The discussion focuses on the application of reduction formulae for integrating powers of tangent, specifically $$\int\tan^n x\,dx$$. The correct formula is established as $$\int\tan^n x\,dx = \frac{\tan^{n-1} x}{n - 1} - \int\tan^{n-2} x\,dx$$. An example using $$n=4$$ illustrates the process, resulting in $$\int\tan^4 x\,dx = \frac{1}{3}\tan^3 x - \tan x + x + C$$. This example demonstrates the step-by-step application of the reduction formula to simplify the integration of higher powers of tangent.
PREREQUISITESStudents and educators in mathematics, particularly those focusing on calculus and trigonometry, as well as anyone seeking to improve their skills in integrating trigonometric functions.