Integral Tan Squared Bbbee1

1. **State the problem:** We need to find the integral $$I = \int \tan^{2}(x) \, dx$$. 2. **Recall the identity:** Use the trigonometric identity $$\tan^{2}(x) = \sec^{2}(x) - 1$$. 3. **Rewrite the integral:** Substitute the identity into the integral: $$I = \int (\sec^{2}(x) - 1) \, dx = \int \sec^{2}(x) \, dx - \int 1 \, dx$$. 4. **Integrate each term:** - The integral of $$\sec^{2}(x)$$ is $$\tan(x) + C$$. - The integral of $$1$$ is $$x + C$$. 5. **Combine results:** $$I = \tan(x) - x + C$$. **Final answer:** $$\boxed{\int \tan^{2}(x) \, dx = \tan(x) - x + C}$$