Question

Integration of sin^p x / cos^p+2 x​

Answer 1

We know for

f(x)=1/4(sin4x+cos4x) ; g(x)

=1/6(sin6x+cos6x)

have f(x)−g(x)=112. My question is

Are there other real p and q such that

f(x)=1/p(sinpx+cospx) ; g(x)

=1/q(sinqx+cosqx)

give us f(x)−g(x)=C for a real