(d*x+c))+9*d^2*f^2*x^2*exp(I*(d*x+c))+8*d*e*f+2*f^2*exp(I*(d*x+c))+9*d^2*e^2*exp(I*(d*x+c))+8*d*f^2*x+18*d^2*e*f*x*exp(I*(d*x+c))+9*d^2*e^2*exp(5*I*(d*x+c))+6*d^2*e^2*exp(3*I*(d*x+c))+12*d^2*e*f*x*exp(3*I*(d*x+c))+18*I*d^2*e^2*exp(4*I*(d*x+c))+44*d*f^2*x*exp(2*I*(d*x+c))+44*d*e*f*exp(2*I*(d*x+c))+6*d^2*f^2*x^2*exp(3*I*(d*x+c))+36*d*f^2*x*exp(4*I*(d*x+c))+36*d*e*f*exp(4*I*(d*x+c))+9*d^2*f^2*x^2*exp(5*I*(d*x+c))-18*I*d^2*e^2*exp(2*I*(d*x+c))-36*I*d^2*e*f*x*exp(2*I*(d*x+c))+36*I*d^2*e*f*x*exp(4*I*(d*x+c))-18*I*d*f^2*x*exp(5*I*(d*x+c))-18*I*d*e*f*exp(5*I*(d*x+c))+18*I*d^2*f^2*x^2*exp(4*I*(d*x+c))-18*I*d^2*f^2*x^2*exp(2*I*(d*x+c))+2*I*d*f^2*x*exp(I*(d*x+c))+2*I*d*e*f*exp(I*(d*x+c)))/(exp(I*(d*x+c))+I)^4/d^3/(exp(I*(d*x+c))-I)^2/a-3/4*f^2*polylog(3,-I*exp(I*(d*x+c)))/a/d^3+3/4*f^2*polylog(3,I*exp(I*(d*x+c)))/a/d^3-1/2/d^3/a*f^2*ln(exp(I*(d*x+c))-I)","B"
283,1,483,210,0.663000," ","int((f*x+e)*sec(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{i \left(-18 i d e \,{\mathrm e}^{2 i \left(d x +c \right)}+9 d f x \,{\mathrm e}^{5 i \left(d x +c \right)}+18 i d e \,{\mathrm e}^{4 i \left(d x +c \right)}-18 i d f x \,{\mathrm e}^{2 i \left(d x +c \right)}+9 d e \,{\mathrm e}^{5 i \left(d x +c \right)}+18 i d f x \,{\mathrm e}^{4 i \left(d x +c \right)}+6 d f x \,{\mathrm e}^{3 i \left(d x +c \right)}-8 i f \,{\mathrm e}^{3 i \left(d x +c \right)}-9 i f \,{\mathrm e}^{5 i \left(d x +c \right)}+6 d e \,{\mathrm e}^{3 i \left(d x +c \right)}+18 f \,{\mathrm e}^{4 i \left(d x +c \right)}+9 d f x \,{\mathrm e}^{i \left(d x +c \right)}+i f \,{\mathrm e}^{i \left(d x +c \right)}+9 d e \,{\mathrm e}^{i \left(d x +c \right)}+22 f \,{\mathrm e}^{2 i \left(d x +c \right)}+4 f \right)}{12 \left({\mathrm e}^{i \left(d x +c \right)}+i\right)^{4} d^{2} \left({\mathrm e}^{i \left(d x +c \right)}-i\right)^{2} a}-\frac{3 e \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{8 a d}+\frac{3 \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right) e}{8 d a}-\frac{3 f \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) x}{8 a d}-\frac{3 f \ln \left(1+i {\mathrm e}^{i \left(d x +c \right)}\right) c}{8 a \,d^{2}}+\frac{3 i f \polylog \left(2, -i {\mathrm e}^{i \left(d x +c \right)}\right)}{8 a \,d^{2}}+\frac{3 f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) x}{8 d a}+\frac{3 f \ln \left(1-i {\mathrm e}^{i \left(d x +c \right)}\right) c}{8 d^{2} a}-\frac{3 i f \polylog \left(2, i {\mathrm e}^{i \left(d x +c \right)}\right)}{8 a \,d^{2}}+\frac{3 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{8 a \,d^{2}}-\frac{3 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{8 d^{2} a}"," ",0,"-1/12*I*(-18*I*d*e*exp(2*I*(d*x+c))+9*d*f*x*exp(5*I*(d*x+c))+18*I*d*e*exp(4*I*(d*x+c))-18*I*d*f*x*exp(2*I*(d*x+c))+9*d*e*exp(5*I*(d*x+c))+18*I*d*f*x*exp(4*I*(d*x+c))+6*d*f*x*exp(3*I*(d*x+c))-8*I*f*exp(3*I*(d*x+c))-9*I*f*exp(5*I*(d*x+c))+6*d*e*exp(3*I*(d*x+c))+18*f*exp(4*I*(d*x+c))+9*d*f*x*exp(I*(d*x+c))+I*f*exp(I*(d*x+c))+9*d*e*exp(I*(d*x+c))+22*f*exp(2*I*(d*x+c))+4*f)/(exp(I*(d*x+c))+I)^4/d^2/(exp(I*(d*x+c))-I)^2/a-3/8/a/d*e*ln(exp(I*(d*x+c))-I)+3/8/d/a*ln(exp(I*(d*x+c))+I)*e-3/8/a/d*f*ln(1+I*exp(I*(d*x+c)))*x-3/8/a/d^2*f*ln(1+I*exp(I*(d*x+c)))*c+3/8*I*f*polylog(2,-I*exp(I*(d*x+c)))/a/d^2+3/8/d/a*f*ln(1-I*exp(I*(d*x+c)))*x+3/8/d^2/a*f*ln(1-I*exp(I*(d*x+c)))*c-3/8*I*f*polylog(2,I*exp(I*(d*x+c)))/a/d^2+3/8/a/d^2*f*c*ln(exp(I*(d*x+c))-I)-3/8/d^2/a*f*c*ln(exp(I*(d*x+c))+I)","B"
284,1,90,69,0.136000," ","int(sec(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{1}{8 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right)}{16 a d}-\frac{1}{8 a d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{4 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right)}{16 a d}"," ",0,"-1/8/a/d/(sin(d*x+c)-1)-3/16/a/d*ln(sin(d*x+c)-1)-1/8/a/d/(1+sin(d*x+c))^2-1/4/a/d/(1+sin(d*x+c))+3/16*ln(1+sin(d*x+c))/a/d","A"
285,0,0,30,6.454000," ","int(sec(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x)","\int \frac{\sec^{3}\left(d x +c \right)}{\left(f x +e \right) \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sec(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x)","F"
286,0,0,30,2.458000," ","int(sec(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x)","\int \frac{\sec^{3}\left(d x +c \right)}{\left(f x +e \right)^{2} \left(a +a \sin \left(d x +c \right)\right)}\, dx"," ",0,"int(sec(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x)","F"
287,0,0,419,0.328000," ","int((f*x+e)^m*cos(d*x+c)^4/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \left(\cos^{4}\left(d x +c \right)\right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*cos(d*x+c)^4/(a+a*sin(d*x+c)),x)","F"
288,0,0,259,0.341000," ","int((f*x+e)^m*cos(d*x+c)^3/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \left(\cos^{3}\left(d x +c \right)\right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*cos(d*x+c)^3/(a+a*sin(d*x+c)),x)","F"
289,0,0,144,0.197000," ","int((f*x+e)^m*cos(d*x+c)^2/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \left(\cos^{2}\left(d x +c \right)\right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*cos(d*x+c)^2/(a+a*sin(d*x+c)),x)","F"
290,0,0,28,0.142000," ","int((f*x+e)^m*cos(d*x+c)/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \cos \left(d x +c \right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*cos(d*x+c)/(a+a*sin(d*x+c)),x)","F"
291,0,0,22,0.002000," ","int((f*x+e)^m/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m}}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m/(a+a*sin(d*x+c)),x)","F"
292,0,0,28,0.201000," ","int((f*x+e)^m*sec(d*x+c)/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \sec \left(d x +c \right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*sec(d*x+c)/(a+a*sin(d*x+c)),x)","F"
293,0,0,30,0.263000," ","int((f*x+e)^m*sec(d*x+c)^2/(a+a*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \left(\sec^{2}\left(d x +c \right)\right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*sec(d*x+c)^2/(a+a*sin(d*x+c)),x)","F"
294,0,0,385,2.120000," ","int((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \cos \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c)),x)","F"
295,0,0,285,1.549000," ","int((f*x+e)^2*cos(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \cos \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*cos(d*x+c)/(a+b*sin(d*x+c)),x)","F"
296,1,1006,187,0.235000," ","int((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{i f \,c^{2}}{d^{2} b}+\frac{i e x}{b}+\frac{i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2}}{d^{2} b \left(-a^{2}+b^{2}\right)}-\frac{i b f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d \left(-a^{2}+b^{2}\right)}+\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \left(-a^{2}+b^{2}\right)}-\frac{i f \,x^{2}}{2 b}+\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \left(-a^{2}+b^{2}\right)}+\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \left(-a^{2}+b^{2}\right)}-\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) a^{2} x}{d b \left(-a^{2}+b^{2}\right)}-\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) a^{2} c}{d^{2} b \left(-a^{2}+b^{2}\right)}+\frac{e \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d b}-\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2} x}{d b \left(-a^{2}+b^{2}\right)}-\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2} c}{d^{2} b \left(-a^{2}+b^{2}\right)}-\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{d b}-\frac{i b f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) a^{2}}{d^{2} b \left(-a^{2}+b^{2}\right)}-\frac{2 i f c x}{d b}-\frac{f c \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d^{2} b}+\frac{2 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} b}"," ",0,"-I/d^2*b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))-I/d^2*b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-I/d^2/b*f*c^2+I/b*e*x+1/d*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x+1/d^2*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c-1/2*I/b*f*x^2+1/d*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+1/d^2*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-1/d/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*a^2*x-1/d^2/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*a^2*c+1/d/b*e*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-1/d/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2*x-1/d^2/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2*c-2/d/b*ln(exp(I*(d*x+c)))*e+I/d^2/b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2+I/d^2/b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*a^2-2*I/d/b*f*c*x-1/d^2/b*f*c*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+2/d^2/b*f*c*ln(exp(I*(d*x+c)))","B"
297,1,19,18,0.003000," ","int(cos(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{b d}"," ",0,"ln(a+b*sin(d*x+c))/b/d","A"
298,0,0,556,2.027000," ","int((f*x+e)^3*cos(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \left(\cos^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
299,0,0,412,1.623000," ","int((f*x+e)^2*cos(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \left(\cos^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*cos(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
300,1,1123,266,0.529000," ","int((f*x+e)*cos(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{a f \,x^{2}}{2 b^{2}}+\frac{a e x}{b^{2}}+\frac{\left(d f x +d e +i f \right) {\mathrm e}^{i \left(d x +c \right)}}{2 d^{2} b}+\frac{\left(d f x +d e -i f \right) {\mathrm e}^{-i \left(d x +c \right)}}{2 d^{2} b}+\frac{i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d \sqrt{-a^{2}+b^{2}}}+\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \sqrt{-a^{2}+b^{2}}}-\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{a^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{b^{2} d \sqrt{-a^{2}+b^{2}}}-\frac{a^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{a^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{b^{2} d \sqrt{-a^{2}+b^{2}}}+\frac{a^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{i a^{2} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{2 i e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \sqrt{-a^{2}+b^{2}}}-\frac{2 i a^{2} e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d \sqrt{-a^{2}+b^{2}}}-\frac{i a^{2} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 i f c \arctan \left(\frac{2 i 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}}}+\frac{2 i a^{2} f c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}"," ",0,"1/2*a*f*x^2/b^2+a*e*x/b^2+1/2*(d*f*x+I*f+d*e)/d^2/b*exp(I*(d*x+c))+1/2*(d*f*x-I*f+d*e)/d^2/b*exp(-I*(d*x+c))-I/d^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))+1/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x+1/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+2*I/d*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-1/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-1/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-a^2/b^2/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x-a^2/b^2/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+a^2/b^2/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+a^2/b^2/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-2*I/b^2/d*a^2*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+I/b^2/d^2*a^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))-I*a^2/b^2/d^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+I/d^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-2*I/d^2*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+2*I/b^2/d^2*a^2*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))","B"
301,1,142,65,0.003000," ","int(cos(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}+\frac{2}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{2 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}"," ",0,"-2/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+2/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/b/(1+tan(1/2*d*x+1/2*c)^2)+2/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))","B"
302,0,0,678,2.839000," ","int((f*x+e)^3*cos(d*x+c)^3/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \left(\cos^{3}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)^3/(a+b*sin(d*x+c)),x)","F"
303,0,0,503,2.675000," ","int((f*x+e)^2*cos(d*x+c)^3/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \left(\cos^{3}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*cos(d*x+c)^3/(a+b*sin(d*x+c)),x)","F"
304,1,1750,320,1.182000," ","int((f*x+e)*cos(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{i a^{2} f \,c^{2}}{d^{2} b^{3}}+\frac{a^{2} f c \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d^{2} b^{3}}-\frac{2 a^{2} f c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} b^{3}}-\frac{i a \left(d f x +d e +i f \right) {\mathrm e}^{i \left(d x +c \right)}}{2 d^{2} b^{2}}+\frac{i a \left(d f x +d e -i f \right) {\mathrm e}^{-i \left(d x +c \right)}}{2 d^{2} b^{2}}-\frac{i f \,c^{2}}{d^{2} b}-\frac{f c \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d^{2} b}+\frac{2 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} b}-\frac{2 f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) a^{2} x}{d b \left(-a^{2}+b^{2}\right)}-\frac{2 f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) a^{2} c}{d^{2} b \left(-a^{2}+b^{2}\right)}-\frac{2 f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2} x}{d b \left(-a^{2}+b^{2}\right)}-\frac{2 f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2} c}{d^{2} b \left(-a^{2}+b^{2}\right)}+\frac{2 i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) a^{2}}{d^{2} b \left(-a^{2}+b^{2}\right)}+\frac{i e x}{b}-\frac{i f \,x^{2}}{2 b}+\frac{e \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d b}-\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{d b}+\frac{2 i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2}}{d^{2} b \left(-a^{2}+b^{2}\right)}-\frac{i b f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d \left(-a^{2}+b^{2}\right)}+\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \left(-a^{2}+b^{2}\right)}+\frac{b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \left(-a^{2}+b^{2}\right)}-\frac{i b f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right)}-\frac{2 i f c x}{d b}+\frac{\left(2 d f x +2 d e +i f \right) {\mathrm e}^{2 i \left(d x +c \right)}}{16 b \,d^{2}}+\frac{\left(2 d f x +2 d e -i f \right) {\mathrm e}^{-2 i \left(d x +c \right)}}{16 b \,d^{2}}-\frac{a^{2} e \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d \,b^{3}}+\frac{2 a^{2} e \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d \,b^{3}}-\frac{i a^{2} e x}{b^{3}}+\frac{a^{4} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d \,b^{3} \left(-a^{2}+b^{2}\right)}+\frac{a^{4} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b^{3} \left(-a^{2}+b^{2}\right)}+\frac{a^{4} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \,b^{3} \left(-a^{2}+b^{2}\right)}+\frac{a^{4} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b^{3} \left(-a^{2}+b^{2}\right)}+\frac{2 i a^{2} f c x}{d \,b^{3}}-\frac{i a^{4} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b^{3} \left(-a^{2}+b^{2}\right)}-\frac{i a^{4} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b^{3} \left(-a^{2}+b^{2}\right)}+\frac{i a^{2} f \,x^{2}}{2 b^{3}}"," ",0,"-1/d/b^3*a^2*e*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+2/d/b^3*a^2*e*ln(exp(I*(d*x+c)))-1/d^2/b*f*c*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+2/d^2/b*f*c*ln(exp(I*(d*x+c)))-I/d^2/b*f*c^2+1/d/b*e*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-2/d/b*ln(exp(I*(d*x+c)))*e-1/2*I/b*f*x^2+I/b*e*x-2/d/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*a^2*x-2/d^2/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*a^2*c-2/d/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2*x-2/d^2/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2*c+1/d*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x+1/d^2*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+1/d*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+1/d^2*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-I/d^2*b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-I/d^2*b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))-2*I/d/b*f*c*x+I/d^2/b^3*a^2*f*c^2+1/d^2/b^3*a^2*f*c*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-2/d^2/b^3*a^2*f*c*ln(exp(I*(d*x+c)))-1/2*I*a*(d*f*x+I*f+d*e)/d^2/b^2*exp(I*(d*x+c))+1/2*I*a*(d*f*x-I*f+d*e)/d^2/b^2*exp(-I*(d*x+c))+1/16*(2*d*f*x+I*f+2*d*e)/b/d^2*exp(2*I*(d*x+c))+1/16*(2*d*f*x-I*f+2*d*e)/b/d^2*exp(-2*I*(d*x+c))-I/b^3*a^2*e*x+1/2*I/b^3*a^2*f*x^2+1/d/b^3*a^4*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x+1/d^2/b^3*a^4*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+1/d/b^3*a^4*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+1/d^2/b^3*a^4*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+2*I/d/b^3*a^2*f*c*x-I/d^2/b^3*a^4*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-I/d^2/b^3*a^4*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))+2*I/d^2/b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2+2*I/d^2/b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*a^2","B"
305,1,72,59,0.004000," ","int(cos(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{\sin^{2}\left(d x +c \right)}{2 b d}+\frac{a \sin \left(d x +c \right)}{b^{2} d}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \,b^{3}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{b d}"," ",0,"-1/2*sin(d*x+c)^2/b/d+a*sin(d*x+c)/b^2/d-1/d/b^3*ln(a+b*sin(d*x+c))*a^2+ln(a+b*sin(d*x+c))/b/d","A"
306,0,0,852,1.664000," ","int((f*x+e)^3*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \sec \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*sec(d*x+c)/(a+b*sin(d*x+c)),x)","F"
307,0,0,609,1.125000," ","int((f*x+e)^2*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \sec \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*sec(d*x+c)/(a+b*sin(d*x+c)),x)","F"
308,1,861,373,0.363000," ","int((f*x+e)*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{4 e \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{d \left(4 a -4 b \right)}-\frac{4 e \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{d \left(4 a +4 b \right)}+\frac{4 f \ln \left(-i \left({\mathrm e}^{i \left(d x +c \right)}+i\right)\right) x}{d \left(4 a -4 b \right)}+\frac{4 f \ln \left(-i \left({\mathrm e}^{i \left(d x +c \right)}+i\right)\right) c}{d^{2} \left(4 a -4 b \right)}-\frac{4 f \ln \left(-i \left(i-{\mathrm e}^{i \left(d x +c \right)}\right)\right) x}{d \left(4 a +4 b \right)}-\frac{4 f \ln \left(-i \left(i-{\mathrm e}^{i \left(d x +c \right)}\right)\right) c}{d^{2} \left(4 a +4 b \right)}-\frac{4 i f \ln \left(-i \left(i-{\mathrm e}^{i \left(d x +c \right)}\right)\right) \ln \left(-i {\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} \left(4 a +4 b \right)}-\frac{f b \ln \left(-\frac{i 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 +b \right) \left(a -b \right)}-\frac{f b \ln \left(-\frac{i 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 +b \right) \left(a -b \right)}-\frac{4 i f \dilog \left(-i {\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} \left(4 a +4 b \right)}-\frac{f b \ln \left(\frac{i 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 +b \right) \left(a -b \right)}-\frac{f b \ln \left(\frac{i 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 +b \right) \left(a -b \right)}+\frac{i f b \dilog \left(-\frac{i 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 +b \right) \left(a -b \right)}+\frac{i f b \dilog \left(\frac{i 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 +b \right) \left(a -b \right)}-\frac{4 i f \dilog \left(-i \left({\mathrm e}^{i \left(d x +c \right)}+i\right)\right)}{d^{2} \left(4 a -4 b \right)}-\frac{e b \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d \left(a +b \right) \left(a -b \right)}+\frac{f c b \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d^{2} \left(a +b \right) \left(a -b \right)}-\frac{4 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{d^{2} \left(4 a -4 b \right)}+\frac{4 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{d^{2} \left(4 a +4 b \right)}"," ",0,"4/d*e/(4*a-4*b)*ln(exp(I*(d*x+c))+I)-4/d*e/(4*a+4*b)*ln(exp(I*(d*x+c))-I)+4/d*f/(4*a-4*b)*ln(-I*(exp(I*(d*x+c))+I))*x+4/d^2*f/(4*a-4*b)*ln(-I*(exp(I*(d*x+c))+I))*c-4/d*f/(4*a+4*b)*ln(-I*(I-exp(I*(d*x+c))))*x-4/d^2*f/(4*a+4*b)*ln(-I*(I-exp(I*(d*x+c))))*c+I/d^2*f*b/(a+b)/(a-b)*dilog((I*b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))-1/d*f*b/(a+b)/(a-b)*ln(-(I*b*exp(I*(d*x+c))-(a^2-b^2)^(1/2)-a)/(a+(a^2-b^2)^(1/2)))*x-1/d^2*f*b/(a+b)/(a-b)*ln(-(I*b*exp(I*(d*x+c))-(a^2-b^2)^(1/2)-a)/(a+(a^2-b^2)^(1/2)))*c-4*I/d^2*f/(4*a+4*b)*ln(-I*(I-exp(I*(d*x+c))))*ln(-I*exp(I*(d*x+c)))-1/d*f*b/(a+b)/(a-b)*ln((I*b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*x-1/d^2*f*b/(a+b)/(a-b)*ln((I*b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*c-4*I/d^2*f/(4*a+4*b)*dilog(-I*exp(I*(d*x+c)))-4*I/d^2*f/(4*a-4*b)*dilog(-I*(exp(I*(d*x+c))+I))+I/d^2*f*b/(a+b)/(a-b)*dilog(-(I*b*exp(I*(d*x+c))-(a^2-b^2)^(1/2)-a)/(a+(a^2-b^2)^(1/2)))-1/d*e*b/(a+b)/(a-b)*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+1/d^2*f*c*b/(a+b)/(a-b)*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-4/d^2*f*c/(4*a-4*b)*ln(exp(I*(d*x+c))+I)+4/d^2*f*c/(4*a+4*b)*ln(exp(I*(d*x+c))-I)","B"
309,1,76,71,0.003000," ","int(sec(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}-\frac{b \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)-1/d*b/(a+b)/(a-b)*ln(a+b*sin(d*x+c))+1/d/(2*a-2*b)*ln(1+sin(d*x+c))","A"
310,0,0,836,6.699000," ","int((f*x+e)^3*sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \left(\sec^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
311,0,0,596,5.488000," ","int((f*x+e)^2*sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \left(\sec^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
312,1,1542,319,0.516000," ","int((f*x+e)*sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{2 \left(f x +e \right) \left(-i a +b \,{\mathrm e}^{i \left(d x +c \right)}\right)}{d \left(-a^{2}+b^{2}\right) \left(1+{\mathrm e}^{2 i \left(d x +c \right)}\right)}+\frac{2 i b^{2} c f \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right) a^{2}}{\left(a^{2}-b^{2}\right) d^{2} \left(a +b \right) \left(a -b \right) \sqrt{-a^{2}+b^{2}}}-\frac{i b^{4} f \ln \left(\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right) x}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d \left(a +b \right) \left(a -b \right)}-\frac{2 i b^{2} e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right) a^{2}}{\left(a^{2}-b^{2}\right) d \left(a +b \right) \left(a -b \right) \sqrt{-a^{2}+b^{2}}}+\frac{2 i b^{4} e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{\left(a^{2}-b^{2}\right) d \left(a +b \right) \left(a -b \right) \sqrt{-a^{2}+b^{2}}}-\frac{i b^{2} f \ln \left(-\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{a^{2}-b^{2}}-a}{a +\sqrt{a^{2}-b^{2}}}\right) a^{2} x}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d \left(a +b \right) \left(a -b \right)}+\frac{i b^{4} f \ln \left(-\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{a^{2}-b^{2}}-a}{a +\sqrt{a^{2}-b^{2}}}\right) x}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d \left(a +b \right) \left(a -b \right)}+\frac{b^{4} f \dilog \left(-\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{a^{2}-b^{2}}-a}{a +\sqrt{a^{2}-b^{2}}}\right)}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d^{2} \left(a +b \right) \left(a -b \right)}-\frac{b^{4} f \dilog \left(\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right)}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d^{2} \left(a +b \right) \left(a -b \right)}+\frac{4 a^{2} f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{\left(a^{2}-b^{2}\right) d^{2} \left(4 a -4 b \right)}+\frac{4 a^{2} f \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{\left(a^{2}-b^{2}\right) d^{2} \left(4 a +4 b \right)}-\frac{4 b^{2} f \ln \left({\mathrm e}^{i \left(d x +c \right)}+i\right)}{\left(a^{2}-b^{2}\right) d^{2} \left(4 a -4 b \right)}-\frac{4 b^{2} f \ln \left({\mathrm e}^{i \left(d x +c \right)}-i\right)}{\left(a^{2}-b^{2}\right) d^{2} \left(4 a +4 b \right)}-\frac{i b^{4} f \ln \left(\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right) c}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d^{2} \left(a +b \right) \left(a -b \right)}-\frac{2 i b^{4} c f \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{\left(a^{2}-b^{2}\right) d^{2} \left(a +b \right) \left(a -b \right) \sqrt{-a^{2}+b^{2}}}-\frac{b^{2} f \dilog \left(-\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{a^{2}-b^{2}}-a}{a +\sqrt{a^{2}-b^{2}}}\right) a^{2}}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d^{2} \left(a +b \right) \left(a -b \right)}+\frac{b^{2} f \dilog \left(\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right) a^{2}}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d^{2} \left(a +b \right) \left(a -b \right)}-\frac{i b^{2} f \ln \left(-\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{a^{2}-b^{2}}-a}{a +\sqrt{a^{2}-b^{2}}}\right) a^{2} c}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d^{2} \left(a +b \right) \left(a -b \right)}+\frac{i b^{2} f \ln \left(\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right) a^{2} x}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d \left(a +b \right) \left(a -b \right)}-\frac{2 a f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{\left(a^{2}-b^{2}\right) d^{2}}+\frac{i b^{4} f \ln \left(-\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{a^{2}-b^{2}}-a}{a +\sqrt{a^{2}-b^{2}}}\right) c}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d^{2} \left(a +b \right) \left(a -b \right)}+\frac{i b^{2} f \ln \left(\frac{i b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{a^{2}-b^{2}}-a}{-a +\sqrt{a^{2}-b^{2}}}\right) a^{2} c}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}} d^{2} \left(a +b \right) \left(a -b \right)}"," ",0,"2*(f*x+e)*(-I*a+b*exp(I*(d*x+c)))/d/(-a^2+b^2)/(1+exp(2*I*(d*x+c)))+2*I/(a^2-b^2)/d^2*b^2*c*f/(a+b)/(a-b)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))*a^2-I/(a^2-b^2)^(3/2)/d*b^4*f/(a+b)/(a-b)*ln((I*b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*x-2*I/(a^2-b^2)/d*b^2*e/(a+b)/(a-b)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))*a^2+2*I/(a^2-b^2)/d*b^4*e/(a+b)/(a-b)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-I/(a^2-b^2)^(3/2)/d*b^2*f/(a+b)/(a-b)*ln(-(I*b*exp(I*(d*x+c))-(a^2-b^2)^(1/2)-a)/(a+(a^2-b^2)^(1/2)))*a^2*x+I/(a^2-b^2)^(3/2)/d*b^4*f/(a+b)/(a-b)*ln(-(I*b*exp(I*(d*x+c))-(a^2-b^2)^(1/2)-a)/(a+(a^2-b^2)^(1/2)))*x+1/(a^2-b^2)^(3/2)/d^2*b^4*f/(a+b)/(a-b)*dilog(-(I*b*exp(I*(d*x+c))-(a^2-b^2)^(1/2)-a)/(a+(a^2-b^2)^(1/2)))-1/(a^2-b^2)^(3/2)/d^2*b^4*f/(a+b)/(a-b)*dilog((I*b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))+4/(a^2-b^2)/d^2*a^2*f/(4*a-4*b)*ln(exp(I*(d*x+c))+I)+4/(a^2-b^2)/d^2*a^2*f/(4*a+4*b)*ln(exp(I*(d*x+c))-I)-4/(a^2-b^2)/d^2*b^2*f/(4*a-4*b)*ln(exp(I*(d*x+c))+I)-4/(a^2-b^2)/d^2*b^2*f/(4*a+4*b)*ln(exp(I*(d*x+c))-I)-I/(a^2-b^2)^(3/2)/d^2*b^4*f/(a+b)/(a-b)*ln((I*b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*c-2*I/(a^2-b^2)/d^2*b^4*c*f/(a+b)/(a-b)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-1/(a^2-b^2)^(3/2)/d^2*b^2*f/(a+b)/(a-b)*dilog(-(I*b*exp(I*(d*x+c))-(a^2-b^2)^(1/2)-a)/(a+(a^2-b^2)^(1/2)))*a^2+1/(a^2-b^2)^(3/2)/d^2*b^2*f/(a+b)/(a-b)*dilog((I*b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*a^2-I/(a^2-b^2)^(3/2)/d^2*b^2*f/(a+b)/(a-b)*ln(-(I*b*exp(I*(d*x+c))-(a^2-b^2)^(1/2)-a)/(a+(a^2-b^2)^(1/2)))*a^2*c+I/(a^2-b^2)^(3/2)/d*b^2*f/(a+b)/(a-b)*ln((I*b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*a^2*x-2/(a^2-b^2)/d^2*a*f*ln(exp(I*(d*x+c)))+I/(a^2-b^2)^(3/2)/d^2*b^4*f/(a+b)/(a-b)*ln(-(I*b*exp(I*(d*x+c))-(a^2-b^2)^(1/2)-a)/(a+(a^2-b^2)^(1/2)))*c+I/(a^2-b^2)^(3/2)/d^2*b^2*f/(a+b)/(a-b)*ln((I*b*exp(I*(d*x+c))+(a^2-b^2)^(1/2)-a)/(-a+(a^2-b^2)^(1/2)))*a^2*c","B"
313,1,117,79,0.005000," ","int(sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{2}{d \left(2 a +2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{d \left(2 a -2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}"," ",0,"-2/d/(2*a+2*b)/(tan(1/2*d*x+1/2*c)-1)-2/d/(2*a-2*b)/(tan(1/2*d*x+1/2*c)+1)-2/d*b^2/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
314,0,0,30,0.371000," ","int((f*x+e)^m*cos(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \left(\cos^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*cos(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
315,0,0,28,0.222000," ","int((f*x+e)^m*cos(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \cos \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*cos(d*x+c)/(a+b*sin(d*x+c)),x)","F"
316,0,0,22,0.000000," ","int((f*x+e)^m/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m}}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m/(a+b*sin(d*x+c)),x)","F"
317,0,0,28,0.133000," ","int((f*x+e)^m*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \sec \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*sec(d*x+c)/(a+b*sin(d*x+c)),x)","F"
318,0,0,30,0.211000," ","int((f*x+e)^m*sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{m} \left(\sec^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^m*sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
319,1,194,74,1.524000," ","int((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c))^2,x)","-\frac{2 i \left(f x +e \right) {\mathrm e}^{i \left(d x +c \right)}}{b d \left(b \,{\mathrm e}^{2 i \left(d x +c \right)}-b +2 i a \,{\mathrm e}^{i \left(d x +c \right)}\right)}-\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}+\frac{i a \sqrt{-a^{2}+b^{2}}-a^{2}+b^{2}}{\sqrt{-a^{2}+b^{2}}\, b}\right)}{\sqrt{-a^{2}+b^{2}}\, d^{2} b}+\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}+\frac{i a \sqrt{-a^{2}+b^{2}}+a^{2}-b^{2}}{\sqrt{-a^{2}+b^{2}}\, b}\right)}{\sqrt{-a^{2}+b^{2}}\, d^{2} b}"," ",0,"-2*I*(f*x+e)*exp(I*(d*x+c))/b/d/(b*exp(2*I*(d*x+c))-b+2*I*a*exp(I*(d*x+c)))-1/(-a^2+b^2)^(1/2)*f/d^2/b*ln(exp(I*(d*x+c))+(I*a*(-a^2+b^2)^(1/2)-a^2+b^2)/(-a^2+b^2)^(1/2)/b)+1/(-a^2+b^2)^(1/2)*f/d^2/b*ln(exp(I*(d*x+c))+(I*a*(-a^2+b^2)^(1/2)+a^2-b^2)/(-a^2+b^2)^(1/2)/b)","C"
320,1,606,250,1.482000," ","int((f*x+e)^2*cos(d*x+c)/(a+b*sin(d*x+c))^2,x)","-\frac{2 i \left(f^{2} x^{2}+2 f e x +e^{2}\right) {\mathrm e}^{i \left(d x +c \right)}}{b d \left(b \,{\mathrm e}^{2 i \left(d x +c \right)}-b +2 i a \,{\mathrm e}^{i \left(d x +c \right)}\right)}+\frac{4 i f e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b \sqrt{-a^{2}+b^{2}}}+\frac{2 f^{2} \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d^{2} b \sqrt{-a^{2}+b^{2}}}+\frac{2 f^{2} \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{3} b \sqrt{-a^{2}+b^{2}}}-\frac{2 f^{2} \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d^{2} b \sqrt{-a^{2}+b^{2}}}-\frac{2 f^{2} \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{3} b \sqrt{-a^{2}+b^{2}}}-\frac{2 i f^{2} \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{3} b \sqrt{-a^{2}+b^{2}}}+\frac{2 i f^{2} \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{3} b \sqrt{-a^{2}+b^{2}}}-\frac{4 i f^{2} c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d^{3} b \sqrt{-a^{2}+b^{2}}}"," ",0,"-2*I*(f^2*x^2+2*e*f*x+e^2)*exp(I*(d*x+c))/b/d/(b*exp(2*I*(d*x+c))-b+2*I*a*exp(I*(d*x+c)))+4*I/d^2/b*f*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+2/d^2/b*f^2/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x+2/d^3/b*f^2/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c-2/d^2/b*f^2/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-2/d^3/b*f^2/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-2*I/d^3/b*f^2/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))+2*I/d^3/b*f^2/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-4*I/d^3/b*f^2*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))","B"
321,0,0,372,2.610000," ","int((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c))^2,x)","\int \frac{\left(f x +e \right)^{3} \cos \left(d x +c \right)}{\left(a +b \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c))^2,x)","F"
322,1,349,110,2.600000," ","int((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c))^3,x)","\frac{2 a^{2} d f x \,{\mathrm e}^{2 i \left(d x +c \right)}-2 b^{2} d f x \,{\mathrm e}^{2 i \left(d x +c \right)}+2 i a^{2} f \,{\mathrm e}^{2 i \left(d x +c \right)}+i b^{2} f \,{\mathrm e}^{2 i \left(d x +c \right)}+2 a^{2} d e \,{\mathrm e}^{2 i \left(d x +c \right)}+b a f \,{\mathrm e}^{3 i \left(d x +c \right)}-2 b^{2} d e \,{\mathrm e}^{2 i \left(d x +c \right)}-i b^{2} f -3 a b f \,{\mathrm e}^{i \left(d x +c \right)}}{\left(b \,{\mathrm e}^{2 i \left(d x +c \right)}-b +2 i a \,{\mathrm e}^{i \left(d x +c \right)}\right)^{2} d^{2} \left(a^{2}-b^{2}\right) b}-\frac{f a \ln \left({\mathrm e}^{i \left(d x +c \right)}+\frac{i a \sqrt{-a^{2}+b^{2}}-a^{2}+b^{2}}{\sqrt{-a^{2}+b^{2}}\, b}\right)}{2 \sqrt{-a^{2}+b^{2}}\, \left(a +b \right) \left(a -b \right) d^{2} b}+\frac{f a \ln \left({\mathrm e}^{i \left(d x +c \right)}+\frac{i a \sqrt{-a^{2}+b^{2}}+a^{2}-b^{2}}{\sqrt{-a^{2}+b^{2}}\, b}\right)}{2 \sqrt{-a^{2}+b^{2}}\, \left(a +b \right) \left(a -b \right) d^{2} b}"," ",0,"(2*a^2*d*f*x*exp(2*I*(d*x+c))-2*b^2*d*f*x*exp(2*I*(d*x+c))+2*I*a^2*f*exp(2*I*(d*x+c))+I*b^2*f*exp(2*I*(d*x+c))+2*a^2*d*e*exp(2*I*(d*x+c))+b*a*f*exp(3*I*(d*x+c))-2*b^2*d*e*exp(2*I*(d*x+c))-I*b^2*f-3*a*b*f*exp(I*(d*x+c)))/(b*exp(2*I*(d*x+c))-b+2*I*a*exp(I*(d*x+c)))^2/d^2/(a^2-b^2)/b-1/2/(-a^2+b^2)^(1/2)*f*a/(a+b)/(a-b)/d^2/b*ln(exp(I*(d*x+c))+(I*a*(-a^2+b^2)^(1/2)-a^2+b^2)/(-a^2+b^2)^(1/2)/b)+1/2/(-a^2+b^2)^(1/2)*f*a/(a+b)/(a-b)/d^2/b*ln(exp(I*(d*x+c))+(I*a*(-a^2+b^2)^(1/2)+a^2-b^2)/(-a^2+b^2)^(1/2)/b)","C"
323,1,946,325,2.945000," ","int((f*x+e)^2*cos(d*x+c)/(a+b*sin(d*x+c))^3,x)","\frac{2 a^{2} d \,f^{2} x^{2} {\mathrm e}^{2 i \left(d x +c \right)}-2 b^{2} d \,f^{2} x^{2} {\mathrm e}^{2 i \left(d x +c \right)}+4 i a^{2} e f \,{\mathrm e}^{2 i \left(d x +c \right)}+4 i a^{2} f^{2} x \,{\mathrm e}^{2 i \left(d x +c \right)}+4 a^{2} d e f x \,{\mathrm e}^{2 i \left(d x +c \right)}+2 b a \,f^{2} x \,{\mathrm e}^{3 i \left(d x +c \right)}-4 b^{2} d e f x \,{\mathrm e}^{2 i \left(d x +c \right)}-2 i b^{2} e f +2 i b^{2} f^{2} x \,{\mathrm e}^{2 i \left(d x +c \right)}+2 a^{2} d \,e^{2} {\mathrm e}^{2 i \left(d x +c \right)}+2 b a e f \,{\mathrm e}^{3 i \left(d x +c \right)}-2 b^{2} d \,e^{2} {\mathrm e}^{2 i \left(d x +c \right)}-2 i b^{2} f^{2} x -6 a b \,f^{2} x \,{\mathrm e}^{i \left(d x +c \right)}+2 i b^{2} e f \,{\mathrm e}^{2 i \left(d x +c \right)}-6 a b e f \,{\mathrm e}^{i \left(d x +c \right)}}{\left(b \,{\mathrm e}^{2 i \left(d x +c \right)}-b +2 i a \,{\mathrm e}^{i \left(d x +c \right)}\right)^{2} d^{2} \left(a^{2}-b^{2}\right) b}+\frac{f^{2} \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{b \left(-a^{2}+b^{2}\right) d^{3}}-\frac{2 f^{2} \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{b \left(-a^{2}+b^{2}\right) d^{3}}-\frac{f^{2} a \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{b \left(-a^{2}+b^{2}\right)^{\frac{3}{2}} d^{2}}-\frac{f^{2} a \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{b \left(-a^{2}+b^{2}\right)^{\frac{3}{2}} d^{3}}+\frac{2 i f^{2} a c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b \left(-a^{2}+b^{2}\right)^{\frac{3}{2}} d^{3}}-\frac{2 i f a e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b \left(-a^{2}+b^{2}\right)^{\frac{3}{2}} d^{2}}-\frac{i f^{2} a \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{b \left(-a^{2}+b^{2}\right)^{\frac{3}{2}} d^{3}}+\frac{f^{2} a \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{b \left(-a^{2}+b^{2}\right)^{\frac{3}{2}} d^{2}}+\frac{f^{2} a \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{b \left(-a^{2}+b^{2}\right)^{\frac{3}{2}} d^{3}}+\frac{i f^{2} a \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{b \left(-a^{2}+b^{2}\right)^{\frac{3}{2}} d^{3}}"," ",0,"2*(a^2*d*f^2*x^2*exp(2*I*(d*x+c))-b^2*d*f^2*x^2*exp(2*I*(d*x+c))+2*I*a^2*e*f*exp(2*I*(d*x+c))+2*I*a^2*f^2*x*exp(2*I*(d*x+c))+2*a^2*d*e*f*x*exp(2*I*(d*x+c))+b*a*f^2*x*exp(3*I*(d*x+c))-2*b^2*d*e*f*x*exp(2*I*(d*x+c))-I*b^2*e*f+I*b^2*f^2*x*exp(2*I*(d*x+c))+a^2*d*e^2*exp(2*I*(d*x+c))+b*a*e*f*exp(3*I*(d*x+c))-b^2*d*e^2*exp(2*I*(d*x+c))-I*b^2*f^2*x-3*a*b*f^2*x*exp(I*(d*x+c))+I*b^2*e*f*exp(2*I*(d*x+c))-3*a*b*e*f*exp(I*(d*x+c)))/(b*exp(2*I*(d*x+c))-b+2*I*a*exp(I*(d*x+c)))^2/d^2/(a^2-b^2)/b+1/b/(-a^2+b^2)/d^3*f^2*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-2/b/(-a^2+b^2)/d^3*f^2*ln(exp(I*(d*x+c)))-1/b/(-a^2+b^2)^(3/2)/d^2*f^2*a*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x-1/b/(-a^2+b^2)^(3/2)/d^3*f^2*a*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+2*I/b/(-a^2+b^2)^(3/2)/d^3*f^2*a*c*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-2*I/b/(-a^2+b^2)^(3/2)/d^2*f*a*e*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-I/b/(-a^2+b^2)^(3/2)/d^3*f^2*a*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+1/b/(-a^2+b^2)^(3/2)/d^2*f^2*a*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+1/b/(-a^2+b^2)^(3/2)/d^3*f^2*a*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+I/b/(-a^2+b^2)^(3/2)/d^3*f^2*a*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))","B"
324,0,0,674,2.771000," ","int((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c))^3,x)","\int \frac{\left(f x +e \right)^{3} \cos \left(d x +c \right)}{\left(a +b \sin \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c))^3,x)","F"
325,0,0,685,4.643000," ","int((f*x+e)^3*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \cos \left(d x +c \right) \cot \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x)","F"
326,0,0,497,3.789000," ","int((f*x+e)^2*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \cos \left(d x +c \right) \cot \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x)","F"
327,1,1207,311,0.510000," ","int((f*x+e)*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{f \,x^{2}}{2 b}-\frac{e x}{b}-\frac{a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d b \sqrt{-a^{2}+b^{2}}}-\frac{a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b \sqrt{-a^{2}+b^{2}}}-\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a d}+\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a d}+\frac{2 i f c b \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \sqrt{-a^{2}+b^{2}}}-\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) f x}{a d}+\frac{f b \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d a \sqrt{-a^{2}+b^{2}}}+\frac{f b \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} a \sqrt{-a^{2}+b^{2}}}-\frac{i f b \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \sqrt{-a^{2}+b^{2}}}+\frac{a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d b \sqrt{-a^{2}+b^{2}}}+\frac{a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b \sqrt{-a^{2}+b^{2}}}+\frac{i f b \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \sqrt{-a^{2}+b^{2}}}+\frac{i f \dilog \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{d^{2} a}+\frac{i f \dilog \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}+\frac{i a f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{b \,d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{f b \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d a \sqrt{-a^{2}+b^{2}}}-\frac{f b \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} a \sqrt{-a^{2}+b^{2}}}-\frac{f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}-\frac{2 i a f c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b \,d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{2 i a e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b d \sqrt{-a^{2}+b^{2}}}-\frac{i a f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b \sqrt{-a^{2}+b^{2}}}-\frac{2 i e b \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d a \sqrt{-a^{2}+b^{2}}}"," ",0,"-1/2*f*x^2/b-e*x/b-1/d/b*a*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-1/d^2/b*a*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-1/a/d*e*ln(exp(I*(d*x+c))+1)+1/a/d*e*ln(exp(I*(d*x+c))-1)-I/d^2/b*a*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))-1/a/d*ln(exp(I*(d*x+c))+1)*f*x+1/d*f*b/a/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+1/d^2*f*b/a/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+2*I/d^2*f*c/a*b/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+1/d/b*a*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x+1/d^2/b*a*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+I/d^2*f*dilog(exp(I*(d*x+c)))/a-I/d^2*f*b/a/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+I/d^2*f*b/a/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))+I/b/d^2*a*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-1/d*f*b/a/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x-1/d^2*f*b/a/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c-1/a/d^2*f*c*ln(exp(I*(d*x+c))-1)-2*I/b/d^2*a*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+2*I/b/d*a*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+I/d^2*f/a*dilog(exp(I*(d*x+c))+1)-2*I/d*e/a*b/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))","B"
328,1,137,70,0.168000," ","int(cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"2/d/b*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/b*arctan(tan(1/2*d*x+1/2*c))+1/a/d*ln(tan(1/2*d*x+1/2*c))","A"
329,0,0,697,8.400000," ","int((f*x+e)^3*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \left(\cos^{2}\left(d x +c \right)\right) \cot \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x)","F"
330,0,0,519,7.231000," ","int((f*x+e)^2*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \left(\cos^{2}\left(d x +c \right)\right) \cot \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x)","F"
331,1,1694,344,2.120000," ","int((f*x+e)*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}+\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) f x}{a d}+\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a d}+\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a d}-\frac{i f \dilog \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{d^{2} a}+\frac{i f \dilog \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}+\frac{2 f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) a c}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{2 f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a x}{d \left(-a^{2}+b^{2}\right)}+\frac{2 f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a c}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{2 f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) a x}{d \left(-a^{2}+b^{2}\right)}+\frac{2 a f c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} b^{2}}-\frac{a f c \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d^{2} b^{2}}-\frac{i a f \,c^{2}}{d^{2} b^{2}}-\frac{2 i f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) a}{d^{2} \left(-a^{2}+b^{2}\right)}-\frac{2 i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{i \left(d f x +d e +i f \right) {\mathrm e}^{i \left(d x +c \right)}}{2 b \,d^{2}}+\frac{f c \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d^{2} a}+\frac{a e \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d \,b^{2}}-\frac{2 a e \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d \,b^{2}}-\frac{i a f \,x^{2}}{2 b^{2}}+\frac{i a e x}{b^{2}}-\frac{i \left(d f x +d e -i f \right) {\mathrm e}^{-i \left(d x +c \right)}}{2 b \,d^{2}}+\frac{i a^{3} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b^{2} \left(-a^{2}+b^{2}\right)}+\frac{i b^{2} f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \left(-a^{2}+b^{2}\right)}+\frac{i b^{2} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \left(-a^{2}+b^{2}\right)}-\frac{b^{2} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d a \left(-a^{2}+b^{2}\right)}-\frac{b^{2} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} a \left(-a^{2}+b^{2}\right)}-\frac{b^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d a \left(-a^{2}+b^{2}\right)}-\frac{b^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} a \left(-a^{2}+b^{2}\right)}-\frac{a^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b^{2} \left(-a^{2}+b^{2}\right)}-\frac{a^{3} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \,b^{2} \left(-a^{2}+b^{2}\right)}-\frac{a^{3} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b^{2} \left(-a^{2}+b^{2}\right)}-\frac{a^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \,b^{2} \left(-a^{2}+b^{2}\right)}-\frac{e \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d a}-\frac{2 i a f c x}{d \,b^{2}}+\frac{i a^{3} f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b^{2} \left(-a^{2}+b^{2}\right)}"," ",0,"-1/a/d^2*f*c*ln(exp(I*(d*x+c))-1)+1/a/d*ln(exp(I*(d*x+c))+1)*f*x+1/a/d*e*ln(exp(I*(d*x+c))+1)+1/a/d*e*ln(exp(I*(d*x+c))-1)+I/d^2*f*dilog(exp(I*(d*x+c)))/a+2/d^2*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*a*c+2/d*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a*x+2/d^2*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a*c+2/d*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*a*x+2/d^2/b^2*a*f*c*ln(exp(I*(d*x+c)))-1/d^2/b^2*a*f*c*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-I/d^2/b^2*a*f*c^2-2*I/d^2*f/(-a^2+b^2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*a-2*I/d^2*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a+1/2*I*(d*f*x+I*f+d*e)/b/d^2*exp(I*(d*x+c))-1/d*e/a*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+1/d^2*f*c/a*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+1/d/b^2*a*e*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-2/d/b^2*a*e*ln(exp(I*(d*x+c)))-I/d^2*f/a*dilog(exp(I*(d*x+c))+1)-1/2*I*a/b^2*f*x^2+I*a/b^2*e*x-1/2*I*(d*f*x-I*f+d*e)/b/d^2*exp(-I*(d*x+c))-2*I/d/b^2*a*f*c*x-1/d*b^2*f/a/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x-1/d^2*b^2*f/a/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c-1/d*b^2*f/a/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-1/d^2*b^2*f/a/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-1/d^2/b^2*a^3*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-1/d/b^2*a^3*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x-1/d^2/b^2*a^3*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c-1/d/b^2*a^3*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+I/d^2/b^2*a^3*f/(-a^2+b^2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))+I/d^2/b^2*a^3*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+I/d^2*b^2*f/a/(-a^2+b^2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))+I/d^2*b^2*f/a/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))","B"
332,1,68,59,0.180000," ","int(cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\sin \left(d x +c \right)}{b d}+\frac{a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2}}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d a}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}"," ",0,"-sin(d*x+c)/b/d+1/d/b^2*a*ln(a+b*sin(d*x+c))-1/d/a*ln(a+b*sin(d*x+c))+ln(sin(d*x+c))/a/d","A"
333,0,0,1044,6.873000," ","int((f*x+e)^3*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \left(\cos^{3}\left(d x +c \right)\right) \cot \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x)","F"
334,0,0,755,6.114000," ","int((f*x+e)^2*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \left(\cos^{3}\left(d x +c \right)\right) \cot \left(d x +c \right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x)","F"
335,1,1850,476,2.140000," ","int((f*x+e)*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{2 a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b \sqrt{-a^{2}+b^{2}}}-\frac{2 i a f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{b \,d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 i e b \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d a \sqrt{-a^{2}+b^{2}}}-\frac{a^{3} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{b^{3} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{2 a f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{b d \sqrt{-a^{2}+b^{2}}}+\frac{2 a f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{b \,d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{b f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d a \sqrt{-a^{2}+b^{2}}}-\frac{b f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} a \sqrt{-a^{2}+b^{2}}}-\frac{a^{3} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{b^{3} d \sqrt{-a^{2}+b^{2}}}-\frac{f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}-\frac{\ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) f x}{a d}+\frac{2 i a^{3} f c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{3} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a d}+\frac{e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a d}-\frac{4 i a f c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b \,d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{2 i f c b \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \sqrt{-a^{2}+b^{2}}}+\frac{a \left(d f x +d e +i f \right) {\mathrm e}^{i \left(d x +c \right)}}{2 b^{2} d^{2}}+\frac{a \left(d f x +d e -i f \right) {\mathrm e}^{-i \left(d x +c \right)}}{2 b^{2} d^{2}}+\frac{a^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{b^{3} d \sqrt{-a^{2}+b^{2}}}+\frac{a^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{b^{3} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i a^{3} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{b^{3} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 i a^{3} e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{3} d \sqrt{-a^{2}+b^{2}}}-\frac{3 f \,x^{2}}{4 b}-\frac{i f b \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \sqrt{-a^{2}+b^{2}}}+\frac{i a^{3} f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{b^{3} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{i b f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a \sqrt{-a^{2}+b^{2}}}-\frac{2 a f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d b \sqrt{-a^{2}+b^{2}}}+\frac{f b \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d a \sqrt{-a^{2}+b^{2}}}+\frac{f b \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} a \sqrt{-a^{2}+b^{2}}}+\frac{2 i a f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{b \,d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{4 i a e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b d \sqrt{-a^{2}+b^{2}}}+\frac{a^{2} f \,x^{2}}{2 b^{3}}-\frac{\left(f x +e \right) \sin \left(2 d x +2 c \right)}{4 d b}+\frac{a^{2} e x}{b^{3}}-\frac{3 e x}{2 b}+\frac{i f \dilog \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{d^{2} a}+\frac{i f \dilog \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} a}-\frac{f \cos \left(2 d x +2 c \right)}{8 d^{2} b}"," ",0,"2*I/d^2*f*c/a*b/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+1/2*a*(d*f*x+I*f+d*e)/b^2/d^2*exp(I*(d*x+c))+1/2*a*(d*f*x-I*f+d*e)/b^2/d^2*exp(-I*(d*x+c))-2/d/b*a*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-2/d^2/b*a*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-1/a/d^2*f*c*ln(exp(I*(d*x+c))-1)-1/a/d*ln(exp(I*(d*x+c))+1)*f*x+2*I*a^3/b^3/d^2*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+a^3/b^3/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+a^3/b^3/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-2*I*a^3/b^3/d*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-I*a^3/b^3/d^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-1/a/d*e*ln(exp(I*(d*x+c))+1)+1/a/d*e*ln(exp(I*(d*x+c))-1)+1/d*f*b/a/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+1/d^2*f*b/a/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-2*I/d*e/a*b/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-I/d^2*f*b/a/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+I/d^2*f/a*dilog(exp(I*(d*x+c))+1)+I/d^2*f*dilog(exp(I*(d*x+c)))/a-4*I/b/d^2*a*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+I/b^3/d^2*a^3*f/(-a^2+b^2)^(1/2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))-1/b^3/d^2*a^3*f/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c+2/b/d*a*f/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x+2/b/d^2*a*f/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c-b/d*f/a/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x-b/d^2*f/a/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c-1/b^3/d*a^3*f/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x+I*b/d^2*f/a/(-a^2+b^2)^(1/2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))+4*I/b/d*a*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-3/4*f*x^2/b+2*I/b/d^2*a*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-2*I/b/d^2*a*f/(-a^2+b^2)^(1/2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))+1/2*a^2*f*x^2/b^3-1/4*(f*x+e)/d/b*sin(2*d*x+2*c)+a^2*e*x/b^3-3/2*e*x/b-1/8*f/d^2/b*cos(2*d*x+2*c)","B"
336,1,334,115,0.197000," ","int(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}"," ",0,"1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*a+2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2-3/d/b*arctan(tan(1/2*d*x+1/2*c))+1/a/d*ln(tan(1/2*d*x+1/2*c))-2/d*a^3/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d/b*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
337,0,0,774,7.300000," ","int((f*x+e)^3*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \cos \left(d x +c \right) \left(\cot^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
338,0,0,561,5.241000," ","int((f*x+e)^2*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \cos \left(d x +c \right) \left(\cot^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
339,1,1732,351,0.579000," ","int((f*x+e)*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{i b^{3} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d^{2} \left(-a^{2}+b^{2}\right)}-\frac{i b^{3} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d^{2} \left(-a^{2}+b^{2}\right)}+\frac{i f \,c^{2}}{d^{2} b}+\frac{f c \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d^{2} b}-\frac{2 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} b}+\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) a^{2} x}{d b \left(-a^{2}+b^{2}\right)}+\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) a^{2} c}{d^{2} b \left(-a^{2}+b^{2}\right)}+\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2} x}{d b \left(-a^{2}+b^{2}\right)}+\frac{f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2} c}{d^{2} b \left(-a^{2}+b^{2}\right)}-\frac{i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) a^{2}}{d^{2} b \left(-a^{2}+b^{2}\right)}-\frac{i e x}{b}+\frac{i f \,x^{2}}{2 b}-\frac{e \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d b}+\frac{2 \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{d b}+\frac{b e \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{a^{2} d}-\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a \,d^{2}}+\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}-\frac{i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2}}{d^{2} b \left(-a^{2}+b^{2}\right)}+\frac{2 i b f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right)}-\frac{2 b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{d \left(-a^{2}+b^{2}\right)}-\frac{2 b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \left(-a^{2}+b^{2}\right)}-\frac{2 b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \left(-a^{2}+b^{2}\right)}-\frac{2 b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{2 i b f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{2 i f c x}{d b}-\frac{i b f \dilog \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a^{2} d^{2}}-\frac{b f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x}{a^{2} d}+\frac{b f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a^{2} d^{2}}+\frac{i b f \dilog \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a^{2} d^{2}}-\frac{b e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a^{2} d}-\frac{b e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a^{2} d}-\frac{b f c \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{a^{2} d^{2}}-\frac{2 i \left(f x +e \right) {\mathrm e}^{i \left(d x +c \right)}}{d a \left({\mathrm e}^{2 i \left(d x +c \right)}-1\right)}+\frac{b^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) c}{a^{2} d^{2} \left(-a^{2}+b^{2}\right)}+\frac{b^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{a^{2} d^{2} \left(-a^{2}+b^{2}\right)}+\frac{b^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}-\sqrt{-a^{2}+b^{2}}}{i a -\sqrt{-a^{2}+b^{2}}}\right) x}{a^{2} d \left(-a^{2}+b^{2}\right)}+\frac{b^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{a^{2} d \left(-a^{2}+b^{2}\right)}"," ",0,"-I/d^2/b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*a^2-I/d^2/b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2-I/a^2*b^3/d^2*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))-I/a^2*b^3/d^2*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+1/d^2/b*f*c*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-2/d^2/b*f*c*ln(exp(I*(d*x+c)))-1/d/b*e*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+2/d/b*ln(exp(I*(d*x+c)))*e-2*I*(f*x+e)*exp(I*(d*x+c))/d/a/(exp(2*I*(d*x+c))-1)-1/a^2/d*b*f*ln(exp(I*(d*x+c))+1)*x+1/a^2/d^2*b*f*c*ln(exp(I*(d*x+c))-1)-I/a^2/d^2*b*f*dilog(exp(I*(d*x+c)))-1/a/d^2*f*ln(exp(I*(d*x+c))+1)+1/a/d^2*f*ln(exp(I*(d*x+c))-1)+1/d/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*a^2*x+1/d^2/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*a^2*c+1/d/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2*x+1/d^2/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2*c-2/d*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x-2/d^2*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c-2/d*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-2/d^2*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+1/a^2*b/d*e*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+I/b/d^2*c^2*f-1/a^2/d*b*e*ln(exp(I*(d*x+c))+1)-1/a^2/d*b*e*ln(exp(I*(d*x+c))-1)+1/2*I/b*f*x^2-I/b*e*x+2*I/b/d*c*f*x+2*I*b/d^2*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+2*I*b/d^2*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))+I/a^2*b/d^2*f*dilog(exp(I*(d*x+c))+1)-1/a^2*b/d^2*f*c*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+1/a^2*b^3/d^2*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*c+1/a^2*b^3/d^2*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+1/a^2*b^3/d*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))-(-a^2+b^2)^(1/2))/(I*a-(-a^2+b^2)^(1/2)))*x+1/a^2*b^3/d*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x","B"
340,1,72,60,0.149000," ","int(cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{b d}+\frac{b \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{2}}-\frac{1}{d a \sin \left(d x +c \right)}-\frac{b \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"-ln(a+b*sin(d*x+c))/b/d+1/d/a^2*b*ln(a+b*sin(d*x+c))-1/d/a/sin(d*x+c)-b*ln(sin(d*x+c))/a^2/d","A"
341,0,0,1052,8.140000," ","int((f*x+e)^3*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \left(\cos^{2}\left(d x +c \right)\right) \left(\cot^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
342,0,0,772,6.583000," ","int((f*x+e)^2*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \left(\cos^{2}\left(d x +c \right)\right) \left(\cot^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
343,1,1863,475,1.865000," ","int((f*x+e)*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{a^{2} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b^{2} \sqrt{-a^{2}+b^{2}}}+\frac{b^{2} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \,a^{2} \sqrt{-a^{2}+b^{2}}}+\frac{b^{2} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} a^{2} \sqrt{-a^{2}+b^{2}}}+\frac{a^{2} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \,b^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i b^{2} f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} a^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i a^{2} f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b^{2} \sqrt{-a^{2}+b^{2}}}+\frac{2 i a^{2} e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d \sqrt{-a^{2}+b^{2}}}-\frac{a^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{b^{2} d \sqrt{-a^{2}+b^{2}}}-\frac{a^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{i a^{2} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 i b^{2} f c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 f \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a \,d^{2}}+\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a \,d^{2}}+\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}-\frac{2 i a^{2} f c \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{2} d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{2 i b^{2} e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d \sqrt{-a^{2}+b^{2}}}+\frac{i b^{2} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{b^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{a^{2} d \sqrt{-a^{2}+b^{2}}}-\frac{b^{2} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{a^{2} d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{i b f \dilog \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a^{2} d^{2}}+\frac{b f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x}{a^{2} d}+\frac{b f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a^{2} d^{2}}-\frac{i b f \dilog \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a^{2} d^{2}}+\frac{4 i f c \arctan \left(\frac{2 i 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}}}-\frac{2 i \left(f x +e \right)}{d a \left({\mathrm e}^{2 i \left(d x +c \right)}-1\right)}+\frac{b e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a^{2} d}-\frac{b e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a^{2} d}-\frac{\left(d f x +d e +i f \right) {\mathrm e}^{i \left(d x +c \right)}}{2 d^{2} b}-\frac{\left(d f x +d e -i f \right) {\mathrm e}^{-i \left(d x +c \right)}}{2 d^{2} b}-\frac{2 i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \sqrt{-a^{2}+b^{2}}}+\frac{2 f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \sqrt{-a^{2}+b^{2}}}+\frac{2 f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{4 i e \arctan \left(\frac{2 i b \,{\mathrm e}^{i \left(d x +c \right)}-2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \sqrt{-a^{2}+b^{2}}}-\frac{a f \,x^{2}}{2 b^{2}}-\frac{a e x}{b^{2}}+\frac{2 i f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2 f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \sqrt{-a^{2}+b^{2}}}-\frac{2 f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \sqrt{-a^{2}+b^{2}}}"," ",0,"-2*I/a^2/d^2*b^2*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+1/d^2/b^2*a^2*f/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c+1/d*b^2/a^2*f/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x+1/d^2*b^2/a^2*f/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c+1/d/b^2*a^2*f/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x-I/d^2*b^2/a^2*f/(-a^2+b^2)^(1/2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))-I/d^2/b^2*a^2*f/(-a^2+b^2)^(1/2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))+1/a^2/d*b*f*ln(exp(I*(d*x+c))+1)*x+1/a^2/d^2*b*f*c*ln(exp(I*(d*x+c))-1)-I/a^2/d^2*b*f*dilog(exp(I*(d*x+c)))-I/a^2/d^2*b*f*dilog(exp(I*(d*x+c))+1)-2/a/d^2*f*ln(exp(I*(d*x+c)))-2*I*(f*x+e)/d/a/(exp(2*I*(d*x+c))-1)+I/a^2/d^2*b^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-1/a^2/d*b^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-1/a^2/d^2*b^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+2*I/a^2/d*b^2*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+1/a/d^2*f*ln(exp(I*(d*x+c))+1)+1/a/d^2*f*ln(exp(I*(d*x+c))-1)-a^2/b^2/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-a^2/b^2/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c+I*a^2/b^2/d^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))+2*I*a^2/b^2/d*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-2*I*a^2/b^2/d^2*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))+2/d*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x+2/d^2*f/(-a^2+b^2)^(1/2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-1/2*(d*f*x+I*f+d*e)/d^2/b*exp(I*(d*x+c))+1/a^2/d*b*e*ln(exp(I*(d*x+c))+1)-1/a^2/d*b*e*ln(exp(I*(d*x+c))-1)-1/2*(d*f*x-I*f+d*e)/d^2/b*exp(-I*(d*x+c))+4*I/d^2*f*c/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))-1/2*a*f*x^2/b^2-a*e*x/b^2-2/d*f/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x-2/d^2*f/(-a^2+b^2)^(1/2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c+2*I/d^2*f/(-a^2+b^2)^(1/2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))-2*I/d^2*f/(-a^2+b^2)^(1/2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-4*I/d*e/(-a^2+b^2)^(1/2)*arctan(1/2*(2*I*b*exp(I*(d*x+c))-2*a)/(-a^2+b^2)^(1/2))","B"
344,1,249,99,0.173000," ","int(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{2}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}+\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-2/d/b/(1+tan(1/2*d*x+1/2*c)^2)-2/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))-1/2/a/d/tan(1/2*d*x+1/2*c)-1/d/a^2*b*ln(tan(1/2*d*x+1/2*c))+2/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2-4/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
345,0,0,1330,11.006000," ","int((f*x+e)^3*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{3} \left(\cos^{3}\left(d x +c \right)\right) \left(\cot^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^3*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
346,0,0,976,10.585000," ","int((f*x+e)^2*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","\int \frac{\left(f x +e \right)^{2} \left(\cos^{3}\left(d x +c \right)\right) \left(\cot^{2}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((f*x+e)^2*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","F"
347,1,2449,594,4.219000," ","int((f*x+e)*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{i b^{3} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d^{2} \left(-a^{2}+b^{2}\right)}-\frac{a^{2} f c \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d^{2} b^{3}}-\frac{i a \left(d f x +d e -i f \right) {\mathrm e}^{-i \left(d x +c \right)}}{2 d^{2} b^{2}}+\frac{2 i f \,c^{2}}{d^{2} b}+\frac{2 f c \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d^{2} b}-\frac{4 f c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} b}+\frac{3 f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2} x}{d b \left(-a^{2}+b^{2}\right)}+\frac{3 f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2} c}{d^{2} b \left(-a^{2}+b^{2}\right)}-\frac{2 i e x}{b}+\frac{i f \,x^{2}}{b}-\frac{2 e \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d b}+\frac{4 \ln \left({\mathrm e}^{i \left(d x +c \right)}\right) e}{d b}-\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a \,d^{2}}+\frac{f \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a \,d^{2}}-\frac{3 i f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) a^{2}}{d^{2} b \left(-a^{2}+b^{2}\right)}+\frac{3 i b f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right)}-\frac{3 b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \left(-a^{2}+b^{2}\right)}-\frac{3 b f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \left(-a^{2}+b^{2}\right)}+\frac{4 i f c x}{d b}-\frac{i b f \dilog \left({\mathrm e}^{i \left(d x +c \right)}\right)}{a^{2} d^{2}}-\frac{b f \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right) x}{a^{2} d}+\frac{b f c \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a^{2} d^{2}}+\frac{i b f \dilog \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a^{2} d^{2}}-\frac{b e \ln \left({\mathrm e}^{i \left(d x +c \right)}+1\right)}{a^{2} d}-\frac{b e \ln \left({\mathrm e}^{i \left(d x +c \right)}-1\right)}{a^{2} d}+\frac{b e \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{a^{2} d}+\frac{i a^{2} e x}{b^{3}}-\frac{b f c \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{a^{2} d^{2}}-\frac{\left(2 d f x +2 d e +i f \right) {\mathrm e}^{2 i \left(d x +c \right)}}{16 b \,d^{2}}-\frac{\left(2 d f x +2 d e -i f \right) {\mathrm e}^{-2 i \left(d x +c \right)}}{16 b \,d^{2}}+\frac{a^{2} e \ln \left(i b \,{\mathrm e}^{2 i \left(d x +c \right)}-2 a \,{\mathrm e}^{i \left(d x +c \right)}-i b \right)}{d \,b^{3}}-\frac{2 a^{2} e \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d \,b^{3}}-\frac{a^{4} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} b^{3} \left(-a^{2}+b^{2}\right)}+\frac{i a^{4} f \dilog \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} b^{3} \left(-a^{2}+b^{2}\right)}-\frac{i a^{2} f \,x^{2}}{2 b^{3}}+\frac{3 a^{2} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{b \,d^{2} \left(-a^{2}+b^{2}\right)}+\frac{b^{3} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{a^{2} d^{2} \left(-a^{2}+b^{2}\right)}+\frac{b^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) c}{a^{2} d^{2} \left(-a^{2}+b^{2}\right)}-\frac{a^{4} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{b^{3} d \left(-a^{2}+b^{2}\right)}-\frac{2 i a^{2} c f x}{b^{3} d}-\frac{i b^{3} f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{a^{2} d^{2} \left(-a^{2}+b^{2}\right)}-\frac{3 i a^{2} f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{b \,d^{2} \left(-a^{2}+b^{2}\right)}+\frac{i a^{4} f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{b^{3} d^{2} \left(-a^{2}+b^{2}\right)}+\frac{3 a^{2} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{b d \left(-a^{2}+b^{2}\right)}+\frac{b^{3} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{a^{2} d \left(-a^{2}+b^{2}\right)}+\frac{b^{3} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{a^{2} d \left(-a^{2}+b^{2}\right)}-\frac{a^{4} f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{b^{3} d^{2} \left(-a^{2}+b^{2}\right)}-\frac{a^{4} f \ln \left(\frac{i a +b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \,b^{3} \left(-a^{2}+b^{2}\right)}-\frac{3 b f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) x}{d \left(-a^{2}+b^{2}\right)}-\frac{3 b f \ln \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right) c}{d^{2} \left(-a^{2}+b^{2}\right)}-\frac{i a^{2} f \,c^{2}}{d^{2} b^{3}}+\frac{2 a^{2} f c \ln \left({\mathrm e}^{i \left(d x +c \right)}\right)}{d^{2} b^{3}}-\frac{2 i \left(f x +e \right) {\mathrm e}^{i \left(d x +c \right)}}{d a \left({\mathrm e}^{2 i \left(d x +c \right)}-1\right)}+\frac{i a \left(d f x +d e +i f \right) {\mathrm e}^{i \left(d x +c \right)}}{2 b^{2} d^{2}}+\frac{3 i b f \dilog \left(\frac{-i a -b \,{\mathrm e}^{i \left(d x +c \right)}+\sqrt{-a^{2}+b^{2}}}{-i a +\sqrt{-a^{2}+b^{2}}}\right)}{d^{2} \left(-a^{2}+b^{2}\right)}"," ",0,"1/d/b^3*a^2*e*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-2/d/b^3*a^2*e*ln(exp(I*(d*x+c)))+2/d^2/b*f*c*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-4/d^2/b*f*c*ln(exp(I*(d*x+c)))+4*I/b/d*c*f*x+1/a^2*b/d*e*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+2*I/b/d^2*c^2*f-1/2*I/b^3*a^2*f*x^2-2/d/b*e*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+4/d/b*ln(exp(I*(d*x+c)))*e-1/a^2/d*b*f*ln(exp(I*(d*x+c))+1)*x+1/a^2/d^2*b*f*c*ln(exp(I*(d*x+c))-1)-I/a^2/d^2*b*f*dilog(exp(I*(d*x+c)))-1/a/d^2*f*ln(exp(I*(d*x+c))+1)+1/a/d^2*f*ln(exp(I*(d*x+c))-1)+3/d/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2*x+3/d^2/b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2*c-3/d*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-3/d^2*b*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-1/a^2/d*b*e*ln(exp(I*(d*x+c))+1)-1/a^2/d*b*e*ln(exp(I*(d*x+c))-1)-3*b/d*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x+I/a^2*b/d^2*f*dilog(exp(I*(d*x+c))+1)-1/a^2*b/d^2*f*c*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)-3*b/d^2*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c-I/d^2/b^3*a^2*f*c^2+3*I*b/d^2*f/(-a^2+b^2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))+3*I*b/d^2*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-1/d^2/b^3*a^2*f*c*ln(I*b*exp(2*I*(d*x+c))-2*a*exp(I*(d*x+c))-I*b)+2/d^2/b^3*a^2*f*c*ln(exp(I*(d*x+c)))+3*a^2/b/d^2*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c+1/a^2*b^3/d^2*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c+1/a^2*b^3/d^2*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-a^4/b^3/d*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x-2*I*a^2/b^3/d*c*f*x-I/a^2*b^3/d^2*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-I/a^2*b^3/d^2*f/(-a^2+b^2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))-3*I*a^2/b/d^2*f/(-a^2+b^2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))-3*I/d^2/b*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*a^2-1/16*(2*d*f*x+I*f+2*d*e)/b/d^2*exp(2*I*(d*x+c))-1/16*(2*d*f*x-I*f+2*d*e)/b/d^2*exp(-2*I*(d*x+c))+3*a^2/b/d*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x+1/a^2*b^3/d*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*x+1/a^2*b^3/d*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-a^4/b^3/d^2*f/(-a^2+b^2)*ln((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))*c+I*a^4/b^3/d^2*f/(-a^2+b^2)*dilog((-I*a-b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(-I*a+(-a^2+b^2)^(1/2)))+I*a^4/b^3/d^2*f/(-a^2+b^2)*dilog((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))-1/d/b^3*a^4*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*x-1/d^2/b^3*a^4*f/(-a^2+b^2)*ln((I*a+b*exp(I*(d*x+c))+(-a^2+b^2)^(1/2))/(I*a+(-a^2+b^2)^(1/2)))*c-1/2*I*a*(d*f*x-I*f+d*e)/b^2/d^2*exp(-I*(d*x+c))-2*I*(f*x+e)*exp(I*(d*x+c))/d/a/(exp(2*I*(d*x+c))-1)+1/2*I*a*(d*f*x+I*f+d*e)/b^2/d^2*exp(I*(d*x+c))+I/b*f*x^2-2*I/b*e*x+I/b^3*a^2*e*x","B"
348,1,124,94,0.173000," ","int(cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{\sin^{2}\left(d x +c \right)}{2 b d}-\frac{a \sin \left(d x +c \right)}{b^{2} d}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \,b^{3}}-\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right)}{b d}+\frac{b \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{2}}-\frac{1}{d a \sin \left(d x +c \right)}-\frac{b \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"1/2*sin(d*x+c)^2/b/d-a*sin(d*x+c)/b^2/d+1/d/b^3*ln(a+b*sin(d*x+c))*a^2-2*ln(a+b*sin(d*x+c))/b/d+1/d/a^2*b*ln(a+b*sin(d*x+c))-1/d/a/sin(d*x+c)-b*ln(sin(d*x+c))/a^2/d","A"