Given:

As we can see f(x) =x¹⁷ .cos⁴x and f(-x) = (-x)¹⁷ .cos⁴(-x) = -x¹⁷ .cos⁴x

i.e. f(x) = -f(-x)

so, it is an odd function.

It is also known that if f(x) is an odd function then,

Hence proved.