\( \int _{}^{}\tan (x)^{2} d x \)

Did you know that the integral of \(\tan^2(x)\) is a classic! To solve \(\int \tan^2(x) \, dx\), we can use the fact that \(\tan^2(x) = \sec^2(x) - 1\). This transforms our integral to \(\int (\sec^2(x) - 1) \, dx\), which is much easier to handle! This gives us \(\tan(x) - x + C\), where \(C\) is the constant of integration. Now, while mastering this integral is fun, be mindful of the trigonometric identities! A common mistake is forgetting that the integral of \(\sec^2(x)\) directly leads to \(\tan(x)\), while the \(-1\) term simply evaluates to \(-x\). Keep these identities sharp, and you’ll be integrating with confidence!