Mathematics

The key is recognizing that $\tan^2 x$ isn't directly integrable, but you can rewrite it using a fundamental trig identity. Since $\tan^2 x = \sec^2 x - 1$, you split the integral into two pieces—one that's a standard derivative form and one that's just a constant. This transforms an awkward trig integral into something straightforward.

The key is recognizing that $\tan^2 x$ isn't directly integrable, but you can rewrite it using a fundamental trig identity. Since $\tan^2 x = \sec^2 x - 1$, you split the integral into two pieces—one that's a standard derivative form and one that's just a constant. This transforms an awkward trig integral into something straightforward.