To integrate the given function, we will use the substitution method. Let's break down the steps to solve this problem.

1. Identify the substitution:
In this case, we will substitute u = log(tanx) because it simplifies the integral by reducing the number of trigonometric functions involved.

2. Find the derivative of the substitution:
To find the derivative of u with respect to x, we can use the chain rule.
du/dx = d(log(tanx))/dx

3. Solve for dx in terms of du:
Rearranging the above equation, we get dx = du/(d(log(tanx))/dx)

4. Substitute the new variables into the integral:
The given integral becomes ∫(3 sec^2x log(tanx)) dx = ∫(3 sec^2x u) (du/(d(log(tanx))/dx))

5. Simplify the integral using the substitution:
∫(3 sec^2x u) (du/(d(log(tanx))/dx)) = 3 ∫sec^2x u du
= 3 ∫u d(secx)
= 3u secx - 3 ∫secx du

6. Evaluate the integral:
The integral of secx with respect to u is log|secx + tanx| + C.

7. Substitute the original variable back in:
Putting u = log(tanx) back into the result, we have:
3u secx - 3 ∫secx du = 3(log(tanx)) secx - 3(log|secx + tanx| + C)

8. Simplify the expression:
Using the properties of logarithms, we can simplify the expression as follows:
3(log(tanx)) secx - 3(log|secx + tanx| + C) = 3log(tanx) secx - 3log|secx + tanx| - 3C

Therefore, the correct answer is option 'C': tanx (log(tanx)-1) + C.