Consider an integral of the type
,
where *R*(*u*,*v*)

**1.** If for all *u*, *v* on the unit circle we have
*R*(-*u*,*v*) = -*R*(*u*,*v*),*y* = cos(*x*).

This in fact means that we consider integrals of the type

where the function *G* itself does not feature trigonometric functions.

Example:

**2.** If for all *u*, *v* on the unit circle we have
*R*(*u*,-*v*) = -*R*(*u*,*v*),*y* = sin(*x*).

This in fact means that we consider integrals of the type

where the function *G* itself does not feature trigonometric functions.

Example:

**3.** If for all *u*, *v* on the unit circle we have
*R*(-*u*,-*v*) = *R*(*u*,*v*),*y* = tan(*x*).

This in fact means that we consider integrals of the type

where the function *G* itself does not feature trigonometric functions.

Example: