# Maple integration test file: "0 Independent test suites\Jeffrey Problems.txt"

lst:=[

# David Jeffrey - Rectifying Transformations for Trig Integration (1997)

# Problem (1.2)
[3/(5-4*cos(x)),x,2,x+2*arctan(sin(x)/(2-cos(x)))],

# Problem (1.4)
[(1+cos(x)+2*sin(x))/(3+cos(x)^2+2*sin(x)-2*cos(x)*sin(x)),x,-43,-arctan((2*cos(x)-sin(x))/(2+sin(x)))],

# Problem (1.5)
[(2+cos(x)+5*sin(x))/(4*cos(x)-2*sin(x)+cos(x)*sin(x)-2*sin(x)^2),x,-25,-log(1-3*cos(x)+sin(x))+log(3+cos(x)+sin(x))],

# Problem (3.3)
[(3+7*cos(x)+2*sin(x))/(1+4*cos(x)+3*cos(x)^2-5*sin(x)-cos(x)*sin(x)),x,-32,-log(1+cos(x)-2*sin(x))+log(3+cos(x)+sin(x))],

# Problem 
[(-1+4*cos(x)+5*cos(x)^2)/(-1-4*cos(x)-3*cos(x)^2+4*cos(x)^3),x,-2,x-2*arctan(sin(x)/(3+cos(x)))-2*arctan((3*sin(x)+7*cos(x)*sin(x))/(1+2*cos(x)+5*cos(x)^2))],

# Problem 
[(-5+2*cos(x)+7*cos(x)^2)/(-1+2*cos(x)-9*cos(x)^2+4*cos(x)^3),x,-2,x-2*arctan(2*cos(x)*sin(x)/(1-cos(x)+2*cos(x)^2))],

# Problem (3.4)
[3/(5+4*sin(x)),x,2,x+2*arctan(cos(x)/(2+sin(x)))],

# Problem (3.6)
[2/(1+cos(x)^2),x,3,x*sqrt(2)-arctan(cos(x)*sin(x)/(1+cos(x)^2+sqrt(2)))*sqrt(2)],

# Problem (3.8)
[1/(p+q*cos(x)+r*sin(x)),x,3,2*arctan((r+(p-q)*tan(1/2*x))/sqrt(p^2-q^2-r^2))/sqrt(p^2-q^2-r^2)]]:
