1. The problem is to practice using reduction formulas for integration, which help simplify integrals of powers of functions. 2. A common reduction formula is for integrals of the form $$I_n = \int \sin^n(x) \, dx$$ or $$I_n = \int \cos^n(x) \, dx$$. 3. For example, the reduction formula for $$I_n = \int \sin^n(x) \, dx$$ is: $$I_n = -\frac{1}{n} \sin^{n-1}(x) \cos(x) + \frac{n-1}{n} I_{n-2}$$ 4. This formula reduces the power from $$n$$ to $$n-2$$, making the integral easier to solve step-by-step. 5. Practice questions: 1. Use the reduction formula to find $$\int \sin^4(x) \, dx$$. 2. Use the reduction formula to evaluate $$\int \cos^5(x) \, dx$$. 3. Derive the reduction formula for $$\int \tan^n(x) \, dx$$. 4. Use the reduction formula to compute $$\int x^n e^x \, dx$$ for integer $$n$$. 5. Apply the reduction formula to $$\int \sec^n(x) \, dx$$ for even $$n$$. 6. These problems help you understand how to break down complex integrals into simpler ones using reduction formulas.