Step 1: Recall the identity for tangent squared: tan^2(x) = sec^2(x) - 1.
Step 2: Substitute this identity into the integral: ∫ (tan(x))^2 dx becomes ∫ (sec^2(x) - 1) dx.
Step 3: Split the integral into two parts: ∫ sec^2(x) dx - ∫ 1 dx.
Step 4: Calculate the first integral: ∫ sec^2(x) dx = tan(x).
Step 5: Calculate the second integral: ∫ 1 dx = x.
Step 6: Combine the results: tan(x) - x + C, where C is the constant of integration.
Integration of Trigonometric Functions – The question tests the ability to integrate the square of the tangent function using trigonometric identities.
Trigonometric Identities – The use of the identity tan^2(x) = sec^2(x) - 1 is crucial for simplifying the integral.
