1. The problem is to find the integral of $\tan^2 x$ with respect to $x$. 2. Recall that $\tan^2 x = \sec^2 x - 1$ from the Pythagorean identity. 3. So, the integral becomes: $$\int \tan^2 x\,dx = \int (\sec^2 x - 1)\,dx$$ 4. We can split the integral: $$\int \sec^2 x\,dx - \int 1\,dx$$ 5. The integral of $\sec^2 x$ is $\tan x$, and the integral of $1$ is $x$, so: $$\tan x - x + C$$ 6. Therefore, the integral of $\tan^2 x$ is: $$\int \tan^2 x\,dx = \tan x - x + C$$