**Finding the Integral of f(tan x)**

To find the integral of f(tan x) with respect to x, denoted as ∫f(tan x)dx, we need to use a substitution method. Let's go through the steps:

1. **Substitution**
Let's substitute u = tan x. This implies du/dx = sec^2 x, and dx = du/sec^2 x.

2. **Rewriting the Integral**
Now, we can rewrite the integral as ∫f(u) * (du/sec^2 x).

3. **Simplifying the Integral**
Recall that sec^2 x = 1 + tan^2 x. So, we can rewrite the integral as ∫f(u) * (du/(1 + u^2)).

4. **Changing the Variable**
We can change the variable of integration from x to u, as all the x terms have been eliminated. The integral becomes ∫f(u) * (du/(1 + u^2)).

5. **Evaluating the Integral**
Now, we can integrate the function f(u) with respect to u using appropriate integration techniques.

6. **Back Substitution**
After integrating with respect to u, we can substitute back u = tan x to obtain the final result.

**Overall Steps:**
To summarize, the steps to find the integral of f(tan x)dx are as follows:

1. Substitute u = tan x.
2. Rewrite the integral using the substitution.
3. Simplify the integral by expressing sec^2 x in terms of tan x.
4. Change the variable of integration from x to u.
5. Integrate the function f(u) with respect to u.
6. Substitute u = tan x back into the result.

Note: The final expression obtained after integrating with respect to u might not be in terms of elementary functions, and it may require further techniques or approximations to evaluate the integral.