# Maple integration test file: "4 Trig functions\4.1 Sine\4.1.12 (e x)^m (a+b sin(c+d x^n))^p.txt"

lst:=[

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

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

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

# p>0
[x^5*(a+b*sin(c+d*x^2)),x,6,1/6*a*x^6+b*cos(c+d*x^2)/d^3-1/2*b*x^4*cos(c+d*x^2)/d+b*x^2*sin(c+d*x^2)/d^2],
[x^3*(a+b*sin(c+d*x^2)),x,5,1/4*a*x^4-1/2*b*x^2*cos(c+d*x^2)/d+1/2*b*sin(c+d*x^2)/d^2],
[x*(a+b*sin(c+d*x^2)),x,4,1/2*a*x^2-1/2*b*cos(c+d*x^2)/d],
[(a+b*sin(c+d*x^2))/x,x,5,a*log(x)+1/2*b*cos(c)*Si(d*x^2)+1/2*b*Ci(d*x^2)*sin(c)],
[(a+b*sin(c+d*x^2))/x^3,x,7,-1/2*a/x^2+1/2*b*d*Ci(d*x^2)*cos(c)-1/2*b*d*Si(d*x^2)*sin(c)-1/2*b*sin(c+d*x^2)/x^2],
[(a+b*sin(c+d*x^2))/x^5,x,8,-1/4*a/x^4-1/4*b*d*cos(c+d*x^2)/x^2-1/4*b*d^2*cos(c)*Si(d*x^2)-1/4*b*d^2*Ci(d*x^2)*sin(c)-1/4*b*sin(c+d*x^2)/x^4],
[x^4*(a+b*sin(c+d*x^2)),x,7,1/5*a*x^5-1/2*b*x^3*cos(c+d*x^2)/d+3/4*b*x*sin(c+d*x^2)/d^2-3/4*b*cos(c)*FresnelS(x*sqrt(d)*sqrt(2/Pi))*sqrt(1/2*Pi)/d^(5/2)-3/4*b*FresnelC(x*sqrt(d)*sqrt(2/Pi))*sin(c)*sqrt(1/2*Pi)/d^(5/2)],
[x^2*(a+b*sin(c+d*x^2)),x,6,1/3*a*x^3-1/2*b*x*cos(c+d*x^2)/d+1/2*b*cos(c)*FresnelC(x*sqrt(d)*sqrt(2/Pi))*sqrt(1/2*Pi)/d^(3/2)-1/2*b*FresnelS(x*sqrt(d)*sqrt(2/Pi))*sin(c)*sqrt(1/2*Pi)/d^(3/2)],
[a+b*sin(c+d*x^2),x,4,a*x+b*cos(c)*FresnelS(x*sqrt(d)*sqrt(2/Pi))*sqrt(1/2*Pi)/sqrt(d)+b*FresnelC(x*sqrt(d)*sqrt(2/Pi))*sin(c)*sqrt(1/2*Pi)/sqrt(d)],
[(a+b*sin(c+d*x^2))/x^2,x,6,-a/x-b*sin(c+d*x^2)/x+b*cos(c)*FresnelC(x*sqrt(d)*sqrt(2/Pi))*sqrt(d)*sqrt(2*Pi)-b*FresnelS(x*sqrt(d)*sqrt(2/Pi))*sin(c)*sqrt(d)*sqrt(2*Pi)],
[(a+b*sin(c+d*x^2))/x^4,x,7,-1/3*a/x^3-2/3*b*d*cos(c+d*x^2)/x-1/3*b*sin(c+d*x^2)/x^3-2/3*b*d^(3/2)*cos(c)*FresnelS(x*sqrt(d)*sqrt(2/Pi))*sqrt(2*Pi)-2/3*b*d^(3/2)*FresnelC(x*sqrt(d)*sqrt(2/Pi))*sin(c)*sqrt(2*Pi)],
[x^5*(a+b*sin(c+d*x^2))^2,x,10,-1/8*b^2*x^2/d^2+1/6*a^2*x^6+1/12*b^2*x^6+2*a*b*cos(c+d*x^2)/d^3-a*b*x^4*cos(c+d*x^2)/d+2*a*b*x^2*sin(c+d*x^2)/d^2+1/8*b^2*cos(c+d*x^2)*sin(c+d*x^2)/d^3-1/4*b^2*x^4*cos(c+d*x^2)*sin(c+d*x^2)/d+1/4*b^2*x^2*sin(c+d*x^2)^2/d^2],
[x^3*(a+b*sin(c+d*x^2))^2,x,7,1/4*a^2*x^4+1/8*b^2*x^4-a*b*x^2*cos(c+d*x^2)/d+a*b*sin(c+d*x^2)/d^2-1/4*b^2*x^2*cos(c+d*x^2)*sin(c+d*x^2)/d+1/8*b^2*sin(c+d*x^2)^2/d^2],
[x*(a+b*sin(c+d*x^2))^2,x,2,1/4*(2*a^2+b^2)*x^2-a*b*cos(c+d*x^2)/d-1/4*b^2*cos(c+d*x^2)*sin(c+d*x^2)/d],
[(a+b*sin(c+d*x^2))^2/x,x,9,-1/4*b^2*Ci(2*d*x^2)*cos(2*c)+1/2*(2*a^2+b^2)*log(x)+a*b*cos(c)*Si(d*x^2)+a*b*Ci(d*x^2)*sin(c)+1/4*b^2*Si(2*d*x^2)*sin(2*c)],
[(a+b*sin(c+d*x^2))^2/x^3,x,13,1/4*(-2*a^2-b^2)/x^2+a*b*d*Ci(d*x^2)*cos(c)+1/4*b^2*cos(2*(c+d*x^2))/x^2+1/2*b^2*d*cos(2*c)*Si(2*d*x^2)-a*b*d*Si(d*x^2)*sin(c)+1/2*b^2*d*Ci(2*d*x^2)*sin(2*c)-a*b*sin(c+d*x^2)/x^2],
[(a+b*sin(c+d*x^2))^2/x^5,x,15,1/8*(-2*a^2-b^2)/x^4+1/2*b^2*d^2*Ci(2*d*x^2)*cos(2*c)-1/2*a*b*d*cos(c+d*x^2)/x^2+1/8*b^2*cos(2*(c+d*x^2))/x^4-1/2*a*b*d^2*cos(c)*Si(d*x^2)-1/2*a*b*d^2*Ci(d*x^2)*sin(c)-1/2*b^2*d^2*Si(2*d*x^2)*sin(2*c)-1/2*a*b*sin(c+d*x^2)/x^4-1/4*b^2*d*sin(2*(c+d*x^2))/x^2],
[x^4*(a+b*sin(c+d*x^2))^2,x,13,1/10*(2*a^2+b^2)*x^5-a*b*x^3*cos(c+d*x^2)/d-3/32*b^2*x*cos(2*c+2*d*x^2)/d^2+3/2*a*b*x*sin(c+d*x^2)/d^2-1/8*b^2*x^3*sin(2*c+2*d*x^2)/d-3/2*a*b*cos(c)*FresnelS(x*sqrt(d)*sqrt(2/Pi))*sqrt(1/2*Pi)/d^(5/2)-3/2*a*b*FresnelC(x*sqrt(d)*sqrt(2/Pi))*sin(c)*sqrt(1/2*Pi)/d^(5/2)+3/64*b^2*cos(2*c)*FresnelC(2*x*sqrt(d)/sqrt(Pi))*sqrt(Pi)/d^(5/2)-3/64*b^2*FresnelS(2*x*sqrt(d)/sqrt(Pi))*sin(2*c)*sqrt(Pi)/d^(5/2)],
[x^2*(a+b*sin(c+d*x^2))^2,x,11,1/6*(2*a^2+b^2)*x^3-a*b*x*cos(c+d*x^2)/d-1/8*b^2*x*sin(2*c+2*d*x^2)/d+a*b*cos(c)*FresnelC(x*sqrt(d)*sqrt(2/Pi))*sqrt(1/2*Pi)/d^(3/2)-a*b*FresnelS(x*sqrt(d)*sqrt(2/Pi))*sin(c)*sqrt(1/2*Pi)/d^(3/2)+1/16*b^2*cos(2*c)*FresnelS(2*x*sqrt(d)/sqrt(Pi))*sqrt(Pi)/d^(3/2)+1/16*b^2*FresnelC(2*x*sqrt(d)/sqrt(Pi))*sin(2*c)*sqrt(Pi)/d^(3/2)],
[(a+b*sin(c+d*x^2))^2,x,8,1/2*(2*a^2+b^2)*x-1/4*b^2*cos(2*c)*FresnelC(2*x*sqrt(d)/sqrt(Pi))*sqrt(Pi)/sqrt(d)+1/4*b^2*FresnelS(2*x*sqrt(d)/sqrt(Pi))*sin(2*c)*sqrt(Pi)/sqrt(d)+a*b*cos(c)*FresnelS(x*sqrt(d)*sqrt(2/Pi))*sqrt(2*Pi)/sqrt(d)+a*b*FresnelC(x*sqrt(d)*sqrt(2/Pi))*sin(c)*sqrt(2*Pi)/sqrt(d)],
[(a+b*sin(c+d*x^2))^2/x^2,x,11,1/2*(-2*a^2-b^2)/x+1/2*b^2*cos(2*c+2*d*x^2)/x-2*a*b*sin(c+d*x^2)/x+b^2*cos(2*c)*FresnelS(2*x*sqrt(d)/sqrt(Pi))*sqrt(d)*sqrt(Pi)+b^2*FresnelC(2*x*sqrt(d)/sqrt(Pi))*sin(2*c)*sqrt(d)*sqrt(Pi)+2*a*b*cos(c)*FresnelC(x*sqrt(d)*sqrt(2/Pi))*sqrt(d)*sqrt(2*Pi)-2*a*b*FresnelS(x*sqrt(d)*sqrt(2/Pi))*sin(c)*sqrt(d)*sqrt(2*Pi)],
[(a+b*sin(c+d*x^2))^2/x^4,x,13,1/6*(-2*a^2-b^2)/x^3-4/3*a*b*d*cos(c+d*x^2)/x+1/6*b^2*cos(2*c+2*d*x^2)/x^3-2/3*a*b*sin(c+d*x^2)/x^3-2/3*b^2*d*sin(2*c+2*d*x^2)/x+4/3*b^2*d^(3/2)*cos(2*c)*FresnelC(2*x*sqrt(d)/sqrt(Pi))*sqrt(Pi)-4/3*b^2*d^(3/2)*FresnelS(2*x*sqrt(d)/sqrt(Pi))*sin(2*c)*sqrt(Pi)-4/3*a*b*d^(3/2)*cos(c)*FresnelS(x*sqrt(d)*sqrt(2/Pi))*sqrt(2*Pi)-4/3*a*b*d^(3/2)*FresnelC(x*sqrt(d)*sqrt(2/Pi))*sin(c)*sqrt(2*Pi)],
[x^5*sin(a+b*x^2)^3,x,7,7/9*cos(a+b*x^2)/b^3-1/3*x^4*cos(a+b*x^2)/b-1/27*cos(a+b*x^2)^3/b^3+2/3*x^2*sin(a+b*x^2)/b^2-1/6*x^4*cos(a+b*x^2)*sin(a+b*x^2)^2/b+1/9*x^2*sin(a+b*x^2)^3/b^2],
[x^3*sin(a+b*x^2)^3,x,4,-1/3*x^2*cos(a+b*x^2)/b+1/3*sin(a+b*x^2)/b^2-1/6*x^2*cos(a+b*x^2)*sin(a+b*x^2)^2/b+1/18*sin(a+b*x^2)^3/b^2],
[x*sin(a+b*x^2)^3,x,3,-1/2*cos(a+b*x^2)/b+1/6*cos(a+b*x^2)^3/b],
[sin(a+b*x^2)^3/x,x,8,3/8*cos(a)*Si(b*x^2)-1/8*cos(3*a)*Si(3*b*x^2)+3/8*Ci(b*x^2)*sin(a)-1/8*Ci(3*b*x^2)*sin(3*a)],
[sin(a+b*x^2)^3/x^3,x,12,3/8*b*Ci(b*x^2)*cos(a)-3/8*b*Ci(3*b*x^2)*cos(3*a)-3/8*b*Si(b*x^2)*sin(a)+3/8*b*Si(3*b*x^2)*sin(3*a)-3/8*sin(a+b*x^2)/x^2+1/8*sin(3*(a+b*x^2))/x^2],
[x^2*sin(a+b*x^2)^3,x,10,-3/8*x*cos(a+b*x^2)/b+1/24*x*cos(3*a+3*b*x^2)/b-1/24*cos(3*a)*FresnelC(x*sqrt(b)*sqrt(6/Pi))*sqrt(1/6*Pi)/b^(3/2)+1/24*FresnelS(x*sqrt(b)*sqrt(6/Pi))*sin(3*a)*sqrt(1/6*Pi)/b^(3/2)+3/8*cos(a)*FresnelC(x*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/b^(3/2)-3/8*FresnelS(x*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/b^(3/2)],
[sin(a+b*x^2)^3,x,8,-1/4*cos(3*a)*FresnelS(x*sqrt(b)*sqrt(6/Pi))*sqrt(1/6*Pi)/sqrt(b)-1/4*FresnelC(x*sqrt(b)*sqrt(6/Pi))*sin(3*a)*sqrt(1/6*Pi)/sqrt(b)+3/4*cos(a)*FresnelS(x*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/sqrt(b)+3/4*FresnelC(x*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/sqrt(b)],
[sin(a+b*x^2)^3/x^2,x,9,-sin(a+b*x^2)^3/x+3/2*cos(a)*FresnelC(x*sqrt(b)*sqrt(2/Pi))*sqrt(b)*sqrt(1/2*Pi)-3/2*FresnelS(x*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(b)*sqrt(1/2*Pi)-1/2*cos(3*a)*FresnelC(x*sqrt(b)*sqrt(6/Pi))*sqrt(b)*sqrt(3/2*Pi)+1/2*FresnelS(x*sqrt(b)*sqrt(6/Pi))*sin(3*a)*sqrt(b)*sqrt(3/2*Pi)],
[x^2*sin(x^2)^3,x,6,-1/2*x*cos(x^2)+1/6*x*cos(x^2)^3-1/24*FresnelC(x*sqrt(6/Pi))*sqrt(1/6*Pi)+3/8*FresnelC(x*sqrt(2/Pi))*sqrt(1/2*Pi),-3/8*x*cos(x^2)+1/24*x*cos(3*x^2)-1/24*FresnelC(x*sqrt(6/Pi))*sqrt(1/6*Pi)+3/8*FresnelC(x*sqrt(2/Pi))*sqrt(1/2*Pi)],
[x^4*cos(x^2)*sin(x^2)^2,x,7,1/4*x*cos(x^2)-1/12*x*cos(x^2)^3+1/6*x^3*sin(x^2)^3+1/48*FresnelC(x*sqrt(6/Pi))*sqrt(1/6*Pi)-3/16*FresnelC(x*sqrt(2/Pi))*sqrt(1/2*Pi),3/16*x*cos(x^2)-1/48*x*cos(3*x^2)+1/6*x^3*sin(x^2)^3+1/48*FresnelC(x*sqrt(6/Pi))*sqrt(1/6*Pi)-3/16*FresnelC(x*sqrt(2/Pi))*sqrt(1/2*Pi)],
[x*sin(a+b*x^2)^7,x,3,-1/2*cos(a+b*x^2)/b+1/2*cos(a+b*x^2)^3/b-3/10*cos(a+b*x^2)^5/b+1/14*cos(a+b*x^2)^7/b],
[(1+sin(x^2))^2/x^3,x,8,(-3/4)/x^2+Ci(x^2)+1/4*cos(2*x^2)/x^2+1/2*Si(2*x^2)-sin(x^2)/x^2],

# p<0
[x^5/(a+b*sin(c+d*x^2)),x,11,-1/2*I*x^4*log(1-I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/(d*sqrt(a^2-b^2))+1/2*I*x^4*log(1-I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/(d*sqrt(a^2-b^2))-x^2*polylog(2,I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/(d^2*sqrt(a^2-b^2))+x^2*polylog(2,I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/(d^2*sqrt(a^2-b^2))-I*polylog(3,I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/(d^3*sqrt(a^2-b^2))+I*polylog(3,I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/(d^3*sqrt(a^2-b^2))],
[x^3/(a+b*sin(c+d*x^2)),x,9,-1/2*I*x^2*log(1-I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/(d*sqrt(a^2-b^2))+1/2*I*x^2*log(1-I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/(d*sqrt(a^2-b^2))-1/2*polylog(2,I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/(d^2*sqrt(a^2-b^2))+1/2*polylog(2,I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/(d^2*sqrt(a^2-b^2))],
[x/(a+b*sin(c+d*x^2)),x,4,arctan((b+a*tan(1/2*(c+d*x^2)))/sqrt(a^2-b^2))/(d*sqrt(a^2-b^2))],
[1/(x*(a+b*sin(c+d*x^2))),x,0,Unintegrable(1/(x*(a+b*sin(c+d*x^2))),x)],
[1/(x^3*(a+b*sin(c+d*x^2))),x,0,Unintegrable(1/(x^3*(a+b*sin(c+d*x^2))),x)],
[x^2/(a+b*sin(c+d*x^2)),x,0,Unintegrable(x^2/(a+b*sin(c+d*x^2)),x)],
[1/(a+b*sin(c+d*x^2)),x,0,Unintegrable(1/(a+b*sin(c+d*x^2)),x)],
[1/(x^2*(a+b*sin(c+d*x^2))),x,0,Unintegrable(1/(x^2*(a+b*sin(c+d*x^2))),x)],
[x^5/(a+b*sin(c+d*x^2))^2,x,19,1/2*I*x^4/((a^2-b^2)*d)-x^2*log(1-I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/((a^2-b^2)*d^2)-1/2*I*a*x^4*log(1-I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d)-x^2*log(1-I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/((a^2-b^2)*d^2)+1/2*I*a*x^4*log(1-I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d)+I*polylog(2,I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/((a^2-b^2)*d^3)-a*x^2*polylog(2,I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d^2)+I*polylog(2,I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/((a^2-b^2)*d^3)+a*x^2*polylog(2,I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d^2)-I*a*polylog(3,I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d^3)+I*a*polylog(3,I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d^3)+1/2*b*x^4*cos(c+d*x^2)/((a^2-b^2)*d*(a+b*sin(c+d*x^2)))],
[x^3/(a+b*sin(c+d*x^2))^2,x,12,-1/2*log(a+b*sin(c+d*x^2))/((a^2-b^2)*d^2)-1/2*I*a*x^2*log(1-I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d)+1/2*I*a*x^2*log(1-I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d)-1/2*a*polylog(2,I*b*exp(I*(c+d*x^2))/(a-sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d^2)+1/2*a*polylog(2,I*b*exp(I*(c+d*x^2))/(a+sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d^2)+1/2*b*x^2*cos(c+d*x^2)/((a^2-b^2)*d*(a+b*sin(c+d*x^2)))],
[x/(a+b*sin(c+d*x^2))^2,x,6,a*arctan((b+a*tan(1/2*(c+d*x^2)))/sqrt(a^2-b^2))/((a^2-b^2)^(3/2)*d)+1/2*b*cos(c+d*x^2)/((a^2-b^2)*d*(a+b*sin(c+d*x^2)))],
[1/(x*(a+b*sin(c+d*x^2))^2),x,0,Unintegrable(1/(x*(a+b*sin(c+d*x^2))^2),x)],
[1/(x^3*(a+b*sin(c+d*x^2))^2),x,0,Unintegrable(1/(x^3*(a+b*sin(c+d*x^2))^2),x)],
[x^2/(a+b*sin(c+d*x^2))^2,x,0,Unintegrable(x^2/(a+b*sin(c+d*x^2))^2,x)],
[1/(a+b*sin(c+d*x^2))^2,x,0,Unintegrable(1/(a+b*sin(c+d*x^2))^2,x)],
[1/(x^2*(a+b*sin(c+d*x^2))^2),x,0,Unintegrable(1/(x^2*(a+b*sin(c+d*x^2))^2),x)],

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

# Integrands of the form (e x)^m (a+b Sin[c+d x^2])^p with m symbolic
[(e*x)^m*(a+b*sin(c+d*x^2))^p,x,0,Unintegrable((e*x)^m*(a+b*sin(c+d*x^2))^p,x)],
[(e*x)^m*(a+b*sin(c+d*x^2))^3,x,13,1/2*a*(2*a^2+3*b^2)*(e*x)^(1+m)/(e*(1+m))+3/16*I*b*(4*a^2+b^2)*exp(I*c)*(e*x)^(1+m)*(-I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),-I*d*x^2)/e-3/16*I*b*(4*a^2+b^2)*(e*x)^(1+m)*(I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),I*d*x^2)/(e*exp(I*c))+3*2^(-7/2-1/2*m)*a*b^2*exp(2*I*c)*(e*x)^(1+m)*(-I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),-2*I*d*x^2)/e+3*2^(-7/2-1/2*m)*a*b^2*(e*x)^(1+m)*(I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),2*I*d*x^2)/(e*exp(2*I*c))-1/16*I*3^(-1/2-1/2*m)*b^3*exp(3*I*c)*(e*x)^(1+m)*(-I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),-3*I*d*x^2)/e+1/16*I*3^(-1/2-1/2*m)*b^3*(e*x)^(1+m)*(I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),3*I*d*x^2)/(e*exp(3*I*c))],
[(e*x)^m*(a+b*sin(c+d*x^2))^2,x,9,1/2*(2*a^2+b^2)*(e*x)^(1+m)/(e*(1+m))+1/2*I*a*b*exp(I*c)*(e*x)^(1+m)*(-I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),-I*d*x^2)/e-1/2*I*a*b*(e*x)^(1+m)*(I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),I*d*x^2)/(e*exp(I*c))+2^(-7/2-1/2*m)*b^2*exp(2*I*c)*(e*x)^(1+m)*(-I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),-2*I*d*x^2)/e+2^(-7/2-1/2*m)*b^2*(e*x)^(1+m)*(I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),2*I*d*x^2)/(e*exp(2*I*c))],
[(e*x)^m*(a+b*sin(c+d*x^2)),x,5,a*(e*x)^(1+m)/(e*(1+m))+1/4*I*b*exp(I*c)*(e*x)^(1+m)*(-I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),-I*d*x^2)/e-1/4*I*b*(e*x)^(1+m)*(I*d*x^2)^(1/2*(-1-m))*GAMMA(1/2*(1+m),I*d*x^2)/(e*exp(I*c))],
[(e*x)^m/(a+b*sin(c+d*x^2)),x,0,Unintegrable((e*x)^m/(a+b*sin(c+d*x^2)),x)],
[(e*x)^m/(a+b*sin(c+d*x^2))^2,x,0,Unintegrable((e*x)^m/(a+b*sin(c+d*x^2))^2,x)],

# Integrands of the form (e x)^m (a+b Sin[c+d x^3])^p

# Integrands of the form x^m (a+b Sin[c+d x^3])^p

# p>0
[x^5*(a+b*sin(c+d*x^3)),x,5,1/6*a*x^6-1/3*b*x^3*cos(c+d*x^3)/d+1/3*b*sin(c+d*x^3)/d^2],
[x^2*(a+b*sin(c+d*x^3)),x,4,1/3*a*x^3-1/3*b*cos(c+d*x^3)/d],
[(a+b*sin(c+d*x^3))/x,x,5,a*log(x)+1/3*b*cos(c)*Si(d*x^3)+1/3*b*Ci(d*x^3)*sin(c)],
[(a+b*sin(c+d*x^3))/x^4,x,7,-1/3*a/x^3+1/3*b*d*Ci(d*x^3)*cos(c)-1/3*b*d*Si(d*x^3)*sin(c)-1/3*b*sin(c+d*x^3)/x^3],
[x^4*(a+b*sin(c+d*x^3)),x,6,1/5*a*x^5-1/3*b*x^2*cos(c+d*x^3)/d-1/9*b*exp(I*c)*x^2*GAMMA(2/3,-I*d*x^3)/(d*(-I*d*x^3)^(2/3))-1/9*b*x^2*GAMMA(2/3,I*d*x^3)/(d*exp(I*c)*(I*d*x^3)^(2/3))],
[x*(a+b*sin(c+d*x^3)),x,5,1/2*a*x^2+1/6*I*b*exp(I*c)*x^2*GAMMA(2/3,-I*d*x^3)/(-I*d*x^3)^(2/3)-1/6*I*b*x^2*GAMMA(2/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(2/3))],
[(a+b*sin(c+d*x^3))/x^2,x,6,-a/x-1/2*b*d*exp(I*c)*x^2*GAMMA(2/3,-I*d*x^3)/(-I*d*x^3)^(2/3)-1/2*b*d*x^2*GAMMA(2/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(2/3))-b*sin(c+d*x^3)/x],
[(a+b*sin(c+d*x^3))/x^5,x,7,-1/4*a/x^4-3/4*b*d*cos(c+d*x^3)/x-3/8*I*b*d^2*exp(I*c)*x^2*GAMMA(2/3,-I*d*x^3)/(-I*d*x^3)^(2/3)+3/8*I*b*d^2*x^2*GAMMA(2/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(2/3))-1/4*b*sin(c+d*x^3)/x^4],
[x^3*(a+b*sin(c+d*x^3)),x,6,1/4*a*x^4-1/3*b*x*cos(c+d*x^3)/d-1/18*b*exp(I*c)*x*GAMMA(1/3,-I*d*x^3)/(d*(-I*d*x^3)^(1/3))-1/18*b*x*GAMMA(1/3,I*d*x^3)/(d*exp(I*c)*(I*d*x^3)^(1/3))],
[a+b*sin(c+d*x^3),x,4,a*x+1/6*I*b*exp(I*c)*x*GAMMA(1/3,-I*d*x^3)/(-I*d*x^3)^(1/3)-1/6*I*b*x*GAMMA(1/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(1/3))],
[(a+b*sin(c+d*x^3))/x^3,x,6,-1/2*a/x^2-1/4*b*d*exp(I*c)*x*GAMMA(1/3,-I*d*x^3)/(-I*d*x^3)^(1/3)-1/4*b*d*x*GAMMA(1/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(1/3))-1/2*b*sin(c+d*x^3)/x^2],
[(a+b*sin(c+d*x^3))/x^6,x,7,-1/5*a/x^5-3/10*b*d*cos(c+d*x^3)/x^2-3/20*I*b*d^2*exp(I*c)*x*GAMMA(1/3,-I*d*x^3)/(-I*d*x^3)^(1/3)+3/20*I*b*d^2*x*GAMMA(1/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(1/3))-1/5*b*sin(c+d*x^3)/x^5],
[x^5*(a+b*sin(c+d*x^3))^2,x,7,1/6*a^2*x^6+1/12*b^2*x^6-2/3*a*b*x^3*cos(c+d*x^3)/d+2/3*a*b*sin(c+d*x^3)/d^2-1/6*b^2*x^3*cos(c+d*x^3)*sin(c+d*x^3)/d+1/12*b^2*sin(c+d*x^3)^2/d^2],
[x^2*(a+b*sin(c+d*x^3))^2,x,2,1/6*(2*a^2+b^2)*x^3-2/3*a*b*cos(c+d*x^3)/d-1/6*b^2*cos(c+d*x^3)*sin(c+d*x^3)/d],
[(a+b*sin(c+d*x^3))^2/x,x,9,-1/6*b^2*Ci(2*d*x^3)*cos(2*c)+1/2*(2*a^2+b^2)*log(x)+2/3*a*b*cos(c)*Si(d*x^3)+2/3*a*b*Ci(d*x^3)*sin(c)+1/6*b^2*Si(2*d*x^3)*sin(2*c)],
[(a+b*sin(c+d*x^3))^2/x^4,x,13,1/6*(-2*a^2-b^2)/x^3+2/3*a*b*d*Ci(d*x^3)*cos(c)+1/6*b^2*cos(2*(c+d*x^3))/x^3+1/3*b^2*d*cos(2*c)*Si(2*d*x^3)-2/3*a*b*d*Si(d*x^3)*sin(c)+1/3*b^2*d*Ci(2*d*x^3)*sin(2*c)-2/3*a*b*sin(c+d*x^3)/x^3],
[x^4*(a+b*sin(c+d*x^3))^2,x,11,1/10*(2*a^2+b^2)*x^5-2/3*a*b*x^2*cos(c+d*x^3)/d-2/9*a*b*exp(I*c)*x^2*GAMMA(2/3,-I*d*x^3)/(d*(-I*d*x^3)^(2/3))-2/9*a*b*x^2*GAMMA(2/3,I*d*x^3)/(d*exp(I*c)*(I*d*x^3)^(2/3))+1/36*I*b^2*exp(2*I*c)*x^2*GAMMA(2/3,-2*I*d*x^3)/(2^(2/3)*d*(-I*d*x^3)^(2/3))-1/36*I*b^2*x^2*GAMMA(2/3,2*I*d*x^3)/(2^(2/3)*d*exp(2*I*c)*(I*d*x^3)^(2/3))-1/12*b^2*x^2*sin(2*c+2*d*x^3)/d],
[x*(a+b*sin(c+d*x^3))^2,x,9,1/4*(2*a^2+b^2)*x^2+1/3*I*a*b*exp(I*c)*x^2*GAMMA(2/3,-I*d*x^3)/(-I*d*x^3)^(2/3)-1/3*I*a*b*x^2*GAMMA(2/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(2/3))+1/12*b^2*exp(2*I*c)*x^2*GAMMA(2/3,-2*I*d*x^3)/(2^(2/3)*(-I*d*x^3)^(2/3))+1/12*b^2*x^2*GAMMA(2/3,2*I*d*x^3)/(2^(2/3)*exp(2*I*c)*(I*d*x^3)^(2/3))],
[(a+b*sin(c+d*x^3))^2/x^2,x,11,1/2*(-2*a^2-b^2)/x+1/2*b^2*cos(2*c+2*d*x^3)/x-a*b*d*exp(I*c)*x^2*GAMMA(2/3,-I*d*x^3)/(-I*d*x^3)^(2/3)-a*b*d*x^2*GAMMA(2/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(2/3))+1/2*I*b^2*d*exp(2*I*c)*x^2*GAMMA(2/3,-2*I*d*x^3)/(2^(2/3)*(-I*d*x^3)^(2/3))-1/2*I*b^2*d*x^2*GAMMA(2/3,2*I*d*x^3)/(2^(2/3)*exp(2*I*c)*(I*d*x^3)^(2/3))-2*a*b*sin(c+d*x^3)/x],
[(a+b*sin(c+d*x^3))^2/x^5,x,13,1/8*(-2*a^2-b^2)/x^4-3/2*a*b*d*cos(c+d*x^3)/x+1/8*b^2*cos(2*c+2*d*x^3)/x^4-3/4*I*a*b*d^2*exp(I*c)*x^2*GAMMA(2/3,-I*d*x^3)/(-I*d*x^3)^(2/3)+3/4*I*a*b*d^2*x^2*GAMMA(2/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(2/3))-3/4*b^2*d^2*exp(2*I*c)*x^2*GAMMA(2/3,-2*I*d*x^3)/(2^(2/3)*(-I*d*x^3)^(2/3))-3/4*b^2*d^2*x^2*GAMMA(2/3,2*I*d*x^3)/(2^(2/3)*exp(2*I*c)*(I*d*x^3)^(2/3))-1/2*a*b*sin(c+d*x^3)/x^4-3/4*b^2*d*sin(2*c+2*d*x^3)/x],
[x^3*(a+b*sin(c+d*x^3))^2,x,11,1/8*(2*a^2+b^2)*x^4-2/3*a*b*x*cos(c+d*x^3)/d-1/9*a*b*exp(I*c)*x*GAMMA(1/3,-I*d*x^3)/(d*(-I*d*x^3)^(1/3))-1/9*a*b*x*GAMMA(1/3,I*d*x^3)/(d*exp(I*c)*(I*d*x^3)^(1/3))+1/72*I*b^2*exp(2*I*c)*x*GAMMA(1/3,-2*I*d*x^3)/(2^(1/3)*d*(-I*d*x^3)^(1/3))-1/72*I*b^2*x*GAMMA(1/3,2*I*d*x^3)/(2^(1/3)*d*exp(2*I*c)*(I*d*x^3)^(1/3))-1/12*b^2*x*sin(2*c+2*d*x^3)/d],
[(a+b*sin(c+d*x^3))^2,x,8,1/2*(2*a^2+b^2)*x+1/3*I*a*b*exp(I*c)*x*GAMMA(1/3,-I*d*x^3)/(-I*d*x^3)^(1/3)-1/3*I*a*b*x*GAMMA(1/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(1/3))+1/12*b^2*exp(2*I*c)*x*GAMMA(1/3,-2*I*d*x^3)/(2^(1/3)*(-I*d*x^3)^(1/3))+1/12*b^2*x*GAMMA(1/3,2*I*d*x^3)/(2^(1/3)*exp(2*I*c)*(I*d*x^3)^(1/3))],
[(a+b*sin(c+d*x^3))^2/x^3,x,11,1/4*(-2*a^2-b^2)/x^2+1/4*b^2*cos(2*c+2*d*x^3)/x^2-1/2*a*b*d*exp(I*c)*x*GAMMA(1/3,-I*d*x^3)/(-I*d*x^3)^(1/3)-1/2*a*b*d*x*GAMMA(1/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(1/3))+1/4*I*b^2*d*exp(2*I*c)*x*GAMMA(1/3,-2*I*d*x^3)/(2^(1/3)*(-I*d*x^3)^(1/3))-1/4*I*b^2*d*x*GAMMA(1/3,2*I*d*x^3)/(2^(1/3)*exp(2*I*c)*(I*d*x^3)^(1/3))-a*b*sin(c+d*x^3)/x^2],
[(a+b*sin(c+d*x^3))^2/x^6,x,13,1/10*(-2*a^2-b^2)/x^5-3/5*a*b*d*cos(c+d*x^3)/x^2+1/10*b^2*cos(2*c+2*d*x^3)/x^5-3/10*I*a*b*d^2*exp(I*c)*x*GAMMA(1/3,-I*d*x^3)/(-I*d*x^3)^(1/3)+3/10*I*a*b*d^2*x*GAMMA(1/3,I*d*x^3)/(exp(I*c)*(I*d*x^3)^(1/3))-3/10*b^2*d^2*exp(2*I*c)*x*GAMMA(1/3,-2*I*d*x^3)/(2^(1/3)*(-I*d*x^3)^(1/3))-3/10*b^2*d^2*x*GAMMA(1/3,2*I*d*x^3)/(2^(1/3)*exp(2*I*c)*(I*d*x^3)^(1/3))-2/5*a*b*sin(c+d*x^3)/x^5-3/10*b^2*d*sin(2*c+2*d*x^3)/x^2],

# p<0
[x^5/(a+b*sin(c+d*x^3)),x,9,-1/3*I*x^3*log(1-I*b*exp(I*(c+d*x^3))/(a-sqrt(a^2-b^2)))/(d*sqrt(a^2-b^2))+1/3*I*x^3*log(1-I*b*exp(I*(c+d*x^3))/(a+sqrt(a^2-b^2)))/(d*sqrt(a^2-b^2))-1/3*polylog(2,I*b*exp(I*(c+d*x^3))/(a-sqrt(a^2-b^2)))/(d^2*sqrt(a^2-b^2))+1/3*polylog(2,I*b*exp(I*(c+d*x^3))/(a+sqrt(a^2-b^2)))/(d^2*sqrt(a^2-b^2))],
[x^2/(a+b*sin(c+d*x^3)),x,4,2/3*arctan((b+a*tan(1/2*(c+d*x^3)))/sqrt(a^2-b^2))/(d*sqrt(a^2-b^2))],
[1/(x*(a+b*sin(c+d*x^3))),x,0,Unintegrable(1/(x*(a+b*sin(c+d*x^3))),x)],
[1/(x^4*(a+b*sin(c+d*x^3))),x,0,Unintegrable(1/(x^4*(a+b*sin(c+d*x^3))),x)],
[x/(a+b*sin(c+d*x^3)),x,0,Unintegrable(x/(a+b*sin(c+d*x^3)),x)],
[1/(x^2*(a+b*sin(c+d*x^3))),x,0,Unintegrable(1/(x^2*(a+b*sin(c+d*x^3))),x)],
[1/(a+b*sin(c+d*x^3)),x,0,Unintegrable(1/(a+b*sin(c+d*x^3)),x)],
[1/(x^3*(a+b*sin(c+d*x^3))),x,0,Unintegrable(1/(x^3*(a+b*sin(c+d*x^3))),x)],
[x^5/(a+b*sin(c+d*x^3))^2,x,12,-1/3*log(a+b*sin(c+d*x^3))/((a^2-b^2)*d^2)-1/3*I*a*x^3*log(1-I*b*exp(I*(c+d*x^3))/(a-sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d)+1/3*I*a*x^3*log(1-I*b*exp(I*(c+d*x^3))/(a+sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d)-1/3*a*polylog(2,I*b*exp(I*(c+d*x^3))/(a-sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d^2)+1/3*a*polylog(2,I*b*exp(I*(c+d*x^3))/(a+sqrt(a^2-b^2)))/((a^2-b^2)^(3/2)*d^2)+1/3*b*x^3*cos(c+d*x^3)/((a^2-b^2)*d*(a+b*sin(c+d*x^3)))],
[x^2/(a+b*sin(c+d*x^3))^2,x,6,2/3*a*arctan((b+a*tan(1/2*(c+d*x^3)))/sqrt(a^2-b^2))/((a^2-b^2)^(3/2)*d)+1/3*b*cos(c+d*x^3)/((a^2-b^2)*d*(a+b*sin(c+d*x^3)))],
[1/(x*(a+b*sin(c+d*x^3))^2),x,0,Unintegrable(1/(x*(a+b*sin(c+d*x^3))^2),x)],
[1/(x^4*(a+b*sin(c+d*x^3))^2),x,0,Unintegrable(1/(x^4*(a+b*sin(c+d*x^3))^2),x)],
[x/(a+b*sin(c+d*x^3))^2,x,0,Unintegrable(x/(a+b*sin(c+d*x^3))^2,x)],
[1/(x^2*(a+b*sin(c+d*x^3))^2),x,0,Unintegrable(1/(x^2*(a+b*sin(c+d*x^3))^2),x)],
[1/(a+b*sin(c+d*x^3))^2,x,0,Unintegrable(1/(a+b*sin(c+d*x^3))^2,x)],
[1/(x^3*(a+b*sin(c+d*x^3))^2),x,0,Unintegrable(1/(x^3*(a+b*sin(c+d*x^3))^2),x)],

# Integrands of the form (e x)^(m/2) (a+b Sin[c+d x^3])^p

# Integrands of the form (e x)^m (a+b Sin[c+d x^3])^p with m symbolic
[(e*x)^m*(a+b*sin(c+d*x^3))^p,x,0,Unintegrable((e*x)^m*(a+b*sin(c+d*x^3))^p,x)],
[(e*x)^m*(a+b*sin(c+d*x^3))^3,x,13,1/2*a*(2*a^2+3*b^2)*(e*x)^(1+m)/(e*(1+m))+1/8*I*b*(4*a^2+b^2)*exp(I*c)*(e*x)^(1+m)*(-I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),-I*d*x^3)/e-1/8*I*b*(4*a^2+b^2)*(e*x)^(1+m)*(I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),I*d*x^3)/(e*exp(I*c))+2^(-7/3-1/3*m)*a*b^2*exp(2*I*c)*(e*x)^(1+m)*(-I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),-2*I*d*x^3)/e+2^(-7/3-1/3*m)*a*b^2*(e*x)^(1+m)*(I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),2*I*d*x^3)/(e*exp(2*I*c))-1/8*I*3^(-4/3-1/3*m)*b^3*exp(3*I*c)*(e*x)^(1+m)*(-I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),-3*I*d*x^3)/e+1/8*I*3^(-4/3-1/3*m)*b^3*(e*x)^(1+m)*(I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),3*I*d*x^3)/(e*exp(3*I*c))],
[(e*x)^m*(a+b*sin(c+d*x^3))^2,x,9,1/2*(2*a^2+b^2)*(e*x)^(1+m)/(e*(1+m))+1/3*I*a*b*exp(I*c)*(e*x)^(1+m)*(-I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),-I*d*x^3)/e-1/3*I*a*b*(e*x)^(1+m)*(I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),I*d*x^3)/(e*exp(I*c))+1/3*2^(-7/3-1/3*m)*b^2*exp(2*I*c)*(e*x)^(1+m)*(-I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),-2*I*d*x^3)/e+1/3*2^(-7/3-1/3*m)*b^2*(e*x)^(1+m)*(I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),2*I*d*x^3)/(e*exp(2*I*c))],
[(e*x)^m*(a+b*sin(c+d*x^3)),x,5,a*(e*x)^(1+m)/(e*(1+m))+1/6*I*b*exp(I*c)*(e*x)^(1+m)*(-I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),-I*d*x^3)/e-1/6*I*b*(e*x)^(1+m)*(I*d*x^3)^(1/3*(-1-m))*GAMMA(1/3*(1+m),I*d*x^3)/(e*exp(I*c))],
[(e*x)^m/(a+b*sin(c+d*x^3)),x,0,Unintegrable((e*x)^m/(a+b*sin(c+d*x^3)),x)],
[(e*x)^m/(a+b*sin(c+d*x^3))^2,x,0,Unintegrable((e*x)^m/(a+b*sin(c+d*x^3))^2,x)],

# Integrands of the form (e x)^m (a+b Sin[c+d / x^1])^p

# Integrands of the form x^m (a+b Sin[c+d / x^1])^p

# p>0
[x^2*sin(a+b/x),x,7,1/6*b^3*Ci(b/x)*cos(a)+1/6*b*x^2*cos(a+b/x)-1/6*b^3*Si(b/x)*sin(a)-1/6*b^2*x*sin(a+b/x)+1/3*x^3*sin(a+b/x)],
[x*sin(a+b/x),x,6,1/2*b*x*cos(a+b/x)+1/2*b^2*cos(a)*Si(b/x)+1/2*b^2*Ci(b/x)*sin(a)+1/2*x^2*sin(a+b/x)],
[sin(a+b/x),x,5,-b*Ci(b/x)*cos(a)+b*Si(b/x)*sin(a)+x*sin(a+b/x)],
[sin(a+b/x)/x,x,3,-cos(a)*Si(b/x)-Ci(b/x)*sin(a)],
[sin(a+b/x)/x^2,x,2,cos(a+b/x)/b],
[sin(a+b/x)/x^3,x,3,cos(a+b/x)/(b*x)-sin(a+b/x)/b^2],
[sin(a+b/x)/x^4,x,4,-2*cos(a+b/x)/b^3+cos(a+b/x)/(b*x^2)-2*sin(a+b/x)/(b^2*x)],
[sin(a+b/x)/x^5,x,5,cos(a+b/x)/(b*x^3)-6*cos(a+b/x)/(b^3*x)+6*sin(a+b/x)/b^4-3*sin(a+b/x)/(b^2*x^2)],
[x^2*sin(a+b/x)^2,x,9,1/6*x^3+1/3*b^2*x*cos(2*(a+b/x))-1/6*x^3*cos(2*(a+b/x))+2/3*b^3*cos(2*a)*Si(2*b/x)+2/3*b^3*Ci(2*b/x)*sin(2*a)+1/6*b*x^2*sin(2*(a+b/x))],
[x*sin(a+b/x)^2,x,8,-b^2*Ci(2*b/x)*cos(2*a)+b^2*Si(2*b/x)*sin(2*a)+1/2*x^2*sin(a+b/x)^2+1/2*b*x*sin(2*(a+b/x))],
[sin(a+b/x)^2,x,6,-b*cos(2*a)*Si(2*b/x)-b*Ci(2*b/x)*sin(2*a)+x*sin(a+b/x)^2],
[sin(a+b/x)^2/x,x,5,1/2*Ci(2*b/x)*cos(2*a)+1/2*log(x)-1/2*Si(2*b/x)*sin(2*a)],
[sin(a+b/x)^2/x^2,x,3,(-1/2)/x+1/2*cos(a+b/x)*sin(a+b/x)/b],
[sin(a+b/x)^2/x^3,x,3,(-1/4)/x^2+1/2*cos(a+b/x)*sin(a+b/x)/(b*x)-1/4*sin(a+b/x)^2/b^2],
[sin(a+b/x)^2/x^4,x,5,(-1/6)/x^3+1/4/(b^2*x)-1/4*cos(a+b/x)*sin(a+b/x)/b^3+1/2*cos(a+b/x)*sin(a+b/x)/(b*x^2)-1/2*sin(a+b/x)^2/(b^2*x)],
[sin(a+b/x)^2/x^5,x,5,(-1/8)/x^4+3/8/(b^2*x^2)+1/2*cos(a+b/x)*sin(a+b/x)/(b*x^3)-3/4*cos(a+b/x)*sin(a+b/x)/(b^3*x)+3/8*sin(a+b/x)^2/b^4-3/4*sin(a+b/x)^2/(b^2*x^2)],

# p<0

# Integrands of the form (e x)^m (a+b Sin[c+d / x^2])^p
[sin(a+b/x^2),x,5,x*sin(a+b/x^2)-cos(a)*FresnelC(sqrt(b)*sqrt(2/Pi)/x)*sqrt(b)*sqrt(2*Pi)+FresnelS(sqrt(b)*sqrt(2/Pi)/x)*sin(a)*sqrt(b)*sqrt(2*Pi)],
[sin(a+b/x^2)/x,x,3,-1/2*cos(a)*Si(b/x^2)-1/2*Ci(b/x^2)*sin(a)],
[sin(a+b/x^2)/x^2,x,4,-cos(a)*FresnelS(sqrt(b)*sqrt(2/Pi)/x)*sqrt(1/2*Pi)/sqrt(b)-FresnelC(sqrt(b)*sqrt(2/Pi)/x)*sin(a)*sqrt(1/2*Pi)/sqrt(b)],
[sin(a+b/x^2)/x^3,x,2,1/2*cos(a+b/x^2)/b],
[sin(a+b/x^2)/x^4,x,5,1/2*cos(a+b/x^2)/(b*x)-1/2*cos(a)*FresnelC(sqrt(b)*sqrt(2/Pi)/x)*sqrt(1/2*Pi)/b^(3/2)+1/2*FresnelS(sqrt(b)*sqrt(2/Pi)/x)*sin(a)*sqrt(1/2*Pi)/b^(3/2)],

# Integrands of the form (e x)^m (a+b Sin[c+d x^(1/2)])^p
[sin(sqrt(x))/sqrt(x),x,2,-2*cos(sqrt(x))],
[sin(sqrt(x))^3/sqrt(x),x,3,-2*cos(sqrt(x))+2/3*cos(sqrt(x))^3],
[sin(sqrt(x)),x,3,2*sin(sqrt(x))-2*cos(sqrt(x))*sqrt(x)],

# Integrands of the form (e x)^m (a+b Sin[c+d x^(1/3)])^p
[sin(x^(1/3))^2,x,5,-3/4*x^(1/3)+1/2*x+3/4*cos(x^(1/3))*sin(x^(1/3))-3/2*x^(2/3)*cos(x^(1/3))*sin(x^(1/3))+3/2*x^(1/3)*sin(x^(1/3))^2],
[sin(x^(1/3))^3,x,7,14/3*cos(x^(1/3))-2*x^(2/3)*cos(x^(1/3))-2/9*cos(x^(1/3))^3+4*x^(1/3)*sin(x^(1/3))-x^(2/3)*cos(x^(1/3))*sin(x^(1/3))^2+2/3*x^(1/3)*sin(x^(1/3))^3],

# Integrands of the form (e x)^m (a+b Sin[c+d x^n])^p
[(e*x)^m*(b*sin(c+d*x^n))^p,x,0,Unintegrable((e*x)^m*(b*sin(c+d*x^n))^p,x)],
[(e*x)^m*(a+b*sin(c+d*x^n))^p,x,0,Unintegrable((e*x)^m*(a+b*sin(c+d*x^n))^p,x)],
[(e*x)^(-1+n)*(b*sin(c+d*x^n))^p,x,3,(e*x)^n*cos(c+d*x^n)*hypergeom([1/2,1/2*(1+p)],[1/2*(3+p)],sin(c+d*x^n)^2)*(b*sin(c+d*x^n))^(1+p)/(b*d*e*n*(1+p)*x^n*sqrt(cos(c+d*x^n)^2))],
[(e*x)^(-1+2*n)*(b*sin(c+d*x^n))^p,x,1,(e*x)^(2*n)*Unintegrable(x^(-1+2*n)*(b*sin(c+d*x^n))^p,x)/(e*x^(2*n))],
[(e*x)^(-1+n)*(a+b*sin(c+d*x^n))^p,x,5,-(e*x)^n*AppellF1(1/2,1/2,-p,3/2,1/2*(1-sin(c+d*x^n)),b*(1-sin(c+d*x^n))/(a+b))*cos(c+d*x^n)*(a+b*sin(c+d*x^n))^p*sqrt(2)/(d*e*n*x^n*((a+b*sin(c+d*x^n))/(a+b))^p*sqrt(1+sin(c+d*x^n)))],
[(e*x)^(-1+2*n)*(a+b*sin(c+d*x^n))^p,x,1,(e*x)^(2*n)*Unintegrable(x^(-1+2*n)*(a+b*sin(c+d*x^n))^p,x)/(e*x^(2*n))],
[sin(a+b*x^n)/x,x,3,cos(a)*Si(b*x^n)/n+Ci(b*x^n)*sin(a)/n],
[sin(a+b*x^n)^2/x,x,5,-1/2*Ci(2*b*x^n)*cos(2*a)/n+1/2*log(x)+1/2*Si(2*b*x^n)*sin(2*a)/n],
[sin(a+b*x^n)^3/x,x,8,3/4*cos(a)*Si(b*x^n)/n-1/4*cos(3*a)*Si(3*b*x^n)/n+3/4*Ci(b*x^n)*sin(a)/n-1/4*Ci(3*b*x^n)*sin(3*a)/n],
[sin(a+b*x^n)^4/x,x,8,-1/2*Ci(2*b*x^n)*cos(2*a)/n+1/8*Ci(4*b*x^n)*cos(4*a)/n+3/8*log(x)+1/2*Si(2*b*x^n)*sin(2*a)/n-1/8*Si(4*b*x^n)*sin(4*a)/n],
[sin(a+b*x^n),x,3,1/2*I*exp(I*a)*x*GAMMA(1/n,-I*b*x^n)/(n*(-I*b*x^n)^(1/n))-1/2*I*x*GAMMA(1/n,I*b*x^n)/(exp(I*a)*n*(I*b*x^n)^(1/n))],
[sin(a+b*x^n)^2,x,5,1/2*x+2^(-2+(-1)/n)*exp(2*I*a)*x*GAMMA(1/n,-2*I*b*x^n)/(n*(-I*b*x^n)^(1/n))+2^(-2+(-1)/n)*x*GAMMA(1/n,2*I*b*x^n)/(exp(2*I*a)*n*(I*b*x^n)^(1/n))],
[sin(a+b*x^n)^3,x,8,3/8*I*exp(I*a)*x*GAMMA(1/n,-I*b*x^n)/(n*(-I*b*x^n)^(1/n))-3/8*I*x*GAMMA(1/n,I*b*x^n)/(exp(I*a)*n*(I*b*x^n)^(1/n))-1/8*I*exp(3*I*a)*x*GAMMA(1/n,-3*I*b*x^n)/(3^(1/n)*n*(-I*b*x^n)^(1/n))+1/8*I*x*GAMMA(1/n,3*I*b*x^n)/(3^(1/n)*exp(3*I*a)*n*(I*b*x^n)^(1/n))],
[x^m*sin(a+b*x^n),x,3,1/2*I*exp(I*a)*x^(1+m)*GAMMA((1+m)/n,-I*b*x^n)/(n*(-I*b*x^n)^((1+m)/n))-1/2*I*x^(1+m)*GAMMA((1+m)/n,I*b*x^n)/(exp(I*a)*n*(I*b*x^n)^((1+m)/n))],
[x^m*sin(a+b*x^n)^2,x,5,1/2*x^(1+m)/(1+m)+exp(2*I*a)*x^(1+m)*GAMMA((1+m)/n,-2*I*b*x^n)/(2^((1+m+2*n)/n)*n*(-I*b*x^n)^((1+m)/n))+x^(1+m)*GAMMA((1+m)/n,2*I*b*x^n)/(2^((1+m+2*n)/n)*exp(2*I*a)*n*(I*b*x^n)^((1+m)/n))],
[x^m*sin(a+b*x^n)^3,x,8,3/8*I*exp(I*a)*x^(1+m)*GAMMA((1+m)/n,-I*b*x^n)/(n*(-I*b*x^n)^((1+m)/n))-3/8*I*x^(1+m)*GAMMA((1+m)/n,I*b*x^n)/(exp(I*a)*n*(I*b*x^n)^((1+m)/n))-1/8*I*exp(3*I*a)*x^(1+m)*GAMMA((1+m)/n,-3*I*b*x^n)/(3^((1+m)/n)*n*(-I*b*x^n)^((1+m)/n))+1/8*I*x^(1+m)*GAMMA((1+m)/n,3*I*b*x^n)/(3^((1+m)/n)*exp(3*I*a)*n*(I*b*x^n)^((1+m)/n))],
[x^(-1+2*n)*sin(a+b*x^n),x,3,-x^n*cos(a+b*x^n)/(b*n)+sin(a+b*x^n)/(b^2*n)],
[x^(-1+2*n)*cos(a+b*x^n),x,3,cos(a+b*x^n)/(b^2*n)+x^n*sin(a+b*x^n)/(b*n)],
[x^(-1-n)*sin(a+b*x^n),x,5,b*Ci(b*x^n)*cos(a)/n-b*Si(b*x^n)*sin(a)/n-sin(a+b*x^n)/(n*x^n)],
[x^(-1-n)*sin(a+b*x^n)^2,x,7,(-1/2)/(n*x^n)+1/2*cos(2*(a+b*x^n))/(n*x^n)+b*cos(2*a)*Si(2*b*x^n)/n+b*Ci(2*b*x^n)*sin(2*a)/n],
[x^(-1-n)*sin(a+b*x^n)^3,x,12,3/4*b*Ci(b*x^n)*cos(a)/n-3/4*b*Ci(3*b*x^n)*cos(3*a)/n-3/4*b*Si(b*x^n)*sin(a)/n+3/4*b*Si(3*b*x^n)*sin(3*a)/n-3/4*sin(a+b*x^n)/(n*x^n)+1/4*sin(3*(a+b*x^n))/(n*x^n)],
[x^(-1-2*n)*sin(a+b*x^n),x,6,-1/2*b*cos(a+b*x^n)/(n*x^n)-1/2*b^2*cos(a)*Si(b*x^n)/n-1/2*b^2*Ci(b*x^n)*sin(a)/n-1/2*sin(a+b*x^n)/(n*x^(2*n))],
[x^(-1-2*n)*sin(a+b*x^n)^2,x,8,(-1/4)/(n*x^(2*n))+b^2*Ci(2*b*x^n)*cos(2*a)/n+1/4*cos(2*(a+b*x^n))/(n*x^(2*n))-b^2*Si(2*b*x^n)*sin(2*a)/n-1/2*b*sin(2*(a+b*x^n))/(n*x^n)],
[x^(-1-2*n)*sin(a+b*x^n)^3,x,14,-3/8*b*cos(a+b*x^n)/(n*x^n)+3/8*b*cos(3*(a+b*x^n))/(n*x^n)-3/8*b^2*cos(a)*Si(b*x^n)/n+9/8*b^2*cos(3*a)*Si(3*b*x^n)/n-3/8*b^2*Ci(b*x^n)*sin(a)/n+9/8*b^2*Ci(3*b*x^n)*sin(3*a)/n-3/8*sin(a+b*x^n)/(n*x^(2*n))+1/8*sin(3*(a+b*x^n))/(n*x^(2*n))],

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

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

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

# n>0
[(e+f*x)^3*sin(b*(c+d*x)^2),x,10,-3/2*f*(d*e-c*f)^2*cos(b*(c+d*x)^2)/(b*d^4)-3/2*f^2*(d*e-c*f)*(c+d*x)*cos(b*(c+d*x)^2)/(b*d^4)-1/2*f^3*(c+d*x)^2*cos(b*(c+d*x)^2)/(b*d^4)+1/2*f^3*sin(b*(c+d*x)^2)/(b^2*d^4)+3/2*f^2*(d*e-c*f)*FresnelC((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(b^(3/2)*d^4)+(d*e-c*f)^3*FresnelS((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(d^4*sqrt(b))],
[(e+f*x)^2*sin(b*(c+d*x)^2),x,7,-f*(d*e-c*f)*cos(b*(c+d*x)^2)/(b*d^3)-1/2*f^2*(c+d*x)*cos(b*(c+d*x)^2)/(b*d^3)+1/2*f^2*FresnelC((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(b^(3/2)*d^3)+(d*e-c*f)^2*FresnelS((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(d^3*sqrt(b))],
[(e+f*x)*sin(b*(c+d*x)^2),x,5,-1/2*f*cos(b*(c+d*x)^2)/(b*d^2)+(d*e-c*f)*FresnelS((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(d^2*sqrt(b))],
[sin(b*(c+d*x)^2),x,1,FresnelS((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(d*sqrt(b))],
[sin(b*(c+d*x)^2)/(e+f*x),x,0,Unintegrable(sin(b*(c+d*x)^2)/(e+f*x),x)],
[sin(b*(c+d*x)^2)/(e+f*x)^2,x,0,Unintegrable(sin(b*(c+d*x)^2)/(e+f*x)^2,x)],

# n<0
[(e+f*x)^3*sin(b/(c+d*x)^2),x,16,-3/2*b*f*(d*e-c*f)^2*Ci(b/(c+d*x)^2)/d^4+2*b*f^2*(d*e-c*f)*(c+d*x)*cos(b/(c+d*x)^2)/d^4+1/4*b*f^3*(c+d*x)^2*cos(b/(c+d*x)^2)/d^4+1/4*b^2*f^3*Si(b/(c+d*x)^2)/d^4+(d*e-c*f)^3*(c+d*x)*sin(b/(c+d*x)^2)/d^4+3/2*f*(d*e-c*f)^2*(c+d*x)^2*sin(b/(c+d*x)^2)/d^4+f^2*(d*e-c*f)*(c+d*x)^3*sin(b/(c+d*x)^2)/d^4+1/4*f^3*(c+d*x)^4*sin(b/(c+d*x)^2)/d^4+2*b^(3/2)*f^2*(d*e-c*f)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sqrt(2*Pi)/d^4-(d*e-c*f)^3*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sqrt(b)*sqrt(2*Pi)/d^4],
[(e+f*x)^2*sin(b/(c+d*x)^2),x,12,-b*f*(d*e-c*f)*Ci(b/(c+d*x)^2)/d^3+2/3*b*f^2*(c+d*x)*cos(b/(c+d*x)^2)/d^3+(d*e-c*f)^2*(c+d*x)*sin(b/(c+d*x)^2)/d^3+f*(d*e-c*f)*(c+d*x)^2*sin(b/(c+d*x)^2)/d^3+1/3*f^2*(c+d*x)^3*sin(b/(c+d*x)^2)/d^3+2/3*b^(3/2)*f^2*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sqrt(2*Pi)/d^3-(d*e-c*f)^2*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sqrt(b)*sqrt(2*Pi)/d^3],
[(e+f*x)*sin(b/(c+d*x)^2),x,8,-1/2*b*f*Ci(b/(c+d*x)^2)/d^2+(d*e-c*f)*(c+d*x)*sin(b/(c+d*x)^2)/d^2+1/2*f*(c+d*x)^2*sin(b/(c+d*x)^2)/d^2-(d*e-c*f)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sqrt(b)*sqrt(2*Pi)/d^2],
[sin(b/(c+d*x)^2),x,3,(c+d*x)*sin(b/(c+d*x)^2)/d-FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sqrt(b)*sqrt(2*Pi)/d],
[sin(b/(c+d*x)^2)/(e+f*x),x,0,Unintegrable(sin(b/(c+d*x)^2)/(e+f*x),x)],
[sin(b/(c+d*x)^2)/(e+f*x)^2,x,0,Unintegrable(sin(b/(c+d*x)^2)/(e+f*x)^2,x)],

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

# n>0
[(e+f*x)^3*sin(a+b*(c+d*x)^2),x,14,-3/2*f*(d*e-c*f)^2*cos(a+b*(c+d*x)^2)/(b*d^4)-3/2*f^2*(d*e-c*f)*(c+d*x)*cos(a+b*(c+d*x)^2)/(b*d^4)-1/2*f^3*(c+d*x)^2*cos(a+b*(c+d*x)^2)/(b*d^4)+1/2*f^3*sin(a+b*(c+d*x)^2)/(b^2*d^4)+3/2*f^2*(d*e-c*f)*cos(a)*FresnelC((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(b^(3/2)*d^4)-3/2*f^2*(d*e-c*f)*FresnelS((c+d*x)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(b^(3/2)*d^4)+(d*e-c*f)^3*cos(a)*FresnelS((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(d^4*sqrt(b))+(d*e-c*f)^3*FresnelC((c+d*x)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(d^4*sqrt(b))],
[(e+f*x)^2*sin(a+b*(c+d*x)^2),x,11,-f*(d*e-c*f)*cos(a+b*(c+d*x)^2)/(b*d^3)-1/2*f^2*(c+d*x)*cos(a+b*(c+d*x)^2)/(b*d^3)+1/2*f^2*cos(a)*FresnelC((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(b^(3/2)*d^3)-1/2*f^2*FresnelS((c+d*x)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(b^(3/2)*d^3)+(d*e-c*f)^2*cos(a)*FresnelS((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(d^3*sqrt(b))+(d*e-c*f)^2*FresnelC((c+d*x)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(d^3*sqrt(b))],
[(e+f*x)*sin(a+b*(c+d*x)^2),x,7,-1/2*f*cos(a+b*(c+d*x)^2)/(b*d^2)+(d*e-c*f)*cos(a)*FresnelS((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(d^2*sqrt(b))+(d*e-c*f)*FresnelC((c+d*x)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(d^2*sqrt(b))],
[sin(a+b*(c+d*x)^2),x,3,cos(a)*FresnelS((c+d*x)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(d*sqrt(b))+FresnelC((c+d*x)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(d*sqrt(b))],
[sin(a+b*(c+d*x)^2)/(e+f*x),x,0,Unintegrable(sin(a+b*(c+d*x)^2)/(e+f*x),x)],
[sin(a+b*(c+d*x)^2)/(e+f*x)^2,x,0,Unintegrable(sin(a+b*(c+d*x)^2)/(e+f*x)^2,x)],
[(e+f*x)^3*sin(a+b*(c+d*x)^3),x,14,-f^2*(d*e-c*f)*cos(a+b*(c+d*x)^3)/(b*d^4)-1/3*f^3*(c+d*x)*cos(a+b*(c+d*x)^3)/(b*d^4)-1/18*exp(I*a)*f^3*(c+d*x)*GAMMA(1/3,-I*b*(c+d*x)^3)/(b*d^4*(-I*b*(c+d*x)^3)^(1/3))+1/6*I*exp(I*a)*(d*e-c*f)^3*(c+d*x)*GAMMA(1/3,-I*b*(c+d*x)^3)/(d^4*(-I*b*(c+d*x)^3)^(1/3))-1/18*f^3*(c+d*x)*GAMMA(1/3,I*b*(c+d*x)^3)/(b*d^4*exp(I*a)*(I*b*(c+d*x)^3)^(1/3))-1/6*I*(d*e-c*f)^3*(c+d*x)*GAMMA(1/3,I*b*(c+d*x)^3)/(d^4*exp(I*a)*(I*b*(c+d*x)^3)^(1/3))+1/2*I*exp(I*a)*f*(d*e-c*f)^2*(c+d*x)^2*GAMMA(2/3,-I*b*(c+d*x)^3)/(d^4*(-I*b*(c+d*x)^3)^(2/3))-1/2*I*f*(d*e-c*f)^2*(c+d*x)^2*GAMMA(2/3,I*b*(c+d*x)^3)/(d^4*exp(I*a)*(I*b*(c+d*x)^3)^(2/3))],
[(e+f*x)^2*sin(a+b*(c+d*x)^3),x,10,-1/3*f^2*cos(a+b*(c+d*x)^3)/(b*d^3)+1/6*I*exp(I*a)*(d*e-c*f)^2*(c+d*x)*GAMMA(1/3,-I*b*(c+d*x)^3)/(d^3*(-I*b*(c+d*x)^3)^(1/3))-1/6*I*(d*e-c*f)^2*(c+d*x)*GAMMA(1/3,I*b*(c+d*x)^3)/(d^3*exp(I*a)*(I*b*(c+d*x)^3)^(1/3))+1/3*I*exp(I*a)*f*(d*e-c*f)*(c+d*x)^2*GAMMA(2/3,-I*b*(c+d*x)^3)/(d^3*(-I*b*(c+d*x)^3)^(2/3))-1/3*I*f*(d*e-c*f)*(c+d*x)^2*GAMMA(2/3,I*b*(c+d*x)^3)/(d^3*exp(I*a)*(I*b*(c+d*x)^3)^(2/3))],
[(e+f*x)*sin(a+b*(c+d*x)^3),x,8,1/6*I*exp(I*a)*(d*e-c*f)*(c+d*x)*GAMMA(1/3,-I*b*(c+d*x)^3)/(d^2*(-I*b*(c+d*x)^3)^(1/3))-1/6*I*(d*e-c*f)*(c+d*x)*GAMMA(1/3,I*b*(c+d*x)^3)/(d^2*exp(I*a)*(I*b*(c+d*x)^3)^(1/3))+1/6*I*exp(I*a)*f*(c+d*x)^2*GAMMA(2/3,-I*b*(c+d*x)^3)/(d^2*(-I*b*(c+d*x)^3)^(2/3))-1/6*I*f*(c+d*x)^2*GAMMA(2/3,I*b*(c+d*x)^3)/(d^2*exp(I*a)*(I*b*(c+d*x)^3)^(2/3))],
[sin(a+b*(c+d*x)^3),x,3,1/6*I*exp(I*a)*(c+d*x)*GAMMA(1/3,-I*b*(c+d*x)^3)/(d*(-I*b*(c+d*x)^3)^(1/3))-1/6*I*(c+d*x)*GAMMA(1/3,I*b*(c+d*x)^3)/(d*exp(I*a)*(I*b*(c+d*x)^3)^(1/3))],
[sin(a+b*(c+d*x)^3)/(e+f*x),x,0,Unintegrable(sin(a+b*(c+d*x)^3)/(e+f*x),x)],
[sin(a+b*(c+d*x)^3)/(e+f*x)^2,x,0,Unintegrable(sin(a+b*(c+d*x)^3)/(e+f*x)^2,x)],

# n<0
[(e+f*x)^2*sin(a+b/(c+d*x)^2),x,18,-b*f*(d*e-c*f)*Ci(b/(c+d*x)^2)*cos(a)/d^3+2/3*b*f^2*(c+d*x)*cos(a+b/(c+d*x)^2)/d^3+b*f*(d*e-c*f)*Si(b/(c+d*x)^2)*sin(a)/d^3+(d*e-c*f)^2*(c+d*x)*sin(a+b/(c+d*x)^2)/d^3+f*(d*e-c*f)*(c+d*x)^2*sin(a+b/(c+d*x)^2)/d^3+1/3*f^2*(c+d*x)^3*sin(a+b/(c+d*x)^2)/d^3+2/3*b^(3/2)*f^2*cos(a)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sqrt(2*Pi)/d^3+2/3*b^(3/2)*f^2*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sin(a)*sqrt(2*Pi)/d^3-(d*e-c*f)^2*cos(a)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sqrt(b)*sqrt(2*Pi)/d^3+(d*e-c*f)^2*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sin(a)*sqrt(b)*sqrt(2*Pi)/d^3],
[(e+f*x)*sin(a+b/(c+d*x)^2),x,12,-1/2*b*f*Ci(b/(c+d*x)^2)*cos(a)/d^2+1/2*b*f*Si(b/(c+d*x)^2)*sin(a)/d^2+(d*e-c*f)*(c+d*x)*sin(a+b/(c+d*x)^2)/d^2+1/2*f*(c+d*x)^2*sin(a+b/(c+d*x)^2)/d^2-(d*e-c*f)*cos(a)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sqrt(b)*sqrt(2*Pi)/d^2+(d*e-c*f)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sin(a)*sqrt(b)*sqrt(2*Pi)/d^2],
[sin(a+b/(c+d*x)^2),x,5,(c+d*x)*sin(a+b/(c+d*x)^2)/d-cos(a)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sqrt(b)*sqrt(2*Pi)/d+FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x))*sin(a)*sqrt(b)*sqrt(2*Pi)/d],
[sin(a+b/(c+d*x)^2)/(e+f*x),x,0,Unintegrable(sin(a+b/(c+d*x)^2)/(e+f*x),x)],
[sin(a+b/(c+d*x)^2)/(e+f*x)^2,x,0,Unintegrable(sin(a+b/(c+d*x)^2)/(e+f*x)^2,x)],
[(e+f*x)^2*sin(a+b/(c+d*x)^3),x,13,-1/3*b*f^2*Ci(b/(c+d*x)^3)*cos(a)/d^3-1/3*I*exp(I*a)*f*(d*e-c*f)*(-I*b/(c+d*x)^3)^(2/3)*(c+d*x)^2*GAMMA(-2/3,-I*b/(c+d*x)^3)/d^3+1/3*I*f*(d*e-c*f)*(I*b/(c+d*x)^3)^(2/3)*(c+d*x)^2*GAMMA(-2/3,I*b/(c+d*x)^3)/(d^3*exp(I*a))-1/6*I*exp(I*a)*(d*e-c*f)^2*(-I*b/(c+d*x)^3)^(1/3)*(c+d*x)*GAMMA(-1/3,-I*b/(c+d*x)^3)/d^3+1/6*I*(d*e-c*f)^2*(I*b/(c+d*x)^3)^(1/3)*(c+d*x)*GAMMA(-1/3,I*b/(c+d*x)^3)/(d^3*exp(I*a))+1/3*b*f^2*Si(b/(c+d*x)^3)*sin(a)/d^3+1/3*f^2*(c+d*x)^3*sin(a+b/(c+d*x)^3)/d^3],
[(e+f*x)*sin(a+b/(c+d*x)^3),x,8,-1/6*I*exp(I*a)*f*(-I*b/(c+d*x)^3)^(2/3)*(c+d*x)^2*GAMMA(-2/3,-I*b/(c+d*x)^3)/d^2+1/6*I*f*(I*b/(c+d*x)^3)^(2/3)*(c+d*x)^2*GAMMA(-2/3,I*b/(c+d*x)^3)/(d^2*exp(I*a))-1/6*I*exp(I*a)*(d*e-c*f)*(-I*b/(c+d*x)^3)^(1/3)*(c+d*x)*GAMMA(-1/3,-I*b/(c+d*x)^3)/d^2+1/6*I*(d*e-c*f)*(I*b/(c+d*x)^3)^(1/3)*(c+d*x)*GAMMA(-1/3,I*b/(c+d*x)^3)/(d^2*exp(I*a))],
[sin(a+b/(c+d*x)^3),x,3,-1/6*I*exp(I*a)*(-I*b/(c+d*x)^3)^(1/3)*(c+d*x)*GAMMA(-1/3,-I*b/(c+d*x)^3)/d+1/6*I*(I*b/(c+d*x)^3)^(1/3)*(c+d*x)*GAMMA(-1/3,I*b/(c+d*x)^3)/(d*exp(I*a))],
[sin(a+b/(c+d*x)^3)/(e+f*x),x,0,Unintegrable(sin(a+b/(c+d*x)^3)/(e+f*x),x)],
[sin(a+b/(c+d*x)^3)/(e+f*x)^2,x,0,Unintegrable(sin(a+b/(c+d*x)^3)/(e+f*x)^2,x)],

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

# n>0
[(e+f*x)^2*sin(a+b*sqrt(c+d*x)),x,14,40*f^2*(c+d*x)^(3/2)*cos(a+b*sqrt(c+d*x))/(b^3*d^3)-4*f*(d*e-c*f)*(c+d*x)^(3/2)*cos(a+b*sqrt(c+d*x))/(b*d^3)-2*f^2*(c+d*x)^(5/2)*cos(a+b*sqrt(c+d*x))/(b*d^3)+240*f^2*sin(a+b*sqrt(c+d*x))/(b^6*d^3)-24*f*(d*e-c*f)*sin(a+b*sqrt(c+d*x))/(b^4*d^3)+2*(d*e-c*f)^2*sin(a+b*sqrt(c+d*x))/(b^2*d^3)-120*f^2*(c+d*x)*sin(a+b*sqrt(c+d*x))/(b^4*d^3)+12*f*(d*e-c*f)*(c+d*x)*sin(a+b*sqrt(c+d*x))/(b^2*d^3)+10*f^2*(c+d*x)^2*sin(a+b*sqrt(c+d*x))/(b^2*d^3)-240*f^2*cos(a+b*sqrt(c+d*x))*sqrt(c+d*x)/(b^5*d^3)+24*f*(d*e-c*f)*cos(a+b*sqrt(c+d*x))*sqrt(c+d*x)/(b^3*d^3)-2*(d*e-c*f)^2*cos(a+b*sqrt(c+d*x))*sqrt(c+d*x)/(b*d^3)],
[(e+f*x)*sin(a+b*sqrt(c+d*x)),x,8,-2*f*(c+d*x)^(3/2)*cos(a+b*sqrt(c+d*x))/(b*d^2)-12*f*sin(a+b*sqrt(c+d*x))/(b^4*d^2)+2*(d*e-c*f)*sin(a+b*sqrt(c+d*x))/(b^2*d^2)+6*f*(c+d*x)*sin(a+b*sqrt(c+d*x))/(b^2*d^2)+12*f*cos(a+b*sqrt(c+d*x))*sqrt(c+d*x)/(b^3*d^2)-2*(d*e-c*f)*cos(a+b*sqrt(c+d*x))*sqrt(c+d*x)/(b*d^2)],
[sin(a+b*sqrt(c+d*x)),x,3,2*sin(a+b*sqrt(c+d*x))/(b^2*d)-2*cos(a+b*sqrt(c+d*x))*sqrt(c+d*x)/(b*d)],
[sin(a+b*sqrt(c+d*x))/(e+f*x),x,8,-cos(a+b*sqrt(-d*e+c*f)/sqrt(f))*Si(b*sqrt(-d*e+c*f)/sqrt(f)-b*sqrt(c+d*x))/f+cos(a-b*sqrt(-d*e+c*f)/sqrt(f))*Si(b*sqrt(-d*e+c*f)/sqrt(f)+b*sqrt(c+d*x))/f+Ci(b*sqrt(-d*e+c*f)/sqrt(f)+b*sqrt(c+d*x))*sin(a-b*sqrt(-d*e+c*f)/sqrt(f))/f+Ci(b*sqrt(-d*e+c*f)/sqrt(f)-b*sqrt(c+d*x))*sin(a+b*sqrt(-d*e+c*f)/sqrt(f))/f],
[sin(a+b*sqrt(c+d*x))/(e+f*x)^2,x,10,-sin(a+b*sqrt(c+d*x))/(f*(e+f*x))-1/2*b*d*Ci(b*sqrt(-d*e+c*f)/sqrt(f)+b*sqrt(c+d*x))*cos(a-b*sqrt(-d*e+c*f)/sqrt(f))/(f^(3/2)*sqrt(-d*e+c*f))+1/2*b*d*Ci(b*sqrt(-d*e+c*f)/sqrt(f)-b*sqrt(c+d*x))*cos(a+b*sqrt(-d*e+c*f)/sqrt(f))/(f^(3/2)*sqrt(-d*e+c*f))+1/2*b*d*Si(b*sqrt(-d*e+c*f)/sqrt(f)+b*sqrt(c+d*x))*sin(a-b*sqrt(-d*e+c*f)/sqrt(f))/(f^(3/2)*sqrt(-d*e+c*f))+1/2*b*d*Si(b*sqrt(-d*e+c*f)/sqrt(f)-b*sqrt(c+d*x))*sin(a+b*sqrt(-d*e+c*f)/sqrt(f))/(f^(3/2)*sqrt(-d*e+c*f))],
[(e+f*x)^2*sin(a+b*(c+d*x)^(3/2)),x,12,-2/3*f^2*(c+d*x)^(3/2)*cos(a+b*(c+d*x)^(3/2))/(b*d^3)+1/3*I*exp(I*a)*(d*e-c*f)^2*(c+d*x)*GAMMA(2/3,-I*b*(c+d*x)^(3/2))/(d^3*(-I*b*(c+d*x)^(3/2))^(2/3))-1/3*I*(d*e-c*f)^2*(c+d*x)*GAMMA(2/3,I*b*(c+d*x)^(3/2))/(d^3*exp(I*a)*(I*b*(c+d*x)^(3/2))^(2/3))+2/3*f^2*sin(a+b*(c+d*x)^(3/2))/(b^2*d^3)-4/3*f*(d*e-c*f)*cos(a+b*(c+d*x)^(3/2))*sqrt(c+d*x)/(b*d^3)-2/9*exp(I*a)*f*(d*e-c*f)*GAMMA(1/3,-I*b*(c+d*x)^(3/2))*sqrt(c+d*x)/(b*d^3*(-I*b*(c+d*x)^(3/2))^(1/3))-2/9*f*(d*e-c*f)*GAMMA(1/3,I*b*(c+d*x)^(3/2))*sqrt(c+d*x)/(b*d^3*exp(I*a)*(I*b*(c+d*x)^(3/2))^(1/3))],
[(e+f*x)*sin(a+b*(c+d*x)^(3/2)),x,9,1/3*I*exp(I*a)*(d*e-c*f)*(c+d*x)*GAMMA(2/3,-I*b*(c+d*x)^(3/2))/(d^2*(-I*b*(c+d*x)^(3/2))^(2/3))-1/3*I*(d*e-c*f)*(c+d*x)*GAMMA(2/3,I*b*(c+d*x)^(3/2))/(d^2*exp(I*a)*(I*b*(c+d*x)^(3/2))^(2/3))-2/3*f*cos(a+b*(c+d*x)^(3/2))*sqrt(c+d*x)/(b*d^2)-1/9*exp(I*a)*f*GAMMA(1/3,-I*b*(c+d*x)^(3/2))*sqrt(c+d*x)/(b*d^2*(-I*b*(c+d*x)^(3/2))^(1/3))-1/9*f*GAMMA(1/3,I*b*(c+d*x)^(3/2))*sqrt(c+d*x)/(b*d^2*exp(I*a)*(I*b*(c+d*x)^(3/2))^(1/3))],
[sin(a+b*(c+d*x)^(3/2)),x,4,1/3*I*exp(I*a)*(c+d*x)*GAMMA(2/3,-I*b*(c+d*x)^(3/2))/(d*(-I*b*(c+d*x)^(3/2))^(2/3))-1/3*I*(c+d*x)*GAMMA(2/3,I*b*(c+d*x)^(3/2))/(d*exp(I*a)*(I*b*(c+d*x)^(3/2))^(2/3))],
[sin(a+b*(c+d*x)^(3/2))/(e+f*x),x,0,Unintegrable(sin(a+b*(c+d*x)^(3/2))/(e+f*x),x)],
[sin(a+b*(c+d*x)^(3/2))/(e+f*x)^2,x,0,Unintegrable(sin(a+b*(c+d*x)^(3/2))/(e+f*x)^2,x)],

# n<0
[(e+f*x)^2*sin(a+b/sqrt(c+d*x)),x,23,-1/180*b^3*f^2*(c+d*x)^(3/2)*cos(a+b/sqrt(c+d*x))/d^3+1/3*b*f*(d*e-c*f)*(c+d*x)^(3/2)*cos(a+b/sqrt(c+d*x))/d^3+1/15*b*f^2*(c+d*x)^(5/2)*cos(a+b/sqrt(c+d*x))/d^3+1/360*b^6*f^2*cos(a)*Si(b/sqrt(c+d*x))/d^3-1/6*b^4*f*(d*e-c*f)*cos(a)*Si(b/sqrt(c+d*x))/d^3+b^2*(d*e-c*f)^2*cos(a)*Si(b/sqrt(c+d*x))/d^3+1/360*b^6*f^2*Ci(b/sqrt(c+d*x))*sin(a)/d^3-1/6*b^4*f*(d*e-c*f)*Ci(b/sqrt(c+d*x))*sin(a)/d^3+b^2*(d*e-c*f)^2*Ci(b/sqrt(c+d*x))*sin(a)/d^3+1/360*b^4*f^2*(c+d*x)*sin(a+b/sqrt(c+d*x))/d^3-1/6*b^2*f*(d*e-c*f)*(c+d*x)*sin(a+b/sqrt(c+d*x))/d^3+(d*e-c*f)^2*(c+d*x)*sin(a+b/sqrt(c+d*x))/d^3-1/60*b^2*f^2*(c+d*x)^2*sin(a+b/sqrt(c+d*x))/d^3+f*(d*e-c*f)*(c+d*x)^2*sin(a+b/sqrt(c+d*x))/d^3+1/3*f^2*(c+d*x)^3*sin(a+b/sqrt(c+d*x))/d^3+1/360*b^5*f^2*cos(a+b/sqrt(c+d*x))*sqrt(c+d*x)/d^3-1/6*b^3*f*(d*e-c*f)*cos(a+b/sqrt(c+d*x))*sqrt(c+d*x)/d^3+b*(d*e-c*f)^2*cos(a+b/sqrt(c+d*x))*sqrt(c+d*x)/d^3],
[(e+f*x)*sin(a+b/sqrt(c+d*x)),x,14,1/6*b*f*(c+d*x)^(3/2)*cos(a+b/sqrt(c+d*x))/d^2-1/12*b^4*f*cos(a)*Si(b/sqrt(c+d*x))/d^2+b^2*(d*e-c*f)*cos(a)*Si(b/sqrt(c+d*x))/d^2-1/12*b^4*f*Ci(b/sqrt(c+d*x))*sin(a)/d^2+b^2*(d*e-c*f)*Ci(b/sqrt(c+d*x))*sin(a)/d^2-1/12*b^2*f*(c+d*x)*sin(a+b/sqrt(c+d*x))/d^2+(d*e-c*f)*(c+d*x)*sin(a+b/sqrt(c+d*x))/d^2+1/2*f*(c+d*x)^2*sin(a+b/sqrt(c+d*x))/d^2-1/12*b^3*f*cos(a+b/sqrt(c+d*x))*sqrt(c+d*x)/d^2+b*(d*e-c*f)*cos(a+b/sqrt(c+d*x))*sqrt(c+d*x)/d^2],
[sin(a+b/sqrt(c+d*x)),x,6,b^2*cos(a)*Si(b/sqrt(c+d*x))/d+b^2*Ci(b/sqrt(c+d*x))*sin(a)/d+(c+d*x)*sin(a+b/sqrt(c+d*x))/d+b*cos(a+b/sqrt(c+d*x))*sqrt(c+d*x)/d],
[sin(a+b/sqrt(c+d*x))/(e+f*x),x,13,-cos(a+b*sqrt(f)/sqrt(-d*e+c*f))*Si(b*sqrt(f)/sqrt(-d*e+c*f)-b/sqrt(c+d*x))/f+cos(a-b*sqrt(f)/sqrt(-d*e+c*f))*Si(b*sqrt(f)/sqrt(-d*e+c*f)+b/sqrt(c+d*x))/f-2*cos(a)*Si(b/sqrt(c+d*x))/f-2*Ci(b/sqrt(c+d*x))*sin(a)/f+Ci(b*sqrt(f)/sqrt(-d*e+c*f)+b/sqrt(c+d*x))*sin(a-b*sqrt(f)/sqrt(-d*e+c*f))/f+Ci(b*sqrt(f)/sqrt(-d*e+c*f)-b/sqrt(c+d*x))*sin(a+b*sqrt(f)/sqrt(-d*e+c*f))/f],
[sin(a+b/sqrt(c+d*x))/(e+f*x)^2,x,10,(c+d*x)*sin(a+b/sqrt(c+d*x))/((d*e-c*f)*(e+f*x))+1/2*b*d*Ci(b*sqrt(f)/sqrt(-d*e+c*f)+b/sqrt(c+d*x))*cos(a-b*sqrt(f)/sqrt(-d*e+c*f))/((-d*e+c*f)^(3/2)*sqrt(f))-1/2*b*d*Ci(b*sqrt(f)/sqrt(-d*e+c*f)-b/sqrt(c+d*x))*cos(a+b*sqrt(f)/sqrt(-d*e+c*f))/((-d*e+c*f)^(3/2)*sqrt(f))-1/2*b*d*Si(b*sqrt(f)/sqrt(-d*e+c*f)+b/sqrt(c+d*x))*sin(a-b*sqrt(f)/sqrt(-d*e+c*f))/((-d*e+c*f)^(3/2)*sqrt(f))-1/2*b*d*Si(b*sqrt(f)/sqrt(-d*e+c*f)-b/sqrt(c+d*x))*sin(a+b*sqrt(f)/sqrt(-d*e+c*f))/((-d*e+c*f)^(3/2)*sqrt(f))],
[(e+f*x)^2*sin(a+b/(c+d*x)^(3/2)),x,14,1/3*b*f^2*(c+d*x)^(3/2)*cos(a+b/(c+d*x)^(3/2))/d^3-2/3*I*exp(I*a)*f*(d*e-c*f)*(-I*b/(c+d*x)^(3/2))^(4/3)*(c+d*x)^2*GAMMA(-4/3,-I*b/(c+d*x)^(3/2))/d^3+2/3*I*f*(d*e-c*f)*(I*b/(c+d*x)^(3/2))^(4/3)*(c+d*x)^2*GAMMA(-4/3,I*b/(c+d*x)^(3/2))/(d^3*exp(I*a))-1/3*I*exp(I*a)*(d*e-c*f)^2*(-I*b/(c+d*x)^(3/2))^(2/3)*(c+d*x)*GAMMA(-2/3,-I*b/(c+d*x)^(3/2))/d^3+1/3*I*(d*e-c*f)^2*(I*b/(c+d*x)^(3/2))^(2/3)*(c+d*x)*GAMMA(-2/3,I*b/(c+d*x)^(3/2))/(d^3*exp(I*a))+1/3*b^2*f^2*cos(a)*Si(b/(c+d*x)^(3/2))/d^3+1/3*b^2*f^2*Ci(b/(c+d*x)^(3/2))*sin(a)/d^3+1/3*f^2*(c+d*x)^3*sin(a+b/(c+d*x)^(3/2))/d^3],
[(e+f*x)*sin(a+b/(c+d*x)^(3/2)),x,8,-1/3*I*exp(I*a)*f*(-I*b/(c+d*x)^(3/2))^(4/3)*(c+d*x)^2*GAMMA(-4/3,-I*b/(c+d*x)^(3/2))/d^2+1/3*I*f*(I*b/(c+d*x)^(3/2))^(4/3)*(c+d*x)^2*GAMMA(-4/3,I*b/(c+d*x)^(3/2))/(d^2*exp(I*a))-1/3*I*exp(I*a)*(d*e-c*f)*(-I*b/(c+d*x)^(3/2))^(2/3)*(c+d*x)*GAMMA(-2/3,-I*b/(c+d*x)^(3/2))/d^2+1/3*I*(d*e-c*f)*(I*b/(c+d*x)^(3/2))^(2/3)*(c+d*x)*GAMMA(-2/3,I*b/(c+d*x)^(3/2))/(d^2*exp(I*a))],
[sin(a+b/(c+d*x)^(3/2)),x,4,-1/3*I*exp(I*a)*(-I*b/(c+d*x)^(3/2))^(2/3)*(c+d*x)*GAMMA(-2/3,-I*b/(c+d*x)^(3/2))/d+1/3*I*(I*b/(c+d*x)^(3/2))^(2/3)*(c+d*x)*GAMMA(-2/3,I*b/(c+d*x)^(3/2))/(d*exp(I*a))],
[sin(a+b/(c+d*x)^(3/2))/(e+f*x),x,0,Unintegrable(sin(a+b/(c+d*x)^(3/2))/(e+f*x),x)],
[sin(a+b/(c+d*x)^(3/2))/(e+f*x)^2,x,0,Unintegrable(sin(a+b/(c+d*x)^(3/2))/(e+f*x)^2,x)],

# Integrands of the form (e+f x)^m Sin[a+b (c+d x)^(n/3)]

# n>0
[(e+f*x)^2*sin(a+b*(c+d*x)^(1/3)),x,20,-120960*f^2*cos(a+b*(c+d*x)^(1/3))/(b^9*d^3)+6*(d*e-c*f)^2*cos(a+b*(c+d*x)^(1/3))/(b^3*d^3)-720*f*(d*e-c*f)*(c+d*x)^(1/3)*cos(a+b*(c+d*x)^(1/3))/(b^5*d^3)+60480*f^2*(c+d*x)^(2/3)*cos(a+b*(c+d*x)^(1/3))/(b^7*d^3)-3*(d*e-c*f)^2*(c+d*x)^(2/3)*cos(a+b*(c+d*x)^(1/3))/(b*d^3)+120*f*(d*e-c*f)*(c+d*x)*cos(a+b*(c+d*x)^(1/3))/(b^3*d^3)-5040*f^2*(c+d*x)^(4/3)*cos(a+b*(c+d*x)^(1/3))/(b^5*d^3)-6*f*(d*e-c*f)*(c+d*x)^(5/3)*cos(a+b*(c+d*x)^(1/3))/(b*d^3)+168*f^2*(c+d*x)^2*cos(a+b*(c+d*x)^(1/3))/(b^3*d^3)-3*f^2*(c+d*x)^(8/3)*cos(a+b*(c+d*x)^(1/3))/(b*d^3)+720*f*(d*e-c*f)*sin(a+b*(c+d*x)^(1/3))/(b^6*d^3)-120960*f^2*(c+d*x)^(1/3)*sin(a+b*(c+d*x)^(1/3))/(b^8*d^3)+6*(d*e-c*f)^2*(c+d*x)^(1/3)*sin(a+b*(c+d*x)^(1/3))/(b^2*d^3)-360*f*(d*e-c*f)*(c+d*x)^(2/3)*sin(a+b*(c+d*x)^(1/3))/(b^4*d^3)+20160*f^2*(c+d*x)*sin(a+b*(c+d*x)^(1/3))/(b^6*d^3)+30*f*(d*e-c*f)*(c+d*x)^(4/3)*sin(a+b*(c+d*x)^(1/3))/(b^2*d^3)-1008*f^2*(c+d*x)^(5/3)*sin(a+b*(c+d*x)^(1/3))/(b^4*d^3)+24*f^2*(c+d*x)^(7/3)*sin(a+b*(c+d*x)^(1/3))/(b^2*d^3)],
[(e+f*x)*sin(a+b*(c+d*x)^(1/3)),x,11,6*(d*e-c*f)*cos(a+b*(c+d*x)^(1/3))/(b^3*d^2)-360*f*(c+d*x)^(1/3)*cos(a+b*(c+d*x)^(1/3))/(b^5*d^2)-3*(d*e-c*f)*(c+d*x)^(2/3)*cos(a+b*(c+d*x)^(1/3))/(b*d^2)+60*f*(c+d*x)*cos(a+b*(c+d*x)^(1/3))/(b^3*d^2)-3*f*(c+d*x)^(5/3)*cos(a+b*(c+d*x)^(1/3))/(b*d^2)+360*f*sin(a+b*(c+d*x)^(1/3))/(b^6*d^2)+6*(d*e-c*f)*(c+d*x)^(1/3)*sin(a+b*(c+d*x)^(1/3))/(b^2*d^2)-180*f*(c+d*x)^(2/3)*sin(a+b*(c+d*x)^(1/3))/(b^4*d^2)+15*f*(c+d*x)^(4/3)*sin(a+b*(c+d*x)^(1/3))/(b^2*d^2)],
[sin(a+b*(c+d*x)^(1/3)),x,4,6*cos(a+b*(c+d*x)^(1/3))/(b^3*d)-3*(c+d*x)^(2/3)*cos(a+b*(c+d*x)^(1/3))/(b*d)+6*(c+d*x)^(1/3)*sin(a+b*(c+d*x)^(1/3))/(b^2*d)],
[sin(a+b*(c+d*x)^(1/3))/(e+f*x),x,11,-cos(a+(-1)^(1/3)*b*(d*e-c*f)^(1/3)/f^(1/3))*Si((-1)^(1/3)*b*(d*e-c*f)^(1/3)/f^(1/3)-b*(c+d*x)^(1/3))/f+cos(a-b*(d*e-c*f)^(1/3)/f^(1/3))*Si(b*(d*e-c*f)^(1/3)/f^(1/3)+b*(c+d*x)^(1/3))/f+cos(a-(-1)^(2/3)*b*(d*e-c*f)^(1/3)/f^(1/3))*Si((-1)^(2/3)*b*(d*e-c*f)^(1/3)/f^(1/3)+b*(c+d*x)^(1/3))/f+Ci(b*(d*e-c*f)^(1/3)/f^(1/3)+b*(c+d*x)^(1/3))*sin(a-b*(d*e-c*f)^(1/3)/f^(1/3))/f+Ci((-1)^(1/3)*b*(d*e-c*f)^(1/3)/f^(1/3)-b*(c+d*x)^(1/3))*sin(a+(-1)^(1/3)*b*(d*e-c*f)^(1/3)/f^(1/3))/f+Ci((-1)^(2/3)*b*(d*e-c*f)^(1/3)/f^(1/3)+b*(c+d*x)^(1/3))*sin(a-(-1)^(2/3)*b*(d*e-c*f)^(1/3)/f^(1/3))/f],
[sin(a+b*(c+d*x)^(1/3))/(e+f*x)^2,x,13,1/3*b*d*Ci(b*(d*e-c*f)^(1/3)/f^(1/3)+b*(c+d*x)^(1/3))*cos(a-b*(d*e-c*f)^(1/3)/f^(1/3))/(f^(4/3)*(d*e-c*f)^(2/3))-1/3*(-1)^(1/3)*b*d*Ci((-1)^(1/3)*b*(d*e-c*f)^(1/3)/f^(1/3)-b*(c+d*x)^(1/3))*cos(a+(-1)^(1/3)*b*(d*e-c*f)^(1/3)/f^(1/3))/(f^(4/3)*(d*e-c*f)^(2/3))+1/3*(-1)^(2/3)*b*d*Ci((-1)^(2/3)*b*(d*e-c*f)^(1/3)/f^(1/3)+b*(c+d*x)^(1/3))*cos(a-(-1)^(2/3)*b*(d*e-c*f)^(1/3)/f^(1/3))/(f^(4/3)*(d*e-c*f)^(2/3))-1/3*b*d*Si(b*(d*e-c*f)^(1/3)/f^(1/3)+b*(c+d*x)^(1/3))*sin(a-b*(d*e-c*f)^(1/3)/f^(1/3))/(f^(4/3)*(d*e-c*f)^(2/3))-1/3*(-1)^(1/3)*b*d*Si((-1)^(1/3)*b*(d*e-c*f)^(1/3)/f^(1/3)-b*(c+d*x)^(1/3))*sin(a+(-1)^(1/3)*b*(d*e-c*f)^(1/3)/f^(1/3))/(f^(4/3)*(d*e-c*f)^(2/3))-1/3*(-1)^(2/3)*b*d*Si((-1)^(2/3)*b*(d*e-c*f)^(1/3)/f^(1/3)+b*(c+d*x)^(1/3))*sin(a-(-1)^(2/3)*b*(d*e-c*f)^(1/3)/f^(1/3))/(f^(4/3)*(d*e-c*f)^(2/3))-sin(a+b*(c+d*x)^(1/3))/(f*(e+f*x))],
[(e+f*x)^2*sin(a+b*(c+d*x)^(2/3)),x,17,6*f*(d*e-c*f)*cos(a+b*(c+d*x)^(2/3))/(b^3*d^3)-3/2*(d*e-c*f)^2*(c+d*x)^(1/3)*cos(a+b*(c+d*x)^(2/3))/(b*d^3)+105/8*f^2*(c+d*x)*cos(a+b*(c+d*x)^(2/3))/(b^3*d^3)-3*f*(d*e-c*f)*(c+d*x)^(4/3)*cos(a+b*(c+d*x)^(2/3))/(b*d^3)-3/2*f^2*(c+d*x)^(7/3)*cos(a+b*(c+d*x)^(2/3))/(b*d^3)-315/16*f^2*(c+d*x)^(1/3)*sin(a+b*(c+d*x)^(2/3))/(b^4*d^3)+6*f*(d*e-c*f)*(c+d*x)^(2/3)*sin(a+b*(c+d*x)^(2/3))/(b^2*d^3)+21/4*f^2*(c+d*x)^(5/3)*sin(a+b*(c+d*x)^(2/3))/(b^2*d^3)+3/2*(d*e-c*f)^2*cos(a)*FresnelC((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(b^(3/2)*d^3)+315/16*f^2*cos(a)*FresnelS((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(b^(9/2)*d^3)+315/16*f^2*FresnelC((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(b^(9/2)*d^3)-3/2*(d*e-c*f)^2*FresnelS((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(b^(3/2)*d^3)],
[(e+f*x)*sin(a+b*(c+d*x)^(2/3)),x,10,3*f*cos(a+b*(c+d*x)^(2/3))/(b^3*d^2)-3/2*(d*e-c*f)*(c+d*x)^(1/3)*cos(a+b*(c+d*x)^(2/3))/(b*d^2)-3/2*f*(c+d*x)^(4/3)*cos(a+b*(c+d*x)^(2/3))/(b*d^2)+3*f*(c+d*x)^(2/3)*sin(a+b*(c+d*x)^(2/3))/(b^2*d^2)+3/2*(d*e-c*f)*cos(a)*FresnelC((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(b^(3/2)*d^2)-3/2*(d*e-c*f)*FresnelS((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(b^(3/2)*d^2)],
[sin(a+b*(c+d*x)^(2/3)),x,5,-3/2*(c+d*x)^(1/3)*cos(a+b*(c+d*x)^(2/3))/(b*d)+3/2*cos(a)*FresnelC((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(b^(3/2)*d)-3/2*FresnelS((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(b^(3/2)*d)],
[sin(a+b*(c+d*x)^(2/3))/(e+f*x),x,0,Unintegrable(sin(a+b*(c+d*x)^(2/3))/(e+f*x),x)],
[sin(a+b*(c+d*x)^(2/3))/(e+f*x)^2,x,0,Unintegrable(sin(a+b*(c+d*x)^(2/3))/(e+f*x)^2,x)],

# n<0
[(e+f*x)^2*sin(a+b/(c+d*x)^(1/3)),x,29,-1/120960*b^9*f^2*Ci(b/(c+d*x)^(1/3))*cos(a)/d^3+1/2*b^3*(d*e-c*f)^2*Ci(b/(c+d*x)^(1/3))*cos(a)/d^3+1/120*b^5*f*(d*e-c*f)*(c+d*x)^(1/3)*cos(a+b/(c+d*x)^(1/3))/d^3-1/120960*b^7*f^2*(c+d*x)^(2/3)*cos(a+b/(c+d*x)^(1/3))/d^3+1/2*b*(d*e-c*f)^2*(c+d*x)^(2/3)*cos(a+b/(c+d*x)^(1/3))/d^3-1/60*b^3*f*(d*e-c*f)*(c+d*x)*cos(a+b/(c+d*x)^(1/3))/d^3+1/20160*b^5*f^2*(c+d*x)^(4/3)*cos(a+b/(c+d*x)^(1/3))/d^3+1/5*b*f*(d*e-c*f)*(c+d*x)^(5/3)*cos(a+b/(c+d*x)^(1/3))/d^3-1/1008*b^3*f^2*(c+d*x)^2*cos(a+b/(c+d*x)^(1/3))/d^3+1/24*b*f^2*(c+d*x)^(8/3)*cos(a+b/(c+d*x)^(1/3))/d^3+1/120*b^6*f*(d*e-c*f)*cos(a)*Si(b/(c+d*x)^(1/3))/d^3+1/120*b^6*f*(d*e-c*f)*Ci(b/(c+d*x)^(1/3))*sin(a)/d^3+1/120960*b^9*f^2*Si(b/(c+d*x)^(1/3))*sin(a)/d^3-1/2*b^3*(d*e-c*f)^2*Si(b/(c+d*x)^(1/3))*sin(a)/d^3+1/120960*b^8*f^2*(c+d*x)^(1/3)*sin(a+b/(c+d*x)^(1/3))/d^3-1/2*b^2*(d*e-c*f)^2*(c+d*x)^(1/3)*sin(a+b/(c+d*x)^(1/3))/d^3+1/120*b^4*f*(d*e-c*f)*(c+d*x)^(2/3)*sin(a+b/(c+d*x)^(1/3))/d^3-1/60480*b^6*f^2*(c+d*x)*sin(a+b/(c+d*x)^(1/3))/d^3+(d*e-c*f)^2*(c+d*x)*sin(a+b/(c+d*x)^(1/3))/d^3-1/20*b^2*f*(d*e-c*f)*(c+d*x)^(4/3)*sin(a+b/(c+d*x)^(1/3))/d^3+1/5040*b^4*f^2*(c+d*x)^(5/3)*sin(a+b/(c+d*x)^(1/3))/d^3+f*(d*e-c*f)*(c+d*x)^2*sin(a+b/(c+d*x)^(1/3))/d^3-1/168*b^2*f^2*(c+d*x)^(7/3)*sin(a+b/(c+d*x)^(1/3))/d^3+1/3*f^2*(c+d*x)^3*sin(a+b/(c+d*x)^(1/3))/d^3],
[(e+f*x)*sin(a+b/(c+d*x)^(1/3)),x,17,1/2*b^3*(d*e-c*f)*Ci(b/(c+d*x)^(1/3))*cos(a)/d^2+1/240*b^5*f*(c+d*x)^(1/3)*cos(a+b/(c+d*x)^(1/3))/d^2+1/2*b*(d*e-c*f)*(c+d*x)^(2/3)*cos(a+b/(c+d*x)^(1/3))/d^2-1/120*b^3*f*(c+d*x)*cos(a+b/(c+d*x)^(1/3))/d^2+1/10*b*f*(c+d*x)^(5/3)*cos(a+b/(c+d*x)^(1/3))/d^2+1/240*b^6*f*cos(a)*Si(b/(c+d*x)^(1/3))/d^2+1/240*b^6*f*Ci(b/(c+d*x)^(1/3))*sin(a)/d^2-1/2*b^3*(d*e-c*f)*Si(b/(c+d*x)^(1/3))*sin(a)/d^2-1/2*b^2*(d*e-c*f)*(c+d*x)^(1/3)*sin(a+b/(c+d*x)^(1/3))/d^2+1/240*b^4*f*(c+d*x)^(2/3)*sin(a+b/(c+d*x)^(1/3))/d^2+(d*e-c*f)*(c+d*x)*sin(a+b/(c+d*x)^(1/3))/d^2-1/40*b^2*f*(c+d*x)^(4/3)*sin(a+b/(c+d*x)^(1/3))/d^2+1/2*f*(c+d*x)^2*sin(a+b/(c+d*x)^(1/3))/d^2],
[sin(a+b/(c+d*x)^(1/3)),x,7,1/2*b^3*Ci(b/(c+d*x)^(1/3))*cos(a)/d+1/2*b*(c+d*x)^(2/3)*cos(a+b/(c+d*x)^(1/3))/d-1/2*b^3*Si(b/(c+d*x)^(1/3))*sin(a)/d-1/2*b^2*(c+d*x)^(1/3)*sin(a+b/(c+d*x)^(1/3))/d+(c+d*x)*sin(a+b/(c+d*x)^(1/3))/d],
[sin(a+b/(c+d*x)^(1/3))/(e+f*x),x,16,-3*cos(a)*Si(b/(c+d*x)^(1/3))/f-cos(a+(-1)^(1/3)*b*f^(1/3)/(d*e-c*f)^(1/3))*Si((-1)^(1/3)*b*f^(1/3)/(d*e-c*f)^(1/3)-b/(c+d*x)^(1/3))/f+cos(a-b*f^(1/3)/(d*e-c*f)^(1/3))*Si(b*f^(1/3)/(d*e-c*f)^(1/3)+b/(c+d*x)^(1/3))/f+cos(a-(-1)^(2/3)*b*f^(1/3)/(d*e-c*f)^(1/3))*Si((-1)^(2/3)*b*f^(1/3)/(d*e-c*f)^(1/3)+b/(c+d*x)^(1/3))/f-3*Ci(b/(c+d*x)^(1/3))*sin(a)/f+Ci(b*f^(1/3)/(d*e-c*f)^(1/3)+b/(c+d*x)^(1/3))*sin(a-b*f^(1/3)/(d*e-c*f)^(1/3))/f+Ci((-1)^(1/3)*b*f^(1/3)/(d*e-c*f)^(1/3)-b/(c+d*x)^(1/3))*sin(a+(-1)^(1/3)*b*f^(1/3)/(d*e-c*f)^(1/3))/f+Ci((-1)^(2/3)*b*f^(1/3)/(d*e-c*f)^(1/3)+b/(c+d*x)^(1/3))*sin(a-(-1)^(2/3)*b*f^(1/3)/(d*e-c*f)^(1/3))/f],
[sin(a+b/(c+d*x)^(1/3))/(e+f*x)^2,x,13,-1/3*b*d*Ci(b*f^(1/3)/(-d*e+c*f)^(1/3)-b/(c+d*x)^(1/3))*cos(a+b*f^(1/3)/(-d*e+c*f)^(1/3))/(f^(2/3)*(-d*e+c*f)^(4/3))+1/3*(-1)^(1/3)*b*d*Ci((-1)^(1/3)*b*f^(1/3)/(-d*e+c*f)^(1/3)+b/(c+d*x)^(1/3))*cos(a-(-1)^(1/3)*b*f^(1/3)/(-d*e+c*f)^(1/3))/(f^(2/3)*(-d*e+c*f)^(4/3))-1/3*(-1)^(2/3)*b*d*Ci((-1)^(2/3)*b*f^(1/3)/(-d*e+c*f)^(1/3)-b/(c+d*x)^(1/3))*cos(a+(-1)^(2/3)*b*f^(1/3)/(-d*e+c*f)^(1/3))/(f^(2/3)*(-d*e+c*f)^(4/3))-1/3*b*d*Si(b*f^(1/3)/(-d*e+c*f)^(1/3)-b/(c+d*x)^(1/3))*sin(a+b*f^(1/3)/(-d*e+c*f)^(1/3))/(f^(2/3)*(-d*e+c*f)^(4/3))-1/3*(-1)^(1/3)*b*d*Si((-1)^(1/3)*b*f^(1/3)/(-d*e+c*f)^(1/3)+b/(c+d*x)^(1/3))*sin(a-(-1)^(1/3)*b*f^(1/3)/(-d*e+c*f)^(1/3))/(f^(2/3)*(-d*e+c*f)^(4/3))-1/3*(-1)^(2/3)*b*d*Si((-1)^(2/3)*b*f^(1/3)/(-d*e+c*f)^(1/3)-b/(c+d*x)^(1/3))*sin(a+(-1)^(2/3)*b*f^(1/3)/(-d*e+c*f)^(1/3))/(f^(2/3)*(-d*e+c*f)^(4/3))+(c+d*x)*sin(a+b/(c+d*x)^(1/3))/((d*e-c*f)*(e+f*x))],
[(e+f*x)^2*sin(a+b/(c+d*x)^(2/3)),x,24,1/2*b^3*f*(d*e-c*f)*Ci(b/(c+d*x)^(2/3))*cos(a)/d^3+2*b*(d*e-c*f)^2*(c+d*x)^(1/3)*cos(a+b/(c+d*x)^(2/3))/d^3-8/315*b^3*f^2*(c+d*x)*cos(a+b/(c+d*x)^(2/3))/d^3+1/2*b*f*(d*e-c*f)*(c+d*x)^(4/3)*cos(a+b/(c+d*x)^(2/3))/d^3+2/21*b*f^2*(c+d*x)^(7/3)*cos(a+b/(c+d*x)^(2/3))/d^3-1/2*b^3*f*(d*e-c*f)*Si(b/(c+d*x)^(2/3))*sin(a)/d^3+16/315*b^4*f^2*(c+d*x)^(1/3)*sin(a+b/(c+d*x)^(2/3))/d^3-1/2*b^2*f*(d*e-c*f)*(c+d*x)^(2/3)*sin(a+b/(c+d*x)^(2/3))/d^3+(d*e-c*f)^2*(c+d*x)*sin(a+b/(c+d*x)^(2/3))/d^3-4/105*b^2*f^2*(c+d*x)^(5/3)*sin(a+b/(c+d*x)^(2/3))/d^3+f*(d*e-c*f)*(c+d*x)^2*sin(a+b/(c+d*x)^(2/3))/d^3+1/3*f^2*(c+d*x)^3*sin(a+b/(c+d*x)^(2/3))/d^3-16/315*b^(9/2)*f^2*cos(a)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sqrt(2*Pi)/d^3+2*b^(3/2)*(d*e-c*f)^2*cos(a)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sqrt(2*Pi)/d^3+2*b^(3/2)*(d*e-c*f)^2*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sin(a)*sqrt(2*Pi)/d^3+16/315*b^(9/2)*f^2*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sin(a)*sqrt(2*Pi)/d^3],
[(e+f*x)*sin(a+b/(c+d*x)^(2/3)),x,15,1/4*b^3*f*Ci(b/(c+d*x)^(2/3))*cos(a)/d^2+2*b*(d*e-c*f)*(c+d*x)^(1/3)*cos(a+b/(c+d*x)^(2/3))/d^2+1/4*b*f*(c+d*x)^(4/3)*cos(a+b/(c+d*x)^(2/3))/d^2-1/4*b^3*f*Si(b/(c+d*x)^(2/3))*sin(a)/d^2-1/4*b^2*f*(c+d*x)^(2/3)*sin(a+b/(c+d*x)^(2/3))/d^2+(d*e-c*f)*(c+d*x)*sin(a+b/(c+d*x)^(2/3))/d^2+1/2*f*(c+d*x)^2*sin(a+b/(c+d*x)^(2/3))/d^2+2*b^(3/2)*(d*e-c*f)*cos(a)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sqrt(2*Pi)/d^2+2*b^(3/2)*(d*e-c*f)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sin(a)*sqrt(2*Pi)/d^2],
[sin(a+b/(c+d*x)^(2/3)),x,7,2*b*(c+d*x)^(1/3)*cos(a+b/(c+d*x)^(2/3))/d+(c+d*x)*sin(a+b/(c+d*x)^(2/3))/d+2*b^(3/2)*cos(a)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sqrt(2*Pi)/d+2*b^(3/2)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sin(a)*sqrt(2*Pi)/d],
[sin(a+b/(c+d*x)^(2/3))/(e+f*x),x,0,Unintegrable(sin(a+b/(c+d*x)^(2/3))/(e+f*x),x)],
[sin(a+b/(c+d*x)^(2/3))/(e+f*x)^2,x,0,Unintegrable(sin(a+b/(c+d*x)^(2/3))/(e+f*x)^2,x)],

# Integrands of the form (e+f x)^m Sin[a+b (c+d x)^(n/3)] when c f-b e=0 

# n>0
[(c*e+d*e*x)^(4/3)*sin(a+b*(c+d*x)^(1/3)),x,9,2160*e*(e*(c+d*x))^(1/3)*cos(a+b*(c+d*x)^(1/3))/(b^7*d*(c+d*x)^(1/3))-1080*e*(c+d*x)^(1/3)*(e*(c+d*x))^(1/3)*cos(a+b*(c+d*x)^(1/3))/(b^5*d)+90*e*(c+d*x)*(e*(c+d*x))^(1/3)*cos(a+b*(c+d*x)^(1/3))/(b^3*d)-3*e*(c+d*x)^(5/3)*(e*(c+d*x))^(1/3)*cos(a+b*(c+d*x)^(1/3))/(b*d)+2160*e*(e*(c+d*x))^(1/3)*sin(a+b*(c+d*x)^(1/3))/(b^6*d)-360*e*(c+d*x)^(2/3)*(e*(c+d*x))^(1/3)*sin(a+b*(c+d*x)^(1/3))/(b^4*d)+18*e*(c+d*x)^(4/3)*(e*(c+d*x))^(1/3)*sin(a+b*(c+d*x)^(1/3))/(b^2*d)],
[(c*e+d*e*x)^(2/3)*sin(a+b*(c+d*x)^(1/3)),x,7,36*(e*(c+d*x))^(2/3)*cos(a+b*(c+d*x)^(1/3))/(b^3*d)-72*(e*(c+d*x))^(2/3)*cos(a+b*(c+d*x)^(1/3))/(b^5*d*(c+d*x)^(2/3))-3*(c+d*x)^(2/3)*(e*(c+d*x))^(2/3)*cos(a+b*(c+d*x)^(1/3))/(b*d)-72*(e*(c+d*x))^(2/3)*sin(a+b*(c+d*x)^(1/3))/(b^4*d*(c+d*x)^(1/3))+12*(c+d*x)^(1/3)*(e*(c+d*x))^(2/3)*sin(a+b*(c+d*x)^(1/3))/(b^2*d)],
[(c*e+d*e*x)^(1/3)*sin(a+b*(c+d*x)^(1/3)),x,6,18*(e*(c+d*x))^(1/3)*cos(a+b*(c+d*x)^(1/3))/(b^3*d)-3*(c+d*x)^(2/3)*(e*(c+d*x))^(1/3)*cos(a+b*(c+d*x)^(1/3))/(b*d)-18*(e*(c+d*x))^(1/3)*sin(a+b*(c+d*x)^(1/3))/(b^4*d*(c+d*x)^(1/3))+9*(c+d*x)^(1/3)*(e*(c+d*x))^(1/3)*sin(a+b*(c+d*x)^(1/3))/(b^2*d)],
[sin(a+b*(c+d*x)^(1/3))/(c*e+d*e*x)^(1/3),x,4,-3*(c+d*x)^(2/3)*cos(a+b*(c+d*x)^(1/3))/(b*d*(e*(c+d*x))^(1/3))+3*(c+d*x)^(1/3)*sin(a+b*(c+d*x)^(1/3))/(b^2*d*(e*(c+d*x))^(1/3))],
[sin(a+b*(c+d*x)^(1/3))/(c*e+d*e*x)^(2/3),x,3,-3*(c+d*x)^(2/3)*cos(a+b*(c+d*x)^(1/3))/(b*d*(e*(c+d*x))^(2/3))],
[sin(a+b*(c+d*x)^(1/3))/(c*e+d*e*x)^(4/3),x,6,3*b*(c+d*x)^(1/3)*Ci(b*(c+d*x)^(1/3))*cos(a)/(d*e*(e*(c+d*x))^(1/3))-3*b*(c+d*x)^(1/3)*Si(b*(c+d*x)^(1/3))*sin(a)/(d*e*(e*(c+d*x))^(1/3))-3*sin(a+b*(c+d*x)^(1/3))/(d*e*(e*(c+d*x))^(1/3))],
[sin(a+b*(c+d*x)^(1/3))/(c*e+d*e*x)^(5/3),x,7,-3/2*b*(c+d*x)^(1/3)*cos(a+b*(c+d*x)^(1/3))/(d*e*(e*(c+d*x))^(2/3))-3/2*b^2*(c+d*x)^(2/3)*cos(a)*Si(b*(c+d*x)^(1/3))/(d*e*(e*(c+d*x))^(2/3))-3/2*b^2*(c+d*x)^(2/3)*Ci(b*(c+d*x)^(1/3))*sin(a)/(d*e*(e*(c+d*x))^(2/3))-3/2*sin(a+b*(c+d*x)^(1/3))/(d*e*(e*(c+d*x))^(2/3))],
[sin(a+b*(c+d*x)^(1/3))/(c*e+d*e*x)^(7/3),x,9,1/8*b^3*cos(a+b*(c+d*x)^(1/3))/(d*e^2*(e*(c+d*x))^(1/3))-1/4*b*cos(a+b*(c+d*x)^(1/3))/(d*e^2*(c+d*x)^(2/3)*(e*(c+d*x))^(1/3))+1/8*b^4*(c+d*x)^(1/3)*cos(a)*Si(b*(c+d*x)^(1/3))/(d*e^2*(e*(c+d*x))^(1/3))+1/8*b^4*(c+d*x)^(1/3)*Ci(b*(c+d*x)^(1/3))*sin(a)/(d*e^2*(e*(c+d*x))^(1/3))-3/4*sin(a+b*(c+d*x)^(1/3))/(d*e^2*(c+d*x)*(e*(c+d*x))^(1/3))+1/8*b^2*sin(a+b*(c+d*x)^(1/3))/(d*e^2*(c+d*x)^(1/3)*(e*(c+d*x))^(1/3))],
[(c*e+d*e*x)^(4/3)*sin(a+b*(c+d*x)^(2/3)),x,9,45/8*e*(e*(c+d*x))^(1/3)*cos(a+b*(c+d*x)^(2/3))/(b^3*d)-3/2*e*(c+d*x)^(4/3)*(e*(c+d*x))^(1/3)*cos(a+b*(c+d*x)^(2/3))/(b*d)+15/4*e*(c+d*x)^(2/3)*(e*(c+d*x))^(1/3)*sin(a+b*(c+d*x)^(2/3))/(b^2*d)-45/8*e*(e*(c+d*x))^(1/3)*cos(a)*FresnelC((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sqrt(Pi)/(b^(7/2)*d*(c+d*x)^(1/3)*sqrt(2))+45/8*e*(e*(c+d*x))^(1/3)*FresnelS((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(Pi)/(b^(7/2)*d*(c+d*x)^(1/3)*sqrt(2))],
[(c*e+d*e*x)^(2/3)*sin(a+b*(c+d*x)^(2/3)),x,8,-3/2*(c+d*x)^(1/3)*(e*(c+d*x))^(2/3)*cos(a+b*(c+d*x)^(2/3))/(b*d)+9/4*(e*(c+d*x))^(2/3)*sin(a+b*(c+d*x)^(2/3))/(b^2*d*(c+d*x)^(1/3))-9/4*(e*(c+d*x))^(2/3)*cos(a)*FresnelS((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sqrt(Pi)/(b^(5/2)*d*(c+d*x)^(2/3)*sqrt(2))-9/4*(e*(c+d*x))^(2/3)*FresnelC((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(Pi)/(b^(5/2)*d*(c+d*x)^(2/3)*sqrt(2))],
[(c*e+d*e*x)^(1/3)*sin(a+b*(c+d*x)^(2/3)),x,5,-3/2*(c+d*x)^(1/3)*(e*(c+d*x))^(1/3)*cos(a+b*(c+d*x)^(2/3))/(b*d)+3/2*(e*(c+d*x))^(1/3)*sin(a+b*(c+d*x)^(2/3))/(b^2*d*(c+d*x)^(1/3))],
[sin(a+b*(c+d*x)^(2/3))/(c*e+d*e*x)^(1/3),x,4,-3/2*(c+d*x)^(1/3)*cos(a+b*(c+d*x)^(2/3))/(b*d*(e*(c+d*x))^(1/3))],
[sin(a+b*(c+d*x)^(2/3))/(c*e+d*e*x)^(2/3),x,6,3*(c+d*x)^(2/3)*cos(a)*FresnelS((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sqrt(1/2*Pi)/(d*(e*(c+d*x))^(2/3)*sqrt(b))+3*(c+d*x)^(2/3)*FresnelC((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(1/2*Pi)/(d*(e*(c+d*x))^(2/3)*sqrt(b))],
[sin(a+b*(c+d*x)^(2/3))/(c*e+d*e*x)^(4/3),x,7,-3*sin(a+b*(c+d*x)^(2/3))/(d*e*(e*(c+d*x))^(1/3))+3*(c+d*x)^(1/3)*cos(a)*FresnelC((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sqrt(b)*sqrt(2*Pi)/(d*e*(e*(c+d*x))^(1/3))-3*(c+d*x)^(1/3)*FresnelS((c+d*x)^(1/3)*sqrt(b)*sqrt(2/Pi))*sin(a)*sqrt(b)*sqrt(2*Pi)/(d*e*(e*(c+d*x))^(1/3))],
[sin(a+b*(c+d*x)^(2/3))/(c*e+d*e*x)^(5/3),x,7,3/2*b*(c+d*x)^(2/3)*Ci(b*(c+d*x)^(2/3))*cos(a)/(d*e*(e*(c+d*x))^(2/3))-3/2*b*(c+d*x)^(2/3)*Si(b*(c+d*x)^(2/3))*sin(a)/(d*e*(e*(c+d*x))^(2/3))-3/2*sin(a+b*(c+d*x)^(2/3))/(d*e*(e*(c+d*x))^(2/3))],

# n<0
[(c*e+d*e*x)^(1/3)*sin(a+b/(c+d*x)^(1/3)),x,9,-1/8*b^3*(e*(c+d*x))^(1/3)*cos(a+b/(c+d*x)^(1/3))/d+1/4*b*(c+d*x)^(2/3)*(e*(c+d*x))^(1/3)*cos(a+b/(c+d*x)^(1/3))/d-1/8*b^4*(e*(c+d*x))^(1/3)*cos(a)*Si(b/(c+d*x)^(1/3))/(d*(c+d*x)^(1/3))-1/8*b^4*(e*(c+d*x))^(1/3)*Ci(b/(c+d*x)^(1/3))*sin(a)/(d*(c+d*x)^(1/3))-1/8*b^2*(c+d*x)^(1/3)*(e*(c+d*x))^(1/3)*sin(a+b/(c+d*x)^(1/3))/d+3/4*(c+d*x)*(e*(c+d*x))^(1/3)*sin(a+b/(c+d*x)^(1/3))/d],
[sin(a+b/(c+d*x)^(1/3))/(c*e+d*e*x)^(1/3),x,7,3/2*b*(c+d*x)^(2/3)*cos(a+b/(c+d*x)^(1/3))/(d*(e*(c+d*x))^(1/3))+3/2*b^2*(c+d*x)^(1/3)*cos(a)*Si(b/(c+d*x)^(1/3))/(d*(e*(c+d*x))^(1/3))+3/2*b^2*(c+d*x)^(1/3)*Ci(b/(c+d*x)^(1/3))*sin(a)/(d*(e*(c+d*x))^(1/3))+3/2*(c+d*x)*sin(a+b/(c+d*x)^(1/3))/(d*(e*(c+d*x))^(1/3))],
[sin(a+b/(c+d*x)^(1/3))/(c*e+d*e*x)^(2/3),x,6,-3*b*(c+d*x)^(2/3)*Ci(b/(c+d*x)^(1/3))*cos(a)/(d*(e*(c+d*x))^(2/3))+3*b*(c+d*x)^(2/3)*Si(b/(c+d*x)^(1/3))*sin(a)/(d*(e*(c+d*x))^(2/3))+3*(c+d*x)*sin(a+b/(c+d*x)^(1/3))/(d*(e*(c+d*x))^(2/3))],
[sin(a+b/(c+d*x)^(1/3))/(c*e+d*e*x)^(4/3),x,3,3*(c+d*x)^(1/3)*cos(a+b/(c+d*x)^(1/3))/(b*d*e*(e*(c+d*x))^(1/3))],
[sin(a+b/(c+d*x)^(1/3))/(c*e+d*e*x)^(5/3),x,4,3*(c+d*x)^(1/3)*cos(a+b/(c+d*x)^(1/3))/(b*d*e*(e*(c+d*x))^(2/3))-3*(c+d*x)^(2/3)*sin(a+b/(c+d*x)^(1/3))/(b^2*d*e*(e*(c+d*x))^(2/3))],
[sin(a+b/(c+d*x)^(1/3))/(c*e+d*e*x)^(7/3),x,6,-18*cos(a+b/(c+d*x)^(1/3))/(b^3*d*e^2*(e*(c+d*x))^(1/3))+3*cos(a+b/(c+d*x)^(1/3))/(b*d*e^2*(c+d*x)^(2/3)*(e*(c+d*x))^(1/3))-9*sin(a+b/(c+d*x)^(1/3))/(b^2*d*e^2*(c+d*x)^(1/3)*(e*(c+d*x))^(1/3))+18*(c+d*x)^(1/3)*sin(a+b/(c+d*x)^(1/3))/(b^4*d*e^2*(e*(c+d*x))^(1/3))],
[sin(a+b/(c+d*x)^(1/3))/(c*e+d*e*x)^(8/3),x,7,-36*cos(a+b/(c+d*x)^(1/3))/(b^3*d*e^2*(e*(c+d*x))^(2/3))+3*cos(a+b/(c+d*x)^(1/3))/(b*d*e^2*(c+d*x)^(2/3)*(e*(c+d*x))^(2/3))+72*(c+d*x)^(2/3)*cos(a+b/(c+d*x)^(1/3))/(b^5*d*e^2*(e*(c+d*x))^(2/3))-12*sin(a+b/(c+d*x)^(1/3))/(b^2*d*e^2*(c+d*x)^(1/3)*(e*(c+d*x))^(2/3))+72*(c+d*x)^(1/3)*sin(a+b/(c+d*x)^(1/3))/(b^4*d*e^2*(e*(c+d*x))^(2/3))],
[(c*e+d*e*x)^(4/3)*sin(a+b/(c+d*x)^(2/3)),x,11,-8/35*b^3*e*(e*(c+d*x))^(1/3)*cos(a+b/(c+d*x)^(2/3))/d+6/35*b*e*(c+d*x)^(4/3)*(e*(c+d*x))^(1/3)*cos(a+b/(c+d*x)^(2/3))/d-4/35*b^2*e*(c+d*x)^(2/3)*(e*(c+d*x))^(1/3)*sin(a+b/(c+d*x)^(2/3))/d+3/7*e*(c+d*x)^2*(e*(c+d*x))^(1/3)*sin(a+b/(c+d*x)^(2/3))/d-8/35*b^(7/2)*e*(e*(c+d*x))^(1/3)*cos(a)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sqrt(2*Pi)/(d*(c+d*x)^(1/3))-8/35*b^(7/2)*e*(e*(c+d*x))^(1/3)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sin(a)*sqrt(2*Pi)/(d*(c+d*x)^(1/3))],
[(c*e+d*e*x)^(2/3)*sin(a+b/(c+d*x)^(2/3)),x,10,2/5*b*(c+d*x)^(1/3)*(e*(c+d*x))^(2/3)*cos(a+b/(c+d*x)^(2/3))/d-4/5*b^2*(e*(c+d*x))^(2/3)*sin(a+b/(c+d*x)^(2/3))/(d*(c+d*x)^(1/3))+3/5*(c+d*x)*(e*(c+d*x))^(2/3)*sin(a+b/(c+d*x)^(2/3))/d+4/5*b^(5/2)*(e*(c+d*x))^(2/3)*cos(a)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sqrt(2)*sqrt(Pi)/(d*(c+d*x)^(2/3))-4/5*b^(5/2)*(e*(c+d*x))^(2/3)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sin(a)*sqrt(2)*sqrt(Pi)/(d*(c+d*x)^(2/3))],
[(c*e+d*e*x)^(1/3)*sin(a+b/(c+d*x)^(2/3)),x,8,3/4*b*(c+d*x)^(1/3)*(e*(c+d*x))^(1/3)*cos(a+b/(c+d*x)^(2/3))/d+3/4*b^2*(e*(c+d*x))^(1/3)*cos(a)*Si(b/(c+d*x)^(2/3))/(d*(c+d*x)^(1/3))+3/4*b^2*(e*(c+d*x))^(1/3)*Ci(b/(c+d*x)^(2/3))*sin(a)/(d*(c+d*x)^(1/3))+3/4*(c+d*x)*(e*(c+d*x))^(1/3)*sin(a+b/(c+d*x)^(2/3))/d],
[sin(a+b/(c+d*x)^(2/3))/(c*e+d*e*x)^(1/3),x,7,-3/2*b*(c+d*x)^(1/3)*Ci(b/(c+d*x)^(2/3))*cos(a)/(d*(e*(c+d*x))^(1/3))+3/2*b*(c+d*x)^(1/3)*Si(b/(c+d*x)^(2/3))*sin(a)/(d*(e*(c+d*x))^(1/3))+3/2*(c+d*x)*sin(a+b/(c+d*x)^(2/3))/(d*(e*(c+d*x))^(1/3))],
[sin(a+b/(c+d*x)^(2/3))/(c*e+d*e*x)^(2/3),x,8,3*(c+d*x)*sin(a+b/(c+d*x)^(2/3))/(d*(e*(c+d*x))^(2/3))-3*(c+d*x)^(2/3)*cos(a)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sqrt(b)*sqrt(2*Pi)/(d*(e*(c+d*x))^(2/3))+3*(c+d*x)^(2/3)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sin(a)*sqrt(b)*sqrt(2*Pi)/(d*(e*(c+d*x))^(2/3))],
[sin(a+b/(c+d*x)^(2/3))/(c*e+d*e*x)^(4/3),x,6,-3*(c+d*x)^(1/3)*cos(a)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sqrt(Pi)/(d*e*(e*(c+d*x))^(1/3)*sqrt(2)*sqrt(b))-3*(c+d*x)^(1/3)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sin(a)*sqrt(Pi)/(d*e*(e*(c+d*x))^(1/3)*sqrt(2)*sqrt(b))],
[sin(a+b/(c+d*x)^(2/3))/(c*e+d*e*x)^(5/3),x,4,3/2*(c+d*x)^(2/3)*cos(a+b/(c+d*x)^(2/3))/(b*d*e*(e*(c+d*x))^(2/3))],
[sin(a+b/(c+d*x)^(2/3))/(c*e+d*e*x)^(7/3),x,5,3/2*cos(a+b/(c+d*x)^(2/3))/(b*d*e^2*(c+d*x)^(1/3)*(e*(c+d*x))^(1/3))-3/2*(c+d*x)^(1/3)*sin(a+b/(c+d*x)^(2/3))/(b^2*d*e^2*(e*(c+d*x))^(1/3))],
[sin(a+b/(c+d*x)^(2/3))/(c*e+d*e*x)^(8/3),x,9,3/2*cos(a+b/(c+d*x)^(2/3))/(b*d*e^2*(c+d*x)^(1/3)*(e*(c+d*x))^(2/3))-9/4*(c+d*x)^(1/3)*sin(a+b/(c+d*x)^(2/3))/(b^2*d*e^2*(e*(c+d*x))^(2/3))+9/4*(c+d*x)^(2/3)*cos(a)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sqrt(1/2*Pi)/(b^(5/2)*d*e^2*(e*(c+d*x))^(2/3))+9/4*(c+d*x)^(2/3)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sin(a)*sqrt(1/2*Pi)/(b^(5/2)*d*e^2*(e*(c+d*x))^(2/3))],
[sin(a+b/(c+d*x)^(2/3))/(c*e+d*e*x)^(10/3),x,10,-45/8*cos(a+b/(c+d*x)^(2/3))/(b^3*d*e^3*(e*(c+d*x))^(1/3))+3/2*cos(a+b/(c+d*x)^(2/3))/(b*d*e^3*(c+d*x)^(4/3)*(e*(c+d*x))^(1/3))-15/4*sin(a+b/(c+d*x)^(2/3))/(b^2*d*e^3*(c+d*x)^(2/3)*(e*(c+d*x))^(1/3))+45/8*(c+d*x)^(1/3)*cos(a)*FresnelC(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sqrt(Pi)/(b^(7/2)*d*e^3*(e*(c+d*x))^(1/3)*sqrt(2))-45/8*(c+d*x)^(1/3)*FresnelS(sqrt(b)*sqrt(2/Pi)/(c+d*x)^(1/3))*sin(a)*sqrt(Pi)/(b^(7/2)*d*e^3*(e*(c+d*x))^(1/3)*sqrt(2))],

# Integrands of the form (e+f x)^m Sin[a+b (c+d x)^n] when n symbolic
[(e*x)^m*sin(a+b*(c+d*x)^n),x,0,Unintegrable((e*x)^m*sin(a+b*(c+d*x)^n),x)],
[x^3*sin(a+b*(c+d*x)^n),x,14,-1/2*I*c^3*exp(I*a)*(c+d*x)*GAMMA(1/n,-I*b*(c+d*x)^n)/(d^4*n*(-I*b*(c+d*x)^n)^(1/n))+1/2*I*c^3*(c+d*x)*GAMMA(1/n,I*b*(c+d*x)^n)/(d^4*exp(I*a)*n*(I*b*(c+d*x)^n)^(1/n))+3/2*I*c^2*exp(I*a)*(c+d*x)^2*GAMMA(2/n,-I*b*(c+d*x)^n)/(d^4*n*(-I*b*(c+d*x)^n)^(2/n))-3/2*I*c^2*(c+d*x)^2*GAMMA(2/n,I*b*(c+d*x)^n)/(d^4*exp(I*a)*n*(I*b*(c+d*x)^n)^(2/n))-3/2*I*c*exp(I*a)*(c+d*x)^3*GAMMA(3/n,-I*b*(c+d*x)^n)/(d^4*n*(-I*b*(c+d*x)^n)^(3/n))+3/2*I*c*(c+d*x)^3*GAMMA(3/n,I*b*(c+d*x)^n)/(d^4*exp(I*a)*n*(I*b*(c+d*x)^n)^(3/n))+1/2*I*exp(I*a)*(c+d*x)^4*GAMMA(4/n,-I*b*(c+d*x)^n)/(d^4*n*(-I*b*(c+d*x)^n)^(4/n))-1/2*I*(c+d*x)^4*GAMMA(4/n,I*b*(c+d*x)^n)/(d^4*exp(I*a)*n*(I*b*(c+d*x)^n)^(4/n))],
[x^2*sin(a+b*(c+d*x)^n),x,11,1/2*I*c^2*exp(I*a)*(c+d*x)*GAMMA(1/n,-I*b*(c+d*x)^n)/(d^3*n*(-I*b*(c+d*x)^n)^(1/n))-1/2*I*c^2*(c+d*x)*GAMMA(1/n,I*b*(c+d*x)^n)/(d^3*exp(I*a)*n*(I*b*(c+d*x)^n)^(1/n))-I*c*exp(I*a)*(c+d*x)^2*GAMMA(2/n,-I*b*(c+d*x)^n)/(d^3*n*(-I*b*(c+d*x)^n)^(2/n))+I*c*(c+d*x)^2*GAMMA(2/n,I*b*(c+d*x)^n)/(d^3*exp(I*a)*n*(I*b*(c+d*x)^n)^(2/n))+1/2*I*exp(I*a)*(c+d*x)^3*GAMMA(3/n,-I*b*(c+d*x)^n)/(d^3*n*(-I*b*(c+d*x)^n)^(3/n))-1/2*I*(c+d*x)^3*GAMMA(3/n,I*b*(c+d*x)^n)/(d^3*exp(I*a)*n*(I*b*(c+d*x)^n)^(3/n))],
[x*sin(a+b*(c+d*x)^n),x,8,-1/2*I*c*exp(I*a)*(c+d*x)*GAMMA(1/n,-I*b*(c+d*x)^n)/(d^2*n*(-I*b*(c+d*x)^n)^(1/n))+1/2*I*c*(c+d*x)*GAMMA(1/n,I*b*(c+d*x)^n)/(d^2*exp(I*a)*n*(I*b*(c+d*x)^n)^(1/n))+1/2*I*exp(I*a)*(c+d*x)^2*GAMMA(2/n,-I*b*(c+d*x)^n)/(d^2*n*(-I*b*(c+d*x)^n)^(2/n))-1/2*I*(c+d*x)^2*GAMMA(2/n,I*b*(c+d*x)^n)/(d^2*exp(I*a)*n*(I*b*(c+d*x)^n)^(2/n))],
[sin(a+b*(c+d*x)^n),x,3,1/2*I*exp(I*a)*(c+d*x)*GAMMA(1/n,-I*b*(c+d*x)^n)/(d*n*(-I*b*(c+d*x)^n)^(1/n))-1/2*I*(c+d*x)*GAMMA(1/n,I*b*(c+d*x)^n)/(d*exp(I*a)*n*(I*b*(c+d*x)^n)^(1/n))],
[sin(a+b*(c+d*x)^n)/x,x,0,Unintegrable(sin(a+b*(c+d*x)^n)/x,x)],
[sin(a+b*(c+d*x)^n)/x^2,x,0,Unintegrable(sin(a+b*(c+d*x)^n)/x^2,x)],

# Integrands of the form (e x)^m (a+b Sin[c+d (f+g x)^n])^p when n symbolic

# Integrands of the form x^m (a+b Sin[c+d (f+g x)^n])^p when n symbolic

# p>0
[x^3*(a+b*sin(c+d*(f+g*x)^n)),x,16,1/4*a*x^4-1/2*I*b*exp(I*c)*f^3*(f+g*x)*GAMMA(1/n,-I*d*(f+g*x)^n)/(g^4*n*(-I*d*(f+g*x)^n)^(1/n))+1/2*I*b*f^3*(f+g*x)*GAMMA(1/n,I*d*(f+g*x)^n)/(exp(I*c)*g^4*n*(I*d*(f+g*x)^n)^(1/n))+3/2*I*b*exp(I*c)*f^2*(f+g*x)^2*GAMMA(2/n,-I*d*(f+g*x)^n)/(g^4*n*(-I*d*(f+g*x)^n)^(2/n))-3/2*I*b*f^2*(f+g*x)^2*GAMMA(2/n,I*d*(f+g*x)^n)/(exp(I*c)*g^4*n*(I*d*(f+g*x)^n)^(2/n))-3/2*I*b*exp(I*c)*f*(f+g*x)^3*GAMMA(3/n,-I*d*(f+g*x)^n)/(g^4*n*(-I*d*(f+g*x)^n)^(3/n))+3/2*I*b*f*(f+g*x)^3*GAMMA(3/n,I*d*(f+g*x)^n)/(exp(I*c)*g^4*n*(I*d*(f+g*x)^n)^(3/n))+1/2*I*b*exp(I*c)*(f+g*x)^4*GAMMA(4/n,-I*d*(f+g*x)^n)/(g^4*n*(-I*d*(f+g*x)^n)^(4/n))-1/2*I*b*(f+g*x)^4*GAMMA(4/n,I*d*(f+g*x)^n)/(exp(I*c)*g^4*n*(I*d*(f+g*x)^n)^(4/n))],
[x^2*(a+b*sin(c+d*(f+g*x)^n)),x,13,1/3*a*x^3+1/2*I*b*exp(I*c)*f^2*(f+g*x)*GAMMA(1/n,-I*d*(f+g*x)^n)/(g^3*n*(-I*d*(f+g*x)^n)^(1/n))-1/2*I*b*f^2*(f+g*x)*GAMMA(1/n,I*d*(f+g*x)^n)/(exp(I*c)*g^3*n*(I*d*(f+g*x)^n)^(1/n))-I*b*exp(I*c)*f*(f+g*x)^2*GAMMA(2/n,-I*d*(f+g*x)^n)/(g^3*n*(-I*d*(f+g*x)^n)^(2/n))+I*b*f*(f+g*x)^2*GAMMA(2/n,I*d*(f+g*x)^n)/(exp(I*c)*g^3*n*(I*d*(f+g*x)^n)^(2/n))+1/2*I*b*exp(I*c)*(f+g*x)^3*GAMMA(3/n,-I*d*(f+g*x)^n)/(g^3*n*(-I*d*(f+g*x)^n)^(3/n))-1/2*I*b*(f+g*x)^3*GAMMA(3/n,I*d*(f+g*x)^n)/(exp(I*c)*g^3*n*(I*d*(f+g*x)^n)^(3/n))],
[x*(a+b*sin(c+d*(f+g*x)^n)),x,10,1/2*a*x^2-1/2*I*b*exp(I*c)*f*(f+g*x)*GAMMA(1/n,-I*d*(f+g*x)^n)/(g^2*n*(-I*d*(f+g*x)^n)^(1/n))+1/2*I*b*f*(f+g*x)*GAMMA(1/n,I*d*(f+g*x)^n)/(exp(I*c)*g^2*n*(I*d*(f+g*x)^n)^(1/n))+1/2*I*b*exp(I*c)*(f+g*x)^2*GAMMA(2/n,-I*d*(f+g*x)^n)/(g^2*n*(-I*d*(f+g*x)^n)^(2/n))-1/2*I*b*(f+g*x)^2*GAMMA(2/n,I*d*(f+g*x)^n)/(exp(I*c)*g^2*n*(I*d*(f+g*x)^n)^(2/n))],
[a+b*sin(c+d*(f+g*x)^n),x,4,a*x+1/2*I*b*exp(I*c)*(f+g*x)*GAMMA(1/n,-I*d*(f+g*x)^n)/(g*n*(-I*d*(f+g*x)^n)^(1/n))-1/2*I*b*(f+g*x)*GAMMA(1/n,I*d*(f+g*x)^n)/(exp(I*c)*g*n*(I*d*(f+g*x)^n)^(1/n))],
[(a+b*sin(c+d*(f+g*x)^n))/x,x,2,a*log(x)+b*Unintegrable(sin(c+d*(f+g*x)^n)/x,x)],
[(a+b*sin(c+d*(f+g*x)^n))/x^2,x,2,-a/x+b*Unintegrable(sin(c+d*(f+g*x)^n)/x^2,x)],
[x^2*(a+b*sin(c+d*(f+g*x)^n))^2,x,28,1/2*(2*a^2+b^2)*f^2*x/g^2-1/2*(2*a^2+b^2)*f*(f+g*x)^2/g^3+1/6*(2*a^2+b^2)*(f+g*x)^3/g^3+I*a*b*exp(I*c)*f^2*(f+g*x)*GAMMA(1/n,-I*d*(f+g*x)^n)/(g^3*n*(-I*d*(f+g*x)^n)^(1/n))-I*a*b*f^2*(f+g*x)*GAMMA(1/n,I*d*(f+g*x)^n)/(exp(I*c)*g^3*n*(I*d*(f+g*x)^n)^(1/n))+2^(-2+(-1)/n)*b^2*exp(2*I*c)*f^2*(f+g*x)*GAMMA(1/n,-2*I*d*(f+g*x)^n)/(g^3*n*(-I*d*(f+g*x)^n)^(1/n))+2^(-2+(-1)/n)*b^2*f^2*(f+g*x)*GAMMA(1/n,2*I*d*(f+g*x)^n)/(exp(2*I*c)*g^3*n*(I*d*(f+g*x)^n)^(1/n))-2*I*a*b*exp(I*c)*f*(f+g*x)^2*GAMMA(2/n,-I*d*(f+g*x)^n)/(g^3*n*(-I*d*(f+g*x)^n)^(2/n))+2*I*a*b*f*(f+g*x)^2*GAMMA(2/n,I*d*(f+g*x)^n)/(exp(I*c)*g^3*n*(I*d*(f+g*x)^n)^(2/n))-2^(-1+(-2)/n)*b^2*exp(2*I*c)*f*(f+g*x)^2*GAMMA(2/n,-2*I*d*(f+g*x)^n)/(g^3*n*(-I*d*(f+g*x)^n)^(2/n))-2^(-1+(-2)/n)*b^2*f*(f+g*x)^2*GAMMA(2/n,2*I*d*(f+g*x)^n)/(exp(2*I*c)*g^3*n*(I*d*(f+g*x)^n)^(2/n))+I*a*b*exp(I*c)*(f+g*x)^3*GAMMA(3/n,-I*d*(f+g*x)^n)/(g^3*n*(-I*d*(f+g*x)^n)^(3/n))-I*a*b*(f+g*x)^3*GAMMA(3/n,I*d*(f+g*x)^n)/(exp(I*c)*g^3*n*(I*d*(f+g*x)^n)^(3/n))+2^(-2+(-3)/n)*b^2*exp(2*I*c)*(f+g*x)^3*GAMMA(3/n,-2*I*d*(f+g*x)^n)/(g^3*n*(-I*d*(f+g*x)^n)^(3/n))+2^(-2+(-3)/n)*b^2*(f+g*x)^3*GAMMA(3/n,2*I*d*(f+g*x)^n)/(exp(2*I*c)*g^3*n*(I*d*(f+g*x)^n)^(3/n))],
[x*(a+b*sin(c+d*(f+g*x)^n))^2,x,19,-1/2*(2*a^2+b^2)*f*x/g+1/4*(2*a^2+b^2)*(f+g*x)^2/g^2-I*a*b*exp(I*c)*f*(f+g*x)*GAMMA(1/n,-I*d*(f+g*x)^n)/(g^2*n*(-I*d*(f+g*x)^n)^(1/n))+I*a*b*f*(f+g*x)*GAMMA(1/n,I*d*(f+g*x)^n)/(exp(I*c)*g^2*n*(I*d*(f+g*x)^n)^(1/n))-2^(-2+(-1)/n)*b^2*exp(2*I*c)*f*(f+g*x)*GAMMA(1/n,-2*I*d*(f+g*x)^n)/(g^2*n*(-I*d*(f+g*x)^n)^(1/n))-2^(-2+(-1)/n)*b^2*f*(f+g*x)*GAMMA(1/n,2*I*d*(f+g*x)^n)/(exp(2*I*c)*g^2*n*(I*d*(f+g*x)^n)^(1/n))+I*a*b*exp(I*c)*(f+g*x)^2*GAMMA(2/n,-I*d*(f+g*x)^n)/(g^2*n*(-I*d*(f+g*x)^n)^(2/n))-I*a*b*(f+g*x)^2*GAMMA(2/n,I*d*(f+g*x)^n)/(exp(I*c)*g^2*n*(I*d*(f+g*x)^n)^(2/n))+4^(-1+(-1)/n)*b^2*exp(2*I*c)*(f+g*x)^2*GAMMA(2/n,-2*I*d*(f+g*x)^n)/(g^2*n*(-I*d*(f+g*x)^n)^(2/n))+4^(-1+(-1)/n)*b^2*(f+g*x)^2*GAMMA(2/n,2*I*d*(f+g*x)^n)/(exp(2*I*c)*g^2*n*(I*d*(f+g*x)^n)^(2/n))],
[(a+b*sin(c+d*(f+g*x)^n))^2,x,8,1/2*(2*a^2+b^2)*x+I*a*b*exp(I*c)*(f+g*x)*GAMMA(1/n,-I*d*(f+g*x)^n)/(g*n*(-I*d*(f+g*x)^n)^(1/n))-I*a*b*(f+g*x)*GAMMA(1/n,I*d*(f+g*x)^n)/(exp(I*c)*g*n*(I*d*(f+g*x)^n)^(1/n))+2^(-2+(-1)/n)*b^2*exp(2*I*c)*(f+g*x)*GAMMA(1/n,-2*I*d*(f+g*x)^n)/(g*n*(-I*d*(f+g*x)^n)^(1/n))+2^(-2+(-1)/n)*b^2*(f+g*x)*GAMMA(1/n,2*I*d*(f+g*x)^n)/(exp(2*I*c)*g*n*(I*d*(f+g*x)^n)^(1/n))],
[(a+b*sin(c+d*(f+g*x)^n))^2/x,x,0,Unintegrable((a+b*sin(c+d*(f+g*x)^n))^2/x,x)],
[(a+b*sin(c+d*(f+g*x)^n))^2/x^2,x,0,Unintegrable((a+b*sin(c+d*(f+g*x)^n))^2/x^2,x)],

# p<0
[x^2/(a+b*sin(c+d*(f+g*x)^n)),x,0,Unintegrable(x^2/(a+b*sin(c+d*(f+g*x)^n)),x)],
[x/(a+b*sin(c+d*(f+g*x)^n)),x,0,Unintegrable(x/(a+b*sin(c+d*(f+g*x)^n)),x)],
[1/(a+b*sin(c+d*(f+g*x)^n)),x,0,Unintegrable(1/(a+b*sin(c+d*(f+g*x)^n)),x)],
[1/(x*(a+b*sin(c+d*(f+g*x)^n))),x,0,Unintegrable(1/(x*(a+b*sin(c+d*(f+g*x)^n))),x)],
[1/(x^2*(a+b*sin(c+d*(f+g*x)^n))),x,0,Unintegrable(1/(x^2*(a+b*sin(c+d*(f+g*x)^n))),x)],
[x^2/(a+b*sin(c+d*(f+g*x)^n))^2,x,0,Unintegrable(x^2/(a+b*sin(c+d*(f+g*x)^n))^2,x)],
[x/(a+b*sin(c+d*(f+g*x)^n))^2,x,0,Unintegrable(x/(a+b*sin(c+d*(f+g*x)^n))^2,x)],
[1/(a+b*sin(c+d*(f+g*x)^n))^2,x,0,Unintegrable(1/(a+b*sin(c+d*(f+g*x)^n))^2,x)],
[1/(x*(a+b*sin(c+d*(f+g*x)^n))^2),x,0,Unintegrable(1/(x*(a+b*sin(c+d*(f+g*x)^n))^2),x)],
[1/(x^2*(a+b*sin(c+d*(f+g*x)^n))^2),x,0,Unintegrable(1/(x^2*(a+b*sin(c+d*(f+g*x)^n))^2),x)],

# Integrands of the form (e x)^m (a+b Sin[c+d (f+g x)^n])^p when p symbolic
[(e*x)^m*(a+b*sin(c+d*(f+g*x)^n))^p,x,0,Unintegrable((e*x)^m*(a+b*sin(c+d*(f+g*x)^n))^p,x)],

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

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

# Integrands of the form (e+f x)^m (a+b Sin[c+d/x])^p

# p>0
[(e+f*x)^2*(a+b*sin(c+d/x)),x,23,a*e^2*x+a*e*f*x^2+1/3*a*f^2*x^3-b*d*e^2*Ci(d/x)*cos(c)+1/6*b*d^3*f^2*Ci(d/x)*cos(c)+b*d*e*f*x*cos(c+d/x)+1/6*b*d*f^2*x^2*cos(c+d/x)+b*d^2*e*f*cos(c)*Si(d/x)+b*d^2*e*f*Ci(d/x)*sin(c)+b*d*e^2*Si(d/x)*sin(c)-1/6*b*d^3*f^2*Si(d/x)*sin(c)+b*e^2*x*sin(c+d/x)-1/6*b*d^2*f^2*x*sin(c+d/x)+b*e*f*x^2*sin(c+d/x)+1/3*b*f^2*x^3*sin(c+d/x)],
[(e+f*x)*(a+b*sin(c+d/x)),x,15,a*e*x+1/2*a*f*x^2-b*d*e*Ci(d/x)*cos(c)+1/2*b*d*f*x*cos(c+d/x)+1/2*b*d^2*f*cos(c)*Si(d/x)+1/2*b*d^2*f*Ci(d/x)*sin(c)+b*d*e*Si(d/x)*sin(c)+b*e*x*sin(c+d/x)+1/2*b*f*x^2*sin(c+d/x)],
[a+b*sin(c+d/x),x,6,a*x-b*d*Ci(d/x)*cos(c)+b*d*Si(d/x)*sin(c)+b*x*sin(c+d/x)],
[(a+b*sin(c+d/x))/(e+f*x),x,12,a*log(f+e/x)/f+a*log(x)/f+b*cos(c-d*f/e)*Si(d*(f/e+1/x))/f-b*cos(c)*Si(d/x)/f-b*Ci(d/x)*sin(c)/f+b*Ci(d*(f/e+1/x))*sin(c-d*f/e)/f],
[(a+b*sin(c+d/x))/(e+f*x)^2,x,7,a/(e*(f+e/x))-b*d*Ci(d*(f/e+1/x))*cos(c-d*f/e)/e^2+b*d*Si(d*(f/e+1/x))*sin(c-d*f/e)/e^2+b*sin(c+d/x)/(e*(f+e/x))],
[(a+b*sin(c+d/x))/(e+f*x)^3,x,15,-1/2*a*f/(e^2*(f+e/x)^2)+a/(e^2*(f+e/x))-b*d*Ci(d*(f/e+1/x))*cos(c-d*f/e)/e^3-1/2*b*d*f*cos(c+d/x)/(e^3*(f+e/x))-1/2*b*d^2*f*cos(c-d*f/e)*Si(d*(f/e+1/x))/e^4-1/2*b*d^2*f*Ci(d*(f/e+1/x))*sin(c-d*f/e)/e^4+b*d*Si(d*(f/e+1/x))*sin(c-d*f/e)/e^3-1/2*b*f*sin(c+d/x)/(e^2*(f+e/x)^2)+b*sin(c+d/x)/(e^2*(f+e/x))],
[(e+f*x)*(a+b*sin(c+d/x))^2,x,27,a^2*e*x+1/2*a^2*f*x^2-2*a*b*d*e*Ci(d/x)*cos(c)-b^2*d^2*f*Ci(2*d/x)*cos(2*c)+a*b*d*f*x*cos(c+d/x)+a*b*d^2*f*cos(c)*Si(d/x)-b^2*d*e*cos(2*c)*Si(2*d/x)+a*b*d^2*f*Ci(d/x)*sin(c)+2*a*b*d*e*Si(d/x)*sin(c)-b^2*d*e*Ci(2*d/x)*sin(2*c)+b^2*d^2*f*Si(2*d/x)*sin(2*c)+2*a*b*e*x*sin(c+d/x)+a*b*f*x^2*sin(c+d/x)+b^2*d*f*x*cos(c+d/x)*sin(c+d/x)+b^2*e*x*sin(c+d/x)^2+1/2*b^2*f*x^2*sin(c+d/x)^2],
[(a+b*sin(c+d/x))^2,x,12,a^2*x-2*a*b*d*Ci(d/x)*cos(c)-b^2*d*cos(2*c)*Si(2*d/x)+2*a*b*d*Si(d/x)*sin(c)-b^2*d*Ci(2*d/x)*sin(2*c)+2*a*b*x*sin(c+d/x)+b^2*x*sin(c+d/x)^2],
[(a+b*sin(c+d/x))^2/(e+f*x),x,22,1/2*b^2*Ci(2*d/x)*cos(2*c)/f-1/2*b^2*Ci(2*d*(f/e+1/x))*cos(2*c-2*d*f/e)/f+a^2*log(f+e/x)/f+1/2*b^2*log(f+e/x)/f+a^2*log(x)/f+1/2*b^2*log(x)/f+2*a*b*cos(c-d*f/e)*Si(d*(f/e+1/x))/f-2*a*b*cos(c)*Si(d/x)/f-2*a*b*Ci(d/x)*sin(c)/f-1/2*b^2*Si(2*d/x)*sin(2*c)/f+1/2*b^2*Si(2*d*(f/e+1/x))*sin(2*c-2*d*f/e)/f+2*a*b*Ci(d*(f/e+1/x))*sin(c-d*f/e)/f],
[(a+b*sin(c+d/x))^2/(e+f*x)^2,x,12,a^2/(e*(f+e/x))-2*a*b*d*Ci(d*(f/e+1/x))*cos(c-d*f/e)/e^2-b^2*d*cos(2*c-2*d*f/e)*Si(2*d*(f/e+1/x))/e^2-b^2*d*Ci(2*d*(f/e+1/x))*sin(2*c-2*d*f/e)/e^2+2*a*b*d*Si(d*(f/e+1/x))*sin(c-d*f/e)/e^2+2*a*b*sin(c+d/x)/(e*(f+e/x))+b^2*sin(c+d/x)^2/(e*(f+e/x))],
[(a+b*sin(c+d/x))^2/(e+f*x)^3,x,27,-1/2*a^2*f/(e^2*(f+e/x)^2)+a^2/(e^2*(f+e/x))+b^2*d^2*f*Ci(2*d*(f/e+1/x))*cos(2*c-2*d*f/e)/e^4-2*a*b*d*Ci(d*(f/e+1/x))*cos(c-d*f/e)/e^3-a*b*d*f*cos(c+d/x)/(e^3*(f+e/x))-a*b*d^2*f*cos(c-d*f/e)*Si(d*(f/e+1/x))/e^4-b^2*d*cos(2*c-2*d*f/e)*Si(2*d*(f/e+1/x))/e^3-b^2*d*Ci(2*d*(f/e+1/x))*sin(2*c-2*d*f/e)/e^3-b^2*d^2*f*Si(2*d*(f/e+1/x))*sin(2*c-2*d*f/e)/e^4-a*b*d^2*f*Ci(d*(f/e+1/x))*sin(c-d*f/e)/e^4+2*a*b*d*Si(d*(f/e+1/x))*sin(c-d*f/e)/e^3-a*b*f*sin(c+d/x)/(e^2*(f+e/x)^2)+2*a*b*sin(c+d/x)/(e^2*(f+e/x))-b^2*d*f*cos(c+d/x)*sin(c+d/x)/(e^3*(f+e/x))-1/2*b^2*f*sin(c+d/x)^2/(e^2*(f+e/x)^2)+b^2*sin(c+d/x)^2/(e^2*(f+e/x))],

# p<0
[(e+f*x)^2/(a+b*sin(c+d/x)),x,0,Unintegrable((e+f*x)^2/(a+b*sin(c+d/x)),x)],
[(e+f*x)/(a+b*sin(c+d/x)),x,0,Unintegrable((e+f*x)/(a+b*sin(c+d/x)),x)],
[1/(a+b*sin(c+d/x)),x,0,Unintegrable(1/(a+b*sin(c+d/x)),x)],
[(e+f*x)/(a+b*sin(c+d/x)),x,0,Unintegrable((e+f*x)/(a+b*sin(c+d/x)),x)],
[(e+f*x)^2/(a+b*sin(c+d/x)),x,0,Unintegrable((e+f*x)^2/(a+b*sin(c+d/x)),x)],
[(e+f*x)^2/(a+b*sin(c+d/x))^2,x,0,Unintegrable((e+f*x)^2/(a+b*sin(c+d/x))^2,x)],
[(e+f*x)/(a+b*sin(c+d/x))^2,x,0,Unintegrable((e+f*x)/(a+b*sin(c+d/x))^2,x)],
[1/(a+b*sin(c+d/x))^2,x,0,Unintegrable(1/(a+b*sin(c+d/x))^2,x)],
[(e+f*x)/(a+b*sin(c+d/x))^2,x,0,Unintegrable((e+f*x)/(a+b*sin(c+d/x))^2,x)],
[(e+f*x)^2/(a+b*sin(c+d/x))^2,x,0,Unintegrable((e+f*x)^2/(a+b*sin(c+d/x))^2,x)],

# Integrands of the form (e+f x)^m (a+b Sin[c+d x^n])^p when p symbolic
[(e+f*x)^m*(a+b*sin(c+d/x))^p,x,0,Unintegrable((e+f*x)^m*(a+b*sin(c+d/x))^p,x)],

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

# Integrands of the form x^m (c Sin[a+b x^n]^p)^(q/3)

# Integrands of the form x^m (c Sin[a+b x^n]^3)^(1/3)

# n>0
[x^m*(c*sin(a+b*x)^3)^(1/3),x,4,-1/2*exp(I*a)*x^m*csc(a+b*x)*GAMMA(1+m,-I*b*x)*(c*sin(a+b*x)^3)^(1/3)/(b*(-I*b*x)^m)-1/2*x^m*csc(a+b*x)*GAMMA(1+m,I*b*x)*(c*sin(a+b*x)^3)^(1/3)/(b*exp(I*a)*(I*b*x)^m)],
[x^3*(c*sin(a+b*x)^3)^(1/3),x,5,-6*(c*sin(a+b*x)^3)^(1/3)/b^4+3*x^2*(c*sin(a+b*x)^3)^(1/3)/b^2+6*x*cot(a+b*x)*(c*sin(a+b*x)^3)^(1/3)/b^3-x^3*cot(a+b*x)*(c*sin(a+b*x)^3)^(1/3)/b],
[x^2*(c*sin(a+b*x)^3)^(1/3),x,4,2*x*(c*sin(a+b*x)^3)^(1/3)/b^2+2*cot(a+b*x)*(c*sin(a+b*x)^3)^(1/3)/b^3-x^2*cot(a+b*x)*(c*sin(a+b*x)^3)^(1/3)/b],
[x*(c*sin(a+b*x)^3)^(1/3),x,3,(c*sin(a+b*x)^3)^(1/3)/b^2-x*cot(a+b*x)*(c*sin(a+b*x)^3)^(1/3)/b],
[(c*sin(a+b*x)^3)^(1/3),x,2,-cot(a+b*x)*(c*sin(a+b*x)^3)^(1/3)/b],
[(c*sin(a+b*x)^3)^(1/3)/x,x,4,cos(a)*csc(a+b*x)*Si(b*x)*(c*sin(a+b*x)^3)^(1/3)+Ci(b*x)*csc(a+b*x)*sin(a)*(c*sin(a+b*x)^3)^(1/3)],
[(c*sin(a+b*x)^3)^(1/3)/x^2,x,5,-(c*sin(a+b*x)^3)^(1/3)/x+b*Ci(b*x)*cos(a)*csc(a+b*x)*(c*sin(a+b*x)^3)^(1/3)-b*csc(a+b*x)*Si(b*x)*sin(a)*(c*sin(a+b*x)^3)^(1/3)],
[(c*sin(a+b*x)^3)^(1/3)/x^3,x,6,-1/2*(c*sin(a+b*x)^3)^(1/3)/x^2-1/2*b*cot(a+b*x)*(c*sin(a+b*x)^3)^(1/3)/x-1/2*b^2*cos(a)*csc(a+b*x)*Si(b*x)*(c*sin(a+b*x)^3)^(1/3)-1/2*b^2*Ci(b*x)*csc(a+b*x)*sin(a)*(c*sin(a+b*x)^3)^(1/3)],
[x^m*(c*sin(a+b*x^2)^3)^(1/3),x,4,1/4*I*exp(I*a)*x^(1+m)*(-I*b*x^2)^(1/2*(-1-m))*csc(a+b*x^2)*GAMMA(1/2*(1+m),-I*b*x^2)*(c*sin(a+b*x^2)^3)^(1/3)-1/4*I*x^(1+m)*(I*b*x^2)^(1/2*(-1-m))*csc(a+b*x^2)*GAMMA(1/2*(1+m),I*b*x^2)*(c*sin(a+b*x^2)^3)^(1/3)/exp(I*a)],
[x^3*(c*sin(a+b*x^2)^3)^(1/3),x,4,1/2*(c*sin(a+b*x^2)^3)^(1/3)/b^2-1/2*x^2*cot(a+b*x^2)*(c*sin(a+b*x^2)^3)^(1/3)/b],
[x^2*(c*sin(a+b*x^2)^3)^(1/3),x,5,-1/2*x*cot(a+b*x^2)*(c*sin(a+b*x^2)^3)^(1/3)/b+1/2*cos(a)*csc(a+b*x^2)*FresnelC(x*sqrt(b)*sqrt(2/Pi))*(c*sin(a+b*x^2)^3)^(1/3)*sqrt(1/2*Pi)/b^(3/2)-1/2*csc(a+b*x^2)*FresnelS(x*sqrt(b)*sqrt(2/Pi))*sin(a)*(c*sin(a+b*x^2)^3)^(1/3)*sqrt(1/2*Pi)/b^(3/2)],
[x*(c*sin(a+b*x^2)^3)^(1/3),x,3,-1/2*cot(a+b*x^2)*(c*sin(a+b*x^2)^3)^(1/3)/b],
[(c*sin(a+b*x^2)^3)^(1/3),x,4,cos(a)*csc(a+b*x^2)*FresnelS(x*sqrt(b)*sqrt(2/Pi))*(c*sin(a+b*x^2)^3)^(1/3)*sqrt(1/2*Pi)/sqrt(b)+csc(a+b*x^2)*FresnelC(x*sqrt(b)*sqrt(2/Pi))*sin(a)*(c*sin(a+b*x^2)^3)^(1/3)*sqrt(1/2*Pi)/sqrt(b)],
[(c*sin(a+b*x^2)^3)^(1/3)/x,x,4,1/2*cos(a)*csc(a+b*x^2)*Si(b*x^2)*(c*sin(a+b*x^2)^3)^(1/3)+1/2*Ci(b*x^2)*csc(a+b*x^2)*sin(a)*(c*sin(a+b*x^2)^3)^(1/3)],
[(c*sin(a+b*x^2)^3)^(1/3)/x^2,x,5,-(c*sin(a+b*x^2)^3)^(1/3)/x+cos(a)*csc(a+b*x^2)*FresnelC(x*sqrt(b)*sqrt(2/Pi))*(c*sin(a+b*x^2)^3)^(1/3)*sqrt(b)*sqrt(2*Pi)-csc(a+b*x^2)*FresnelS(x*sqrt(b)*sqrt(2/Pi))*sin(a)*(c*sin(a+b*x^2)^3)^(1/3)*sqrt(b)*sqrt(2*Pi)],
[(c*sin(a+b*x^2)^3)^(1/3)/x^3,x,6,-1/2*(c*sin(a+b*x^2)^3)^(1/3)/x^2+1/2*b*Ci(b*x^2)*cos(a)*csc(a+b*x^2)*(c*sin(a+b*x^2)^3)^(1/3)-1/2*b*csc(a+b*x^2)*Si(b*x^2)*sin(a)*(c*sin(a+b*x^2)^3)^(1/3)],

# n<0

# n symbolic
[x^m*(c*sin(a+b*x^n)^3)^(1/3),x,4,1/2*I*exp(I*a)*x^(1+m)*csc(a+b*x^n)*GAMMA((1+m)/n,-I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(n*(-I*b*x^n)^((1+m)/n))-1/2*I*x^(1+m)*csc(a+b*x^n)*GAMMA((1+m)/n,I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(exp(I*a)*n*(I*b*x^n)^((1+m)/n))],
[x^3*(c*sin(a+b*x^n)^3)^(1/3),x,4,1/2*I*exp(I*a)*x^4*csc(a+b*x^n)*GAMMA(4/n,-I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(n*(-I*b*x^n)^(4/n))-1/2*I*x^4*csc(a+b*x^n)*GAMMA(4/n,I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(exp(I*a)*n*(I*b*x^n)^(4/n))],
[x^2*(c*sin(a+b*x^n)^3)^(1/3),x,4,1/2*I*exp(I*a)*x^3*csc(a+b*x^n)*GAMMA(3/n,-I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(n*(-I*b*x^n)^(3/n))-1/2*I*x^3*csc(a+b*x^n)*GAMMA(3/n,I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(exp(I*a)*n*(I*b*x^n)^(3/n))],
[x*(c*sin(a+b*x^n)^3)^(1/3),x,4,1/2*I*exp(I*a)*x^2*csc(a+b*x^n)*GAMMA(2/n,-I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(n*(-I*b*x^n)^(2/n))-1/2*I*x^2*csc(a+b*x^n)*GAMMA(2/n,I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(exp(I*a)*n*(I*b*x^n)^(2/n))],
[(c*sin(a+b*x^n)^3)^(1/3),x,4,1/2*I*exp(I*a)*x*csc(a+b*x^n)*GAMMA(1/n,-I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(n*(-I*b*x^n)^(1/n))-1/2*I*x*csc(a+b*x^n)*GAMMA(1/n,I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(exp(I*a)*n*(I*b*x^n)^(1/n))],
[(c*sin(a+b*x^n)^3)^(1/3)/x,x,4,cos(a)*csc(a+b*x^n)*Si(b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/n+Ci(b*x^n)*csc(a+b*x^n)*sin(a)*(c*sin(a+b*x^n)^3)^(1/3)/n],
[(c*sin(a+b*x^n)^3)^(1/3)/x^2,x,4,1/2*I*exp(I*a)*(-I*b*x^n)^(1/n)*csc(a+b*x^n)*GAMMA((-1)/n,-I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(n*x)-1/2*I*(I*b*x^n)^(1/n)*csc(a+b*x^n)*GAMMA((-1)/n,I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(exp(I*a)*n*x)],
[(c*sin(a+b*x^n)^3)^(1/3)/x^3,x,4,1/2*I*exp(I*a)*(-I*b*x^n)^(2/n)*csc(a+b*x^n)*GAMMA((-2)/n,-I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(n*x^2)-1/2*I*(I*b*x^n)^(2/n)*csc(a+b*x^n)*GAMMA((-2)/n,I*b*x^n)*(c*sin(a+b*x^n)^3)^(1/3)/(exp(I*a)*n*x^2)],

# Integrands of the form x^m (c Sin[a+b x^n]^3)^(2/3)

# n>0
[x^m*(c*sin(a+b*x)^3)^(2/3),x,6,1/2*x^(1+m)*csc(a+b*x)^2*(c*sin(a+b*x)^3)^(2/3)/(1+m)+I*2^(-3-m)*exp(2*I*a)*x^m*csc(a+b*x)^2*GAMMA(1+m,-2*I*b*x)*(c*sin(a+b*x)^3)^(2/3)/(b*(-I*b*x)^m)-I*2^(-3-m)*x^m*csc(a+b*x)^2*GAMMA(1+m,2*I*b*x)*(c*sin(a+b*x)^3)^(2/3)/(b*exp(2*I*a)*(I*b*x)^m)],
[x^3*(c*sin(a+b*x)^3)^(2/3),x,5,-3/8*(c*sin(a+b*x)^3)^(2/3)/b^4+3/4*x^2*(c*sin(a+b*x)^3)^(2/3)/b^2+3/4*x*cot(a+b*x)*(c*sin(a+b*x)^3)^(2/3)/b^3-1/2*x^3*cot(a+b*x)*(c*sin(a+b*x)^3)^(2/3)/b-3/8*x^2*csc(a+b*x)^2*(c*sin(a+b*x)^3)^(2/3)/b^2+1/8*x^4*csc(a+b*x)^2*(c*sin(a+b*x)^3)^(2/3)],
[x^2*(c*sin(a+b*x)^3)^(2/3),x,5,1/2*x*(c*sin(a+b*x)^3)^(2/3)/b^2+1/4*cot(a+b*x)*(c*sin(a+b*x)^3)^(2/3)/b^3-1/2*x^2*cot(a+b*x)*(c*sin(a+b*x)^3)^(2/3)/b-1/4*x*csc(a+b*x)^2*(c*sin(a+b*x)^3)^(2/3)/b^2+1/6*x^3*csc(a+b*x)^2*(c*sin(a+b*x)^3)^(2/3)],
[x*(c*sin(a+b*x)^3)^(2/3),x,3,1/4*(c*sin(a+b*x)^3)^(2/3)/b^2-1/2*x*cot(a+b*x)*(c*sin(a+b*x)^3)^(2/3)/b+1/4*x^2*csc(a+b*x)^2*(c*sin(a+b*x)^3)^(2/3)],
[(c*sin(a+b*x)^3)^(2/3),x,3,-1/2*cot(a+b*x)*(c*sin(a+b*x)^3)^(2/3)/b+1/2*x*csc(a+b*x)^2*(c*sin(a+b*x)^3)^(2/3)],
[(c*sin(a+b*x)^3)^(2/3)/x,x,6,-1/2*Ci(2*b*x)*cos(2*a)*csc(a+b*x)^2*(c*sin(a+b*x)^3)^(2/3)+1/2*csc(a+b*x)^2*log(x)*(c*sin(a+b*x)^3)^(2/3)+1/2*csc(a+b*x)^2*Si(2*b*x)*sin(2*a)*(c*sin(a+b*x)^3)^(2/3)],
[(c*sin(a+b*x)^3)^(2/3)/x^2,x,6,-(c*sin(a+b*x)^3)^(2/3)/x+b*cos(2*a)*csc(a+b*x)^2*Si(2*b*x)*(c*sin(a+b*x)^3)^(2/3)+b*Ci(2*b*x)*csc(a+b*x)^2*sin(2*a)*(c*sin(a+b*x)^3)^(2/3)],
[(c*sin(a+b*x)^3)^(2/3)/x^3,x,8,-1/2*(c*sin(a+b*x)^3)^(2/3)/x^2-b*cot(a+b*x)*(c*sin(a+b*x)^3)^(2/3)/x+b^2*Ci(2*b*x)*cos(2*a)*csc(a+b*x)^2*(c*sin(a+b*x)^3)^(2/3)-b^2*csc(a+b*x)^2*Si(2*b*x)*sin(2*a)*(c*sin(a+b*x)^3)^(2/3)],
[x^m*(c*sin(a+b*x^2)^3)^(2/3),x,6,1/2*x^(1+m)*csc(a+b*x^2)^2*(c*sin(a+b*x^2)^3)^(2/3)/(1+m)+2^(-7/2-1/2*m)*exp(2*I*a)*x^(1+m)*(-I*b*x^2)^(1/2*(-1-m))*csc(a+b*x^2)^2*GAMMA(1/2*(1+m),-2*I*b*x^2)*(c*sin(a+b*x^2)^3)^(2/3)+2^(-7/2-1/2*m)*x^(1+m)*(I*b*x^2)^(1/2*(-1-m))*csc(a+b*x^2)^2*GAMMA(1/2*(1+m),2*I*b*x^2)*(c*sin(a+b*x^2)^3)^(2/3)/exp(2*I*a)],
[x^3*(c*sin(a+b*x^2)^3)^(2/3),x,4,1/8*(c*sin(a+b*x^2)^3)^(2/3)/b^2-1/4*x^2*cot(a+b*x^2)*(c*sin(a+b*x^2)^3)^(2/3)/b+1/8*x^4*csc(a+b*x^2)^2*(c*sin(a+b*x^2)^3)^(2/3)],
[x^2*(c*sin(a+b*x^2)^3)^(2/3),x,7,1/6*x^3*csc(a+b*x^2)^2*(c*sin(a+b*x^2)^3)^(2/3)-1/8*x*csc(a+b*x^2)^2*(c*sin(a+b*x^2)^3)^(2/3)*sin(2*a+2*b*x^2)/b+1/16*cos(2*a)*csc(a+b*x^2)^2*FresnelS(2*x*sqrt(b)/sqrt(Pi))*(c*sin(a+b*x^2)^3)^(2/3)*sqrt(Pi)/b^(3/2)+1/16*csc(a+b*x^2)^2*FresnelC(2*x*sqrt(b)/sqrt(Pi))*sin(2*a)*(c*sin(a+b*x^2)^3)^(2/3)*sqrt(Pi)/b^(3/2)],
[x*(c*sin(a+b*x^2)^3)^(2/3),x,4,-1/4*cot(a+b*x^2)*(c*sin(a+b*x^2)^3)^(2/3)/b+1/4*x^2*csc(a+b*x^2)^2*(c*sin(a+b*x^2)^3)^(2/3)],
[(c*sin(a+b*x^2)^3)^(2/3),x,6,1/2*x*csc(a+b*x^2)^2*(c*sin(a+b*x^2)^3)^(2/3)-1/4*cos(2*a)*csc(a+b*x^2)^2*FresnelC(2*x*sqrt(b)/sqrt(Pi))*(c*sin(a+b*x^2)^3)^(2/3)*sqrt(Pi)/sqrt(b)+1/4*csc(a+b*x^2)^2*FresnelS(2*x*sqrt(b)/sqrt(Pi))*sin(2*a)*(c*sin(a+b*x^2)^3)^(2/3)*sqrt(Pi)/sqrt(b)],
[(c*sin(a+b*x^2)^3)^(2/3)/x,x,6,-1/4*Ci(2*b*x^2)*cos(2*a)*csc(a+b*x^2)^2*(c*sin(a+b*x^2)^3)^(2/3)+1/2*csc(a+b*x^2)^2*log(x)*(c*sin(a+b*x^2)^3)^(2/3)+1/4*csc(a+b*x^2)^2*Si(2*b*x^2)*sin(2*a)*(c*sin(a+b*x^2)^3)^(2/3)],
[(c*sin(a+b*x^2)^3)^(2/3)/x^2,x,7,-(c*sin(a+b*x^2)^3)^(2/3)/x+cos(2*a)*csc(a+b*x^2)^2*FresnelS(2*x*sqrt(b)/sqrt(Pi))*(c*sin(a+b*x^2)^3)^(2/3)*sqrt(b)*sqrt(Pi)+csc(a+b*x^2)^2*FresnelC(2*x*sqrt(b)/sqrt(Pi))*sin(2*a)*(c*sin(a+b*x^2)^3)^(2/3)*sqrt(b)*sqrt(Pi)],
[(c*sin(a+b*x^2)^3)^(2/3)/x^3,x,8,-1/4*csc(a+b*x^2)^2*(c*sin(a+b*x^2)^3)^(2/3)/x^2+1/4*cos(2*(a+b*x^2))*csc(a+b*x^2)^2*(c*sin(a+b*x^2)^3)^(2/3)/x^2+1/2*b*cos(2*a)*csc(a+b*x^2)^2*Si(2*b*x^2)*(c*sin(a+b*x^2)^3)^(2/3)+1/2*b*Ci(2*b*x^2)*csc(a+b*x^2)^2*sin(2*a)*(c*sin(a+b*x^2)^3)^(2/3)],

# n<0

# n symbolic
[x^m*(c*sin(a+b*x^n)^3)^(2/3),x,6,1/2*x^(1+m)*csc(a+b*x^n)^2*(c*sin(a+b*x^n)^3)^(2/3)/(1+m)+exp(2*I*a)*x^(1+m)*csc(a+b*x^n)^2*GAMMA((1+m)/n,-2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(2^((1+m+2*n)/n)*n*(-I*b*x^n)^((1+m)/n))+x^(1+m)*csc(a+b*x^n)^2*GAMMA((1+m)/n,2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(2^((1+m+2*n)/n)*exp(2*I*a)*n*(I*b*x^n)^((1+m)/n))],
[x^3*(c*sin(a+b*x^n)^3)^(2/3),x,6,1/8*x^4*csc(a+b*x^n)^2*(c*sin(a+b*x^n)^3)^(2/3)+4^(-1+(-2)/n)*exp(2*I*a)*x^4*csc(a+b*x^n)^2*GAMMA(4/n,-2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(n*(-I*b*x^n)^(4/n))+4^(-1+(-2)/n)*x^4*csc(a+b*x^n)^2*GAMMA(4/n,2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(exp(2*I*a)*n*(I*b*x^n)^(4/n))],
[x^2*(c*sin(a+b*x^n)^3)^(2/3),x,6,1/6*x^3*csc(a+b*x^n)^2*(c*sin(a+b*x^n)^3)^(2/3)+2^(-2+(-3)/n)*exp(2*I*a)*x^3*csc(a+b*x^n)^2*GAMMA(3/n,-2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(n*(-I*b*x^n)^(3/n))+2^(-2+(-3)/n)*x^3*csc(a+b*x^n)^2*GAMMA(3/n,2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(exp(2*I*a)*n*(I*b*x^n)^(3/n))],
[x*(c*sin(a+b*x^n)^3)^(2/3),x,6,1/4*x^2*csc(a+b*x^n)^2*(c*sin(a+b*x^n)^3)^(2/3)+4^(-1+(-1)/n)*exp(2*I*a)*x^2*csc(a+b*x^n)^2*GAMMA(2/n,-2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(n*(-I*b*x^n)^(2/n))+4^(-1+(-1)/n)*x^2*csc(a+b*x^n)^2*GAMMA(2/n,2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(exp(2*I*a)*n*(I*b*x^n)^(2/n))],
[(c*sin(a+b*x^n)^3)^(2/3),x,6,1/2*x*csc(a+b*x^n)^2*(c*sin(a+b*x^n)^3)^(2/3)+2^(-2+(-1)/n)*exp(2*I*a)*x*csc(a+b*x^n)^2*GAMMA(1/n,-2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(n*(-I*b*x^n)^(1/n))+2^(-2+(-1)/n)*x*csc(a+b*x^n)^2*GAMMA(1/n,2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(exp(2*I*a)*n*(I*b*x^n)^(1/n))],
[(c*sin(a+b*x^n)^3)^(2/3)/x,x,6,-1/2*Ci(2*b*x^n)*cos(2*a)*csc(a+b*x^n)^2*(c*sin(a+b*x^n)^3)^(2/3)/n+1/2*csc(a+b*x^n)^2*log(x)*(c*sin(a+b*x^n)^3)^(2/3)+1/2*csc(a+b*x^n)^2*Si(2*b*x^n)*sin(2*a)*(c*sin(a+b*x^n)^3)^(2/3)/n],
[(c*sin(a+b*x^n)^3)^(2/3)/x^2,x,6,-1/2*csc(a+b*x^n)^2*(c*sin(a+b*x^n)^3)^(2/3)/x+2^(-2+1/n)*exp(2*I*a)*(-I*b*x^n)^(1/n)*csc(a+b*x^n)^2*GAMMA((-1)/n,-2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(n*x)+2^(-2+1/n)*(I*b*x^n)^(1/n)*csc(a+b*x^n)^2*GAMMA((-1)/n,2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(exp(2*I*a)*n*x)],
[(c*sin(a+b*x^n)^3)^(2/3)/x^3,x,6,-1/4*csc(a+b*x^n)^2*(c*sin(a+b*x^n)^3)^(2/3)/x^2+4^(-1+1/n)*exp(2*I*a)*(-I*b*x^n)^(2/n)*csc(a+b*x^n)^2*GAMMA((-2)/n,-2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(n*x^2)+4^(-1+1/n)*(I*b*x^n)^(2/n)*csc(a+b*x^n)^2*GAMMA((-2)/n,2*I*b*x^n)*(c*sin(a+b*x^n)^3)^(2/3)/(exp(2*I*a)*n*x^2)]]:
