We need to use:

with a = 3

We simplify the denominator of the question before proceeding to integrate:

(Some explanation for what we just did:)

9^3/2 = (√9)³ = 3³ = 27

tan² θ + 1 = sec² θ

(a²)^3/2 = a³

Now, substituting

and

into the given integral gives us:

We now need to get our answer in terms of x (since the question was in terms of x).

Since we let x = 3 tan θ, we get

and we can draw a triangle to find the value of sin θ :

Hence, we notice that

Therefore, we can conclude that: