integral(sin(2x)+5tan^2 x csc^2 x)dx=

Answer 1

in the first term, let u = 2x
Int(sin(2x)) = 1/2 Int(sin(u) du)

in the second term, let u = cot(x), so du = - csc^2 x dx
int(5tan^2 x csc^2 x) = -5 Int(1/u^2 du), a simple power rule term