Use u-substitution. Let u = sec(x).

cos²(x) – sin²(x) = cos(2x)

Use u-substitution. Let u = sin(2x).

Note: Given dx, x is the only variable.

$\left.=\frac{3}{5}ax^{5/3}-bx\right|_0^a$

The integrand is a multiple of an inverse trigonometric function. Which one?