To find the integral of $\tan^2 x$, we can use the trigonometric identity: $\tan^2 x = \sec^2 x - 1$

So, the integral becomes: $\int \tan^2 x \, dx = \int (\sec^2 x - 1) \, dx$

We can split this into two separate integrals: $\int (\sec^2 x - 1) \, dx = \int \sec^2 x \, dx - \int 1 \, dx$

Now, we integrate each term separately: $\int \sec^2 x \, dx = \tan x + C_1$ $\int 1 \, dx = x + C_2$

Combining these results, we get: $\int (\sec^2 x - 1) \, dx = \tan x - x + C$

where $C$ is the constant of integration, which is $C = C_1 - C_2$.

Thus, the final answer is: $\int \tan^2 x \, dx = \tan x - x + C$

Would you like more details or have any questions about this solution?

Here are 5 related questions you can ask:

1. How do you integrate $\sec^2 x$?
2. What is the integral of $\tan x$?
3. Can you explain how to use substitution in integrals?
4. How do you find the derivative of $\tan x$?
5. What are some applications of integrals in real life?

Tip: When dealing with trigonometric integrals, using identities to simplify the integrand can often make the integration process easier.