1. The problem is to evaluate the integral $$\int \frac{7}{2x^{9/4}} \, dx$$. 2. Rewrite the integrand using properties of exponents: $$\frac{7}{2x^{9/4}} = \frac{7}{2} x^{-9/4}$$. 3. The integral becomes $$\int \frac{7}{2} x^{-9/4} \, dx = \frac{7}{2} \int x^{-9/4} \, dx$$. 4. Use the power rule for integration: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$, valid for $$n \neq -1$$. 5. Here, $$n = -\frac{9}{4}$$, so $$n+1 = -\frac{9}{4} + 1 = -\frac{5}{4}$$. 6. Applying the power rule: $$\int x^{-9/4} \, dx = \frac{x^{-5/4}}{-5/4} + C = -\frac{4}{5} x^{-5/4} + C$$. 7. Multiply by the constant $$\frac{7}{2}$$: $$\frac{7}{2} \times -\frac{4}{5} x^{-5/4} = -\frac{28}{10} x^{-5/4} = -\frac{14}{5} x^{-5/4}$$. 8. Therefore, the integral evaluates to $$-\frac{14}{5} x^{-5/4} + C$$. Final answer: $$\boxed{-\frac{14}{5} x^{-5/4} + C}$$