# Maple integration test file: "4 Trig functions\4.1 Sine\4.1.13 (d+e x)^m sin(a+b x+c x^2)^n.txt"

lst:=[

# Integrands of the form (d+e x)^m Sin[a+b x+c x^2]^n

# Integrands of the form x^m Sin[a+b x+c x^2]^n
[x^2*sin(a+b*x+c*x^2),x,8,1/4*b*cos(a+b*x+c*x^2)/c^2-1/2*x*cos(a+b*x+c*x^2)/c+1/2*cos(a-1/4*b^2/c)*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/c^(3/2)+1/4*b^2*cos(a-1/4*b^2/c)*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/c^(5/2)+1/4*b^2*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a-1/4*b^2/c)*sqrt(1/2*Pi)/c^(5/2)-1/2*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a-1/4*b^2/c)*sqrt(1/2*Pi)/c^(3/2)],
[x*sin(a+b*x+c*x^2),x,4,-1/2*cos(a+b*x+c*x^2)/c-1/2*b*cos(a-1/4*b^2/c)*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/c^(3/2)-1/2*b*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a-1/4*b^2/c)*sqrt(1/2*Pi)/c^(3/2)],
[sin(a+b*x+c*x^2),x,3,cos(a-1/4*b^2/c)*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/sqrt(c)+FresnelC((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a-1/4*b^2/c)*sqrt(1/2*Pi)/sqrt(c)],
[sin(a+b*x+c*x^2)/x,x,0,Unintegrable(sin(a+b*x+c*x^2)/x,x)],
[-b*cos(a+b*x+c*x^2)/x+sin(a+b*x+c*x^2)/x^2,x,5,-sin(a+b*x+c*x^2)/x+cos(a-1/4*b^2/c)*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(c)*sqrt(2*Pi)-FresnelS((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a-1/4*b^2/c)*sqrt(c)*sqrt(2*Pi)],
[x^2*sin(a+b*x-c*x^2),x,8,1/4*b*cos(a+b*x-c*x^2)/c^2+1/2*x*cos(a+b*x-c*x^2)/c+1/2*cos(a+1/4*b^2/c)*FresnelC((b-2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/c^(3/2)+1/4*b^2*cos(a+1/4*b^2/c)*FresnelS((b-2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/c^(5/2)-1/4*b^2*FresnelC((b-2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a+1/4*b^2/c)*sqrt(1/2*Pi)/c^(5/2)+1/2*FresnelS((b-2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a+1/4*b^2/c)*sqrt(1/2*Pi)/c^(3/2)],
[x*sin(a+b*x-c*x^2),x,4,1/2*cos(a+b*x-c*x^2)/c+1/2*b*cos(a+1/4*b^2/c)*FresnelS((b-2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/c^(3/2)-1/2*b*FresnelC((b-2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a+1/4*b^2/c)*sqrt(1/2*Pi)/c^(3/2)],
[sin(a+b*x-c*x^2),x,3,cos(a+1/4*b^2/c)*FresnelS((b-2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/sqrt(c)-FresnelC((b-2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a+1/4*b^2/c)*sqrt(1/2*Pi)/sqrt(c)],
[sin(a+b*x-c*x^2)/x,x,0,Unintegrable(sin(a+b*x-c*x^2)/x,x)],
[-b*cos(a+b*x-c*x^2)/x+sin(a+b*x-c*x^2)/x^2,x,5,-sin(a+b*x-c*x^2)/x+cos(a+1/4*b^2/c)*FresnelC((b-2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(c)*sqrt(2*Pi)+FresnelS((b-2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a+1/4*b^2/c)*sqrt(c)*sqrt(2*Pi)],
[x^2*sin(1/4+x+x^2),x,6,1/4*cos(1/4+x+x^2)-1/2*x*cos(1/4+x+x^2)+1/2*FresnelC((1+2*x)/sqrt(2*Pi))*sqrt(1/2*Pi)+1/4*FresnelS((1+2*x)/sqrt(2*Pi))*sqrt(1/2*Pi)],
[x*sin(1/4+x+x^2),x,3,-1/2*cos(1/4+x+x^2)-1/2*FresnelS((1+2*x)/sqrt(2*Pi))*sqrt(1/2*Pi)],
[sin(1/4+x+x^2),x,2,FresnelS((1+2*x)/sqrt(2*Pi))*sqrt(1/2*Pi)],
[sin(1/4+x+x^2)/x,x,0,Unintegrable(sin(1/4+x+x^2)/x,x)],
[sin(1/4+x+x^2)/x^2,x,3,-sin(1/4+x+x^2)/x+FresnelC((1+2*x)/sqrt(2*Pi))*sqrt(2*Pi)+Unintegrable(cos(1/4+x+x^2)/x,x)],
[x^2*sin(a+b*x+c*x^2)^2,x,10,1/6*x^3+1/16*b*sin(2*a+2*b*x+2*c*x^2)/c^2-1/8*x*sin(2*a+2*b*x+2*c*x^2)/c-1/16*b^2*cos(2*a-1/2*b^2/c)*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/c^(5/2)+1/16*cos(2*a-1/2*b^2/c)*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/c^(3/2)+1/16*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a-1/2*b^2/c)*sqrt(Pi)/c^(3/2)+1/16*b^2*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a-1/2*b^2/c)*sqrt(Pi)/c^(5/2)],
[x*sin(a+b*x+c*x^2)^2,x,6,1/4*x^2-1/8*sin(2*a+2*b*x+2*c*x^2)/c+1/8*b*cos(2*a-1/2*b^2/c)*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/c^(3/2)-1/8*b*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a-1/2*b^2/c)*sqrt(Pi)/c^(3/2)],
[sin(a+b*x+c*x^2)^2,x,5,1/2*x-1/4*cos(2*a-1/2*b^2/c)*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/sqrt(c)+1/4*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a-1/2*b^2/c)*sqrt(Pi)/sqrt(c)],
[sin(a+b*x+c*x^2)^2/x,x,2,1/2*log(x)-1/2*Unintegrable(cos(2*a+2*b*x+2*c*x^2)/x,x)],
[x^2*sin(a+b*x-c*x^2)^2,x,10,1/6*x^3+1/16*b*sin(2*a+2*b*x-2*c*x^2)/c^2+1/8*x*sin(2*a+2*b*x-2*c*x^2)/c+1/16*b^2*cos(2*a+1/2*b^2/c)*FresnelC((b-2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/c^(5/2)-1/16*cos(2*a+1/2*b^2/c)*FresnelS((b-2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/c^(3/2)+1/16*FresnelC((b-2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a+1/2*b^2/c)*sqrt(Pi)/c^(3/2)+1/16*b^2*FresnelS((b-2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a+1/2*b^2/c)*sqrt(Pi)/c^(5/2)],
[x*sin(a+b*x-c*x^2)^2,x,6,1/4*x^2+1/8*sin(2*a+2*b*x-2*c*x^2)/c+1/8*b*cos(2*a+1/2*b^2/c)*FresnelC((b-2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/c^(3/2)+1/8*b*FresnelS((b-2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a+1/2*b^2/c)*sqrt(Pi)/c^(3/2)],
[sin(a+b*x-c*x^2)^2,x,5,1/2*x+1/4*cos(2*a+1/2*b^2/c)*FresnelC((b-2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/sqrt(c)+1/4*FresnelS((b-2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a+1/2*b^2/c)*sqrt(Pi)/sqrt(c)],
[sin(a+b*x-c*x^2)^2/x,x,2,1/2*log(x)-1/2*Unintegrable(cos(2*a+2*b*x-2*c*x^2)/x,x)],
[x^2*sin(1/4+x+x^2)^2,x,8,1/6*x^3+1/16*sin(1/2+2*x+2*x^2)-1/8*x*sin(1/2+2*x+2*x^2)-1/16*FresnelC((1+2*x)/sqrt(Pi))*sqrt(Pi)+1/16*FresnelS((1+2*x)/sqrt(Pi))*sqrt(Pi)],
[x*sin(1/4+x+x^2)^2,x,5,1/4*x^2-1/8*sin(1/2+2*x+2*x^2)+1/8*FresnelC((1+2*x)/sqrt(Pi))*sqrt(Pi)],
[sin(1/4+x+x^2)^2,x,4,1/2*x-1/4*FresnelC((1+2*x)/sqrt(Pi))*sqrt(Pi)],
[sin(1/4+x+x^2)^2/x,x,2,1/2*log(x)-1/2*Unintegrable(cos(1/2+2*x+2*x^2)/x,x)],
[sin(1/4+x+x^2)^2/x^2,x,5,(-1/2)/x+1/2*cos(1/2+2*x+2*x^2)/x+FresnelS((1+2*x)/sqrt(Pi))*sqrt(Pi)+Unintegrable(sin(1/2+2*x+2*x^2)/x,x)],

# Integrands of the form (d+e x)^m Sin[a+b x+c x^2]^n
[(d+e*x)^2*sin(a+b*x+c*x^2),x,8,-1/4*e*(2*c*d-b*e)*cos(a+b*x+c*x^2)/c^2-1/2*e*(d+e*x)*cos(a+b*x+c*x^2)/c+1/2*e^2*cos(a-1/4*b^2/c)*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/c^(3/2)+1/4*(2*c*d-b*e)^2*cos(a-1/4*b^2/c)*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/c^(5/2)+1/4*(2*c*d-b*e)^2*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a-1/4*b^2/c)*sqrt(1/2*Pi)/c^(5/2)-1/2*e^2*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a-1/4*b^2/c)*sqrt(1/2*Pi)/c^(3/2)],
[(d+e*x)*sin(a+b*x+c*x^2),x,4,-1/2*e*cos(a+b*x+c*x^2)/c+1/2*(2*c*d-b*e)*cos(a-1/4*b^2/c)*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/c^(3/2)+1/2*(2*c*d-b*e)*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a-1/4*b^2/c)*sqrt(1/2*Pi)/c^(3/2)],
[sin(a+b*x+c*x^2),x,3,cos(a-1/4*b^2/c)*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sqrt(1/2*Pi)/sqrt(c)+FresnelC((b+2*c*x)/(sqrt(c)*sqrt(2*Pi)))*sin(a-1/4*b^2/c)*sqrt(1/2*Pi)/sqrt(c)],
[sin(a+b*x+c*x^2)/(d+e*x),x,0,Unintegrable(sin(a+b*x+c*x^2)/(d+e*x),x)],
[(d+e*x)^2*sin(a+b*x+c*x^2)^2,x,10,1/6*(d+e*x)^3/e-1/16*e*(2*c*d-b*e)*sin(2*a+2*b*x+2*c*x^2)/c^2-1/8*e*(d+e*x)*sin(2*a+2*b*x+2*c*x^2)/c-1/16*(2*c*d-b*e)^2*cos(2*a-1/2*b^2/c)*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/c^(5/2)+1/16*e^2*cos(2*a-1/2*b^2/c)*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/c^(3/2)+1/16*e^2*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a-1/2*b^2/c)*sqrt(Pi)/c^(3/2)+1/16*(2*c*d-b*e)^2*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a-1/2*b^2/c)*sqrt(Pi)/c^(5/2)],
[(d+e*x)*sin(a+b*x+c*x^2)^2,x,6,1/4*(d+e*x)^2/e-1/8*e*sin(2*a+2*b*x+2*c*x^2)/c-1/8*(2*c*d-b*e)*cos(2*a-1/2*b^2/c)*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/c^(3/2)+1/8*(2*c*d-b*e)*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a-1/2*b^2/c)*sqrt(Pi)/c^(3/2)],
[sin(a+b*x+c*x^2)^2,x,5,1/2*x-1/4*cos(2*a-1/2*b^2/c)*FresnelC((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sqrt(Pi)/sqrt(c)+1/4*FresnelS((b+2*c*x)/(sqrt(c)*sqrt(Pi)))*sin(2*a-1/2*b^2/c)*sqrt(Pi)/sqrt(c)],
[sin(a+b*x+c*x^2)^2/(d+e*x),x,2,1/2*log(d+e*x)/e-1/2*Unintegrable(cos(2*a+2*b*x+2*c*x^2)/(d+e*x),x)]]:
