=

Adding the powers , -3 + -5 = -8

Since it is an even number, we will divide numerator and denominator by cos⁸x

=

= = =

= ∫

We know, (a + b)³ = a³ + b³ + 3a²b + 3ab²

Here, a = 1 and b = tan²x

Hence, ∫ = ∫

Let tan x = t, then dt = d(tanx) = sec²xdx

Put these values in above equation:

= ( since ∫xⁿ dx = + c and ∫t⁻¹ dt = logt)

=

=