The integration of these functions can be performed by the substitution of
or
by a function in terms of
respectively.
By the double-angle formula,
. Rearranging to make
the subject,
.
We know by the Pythagorean identity
that
, so
. Rearranging,
.
By substituting
for
,
. Similarly for
,
These can be integrated by using the primitives of cosine and sine
For cos2 α
For sin2 α