1. **Problem:** Compute the integral $$\int \frac{t^2 - 2t^4}{t^4} dt$$. 2. **Rewrite the integrand:** Simplify the expression inside the integral by dividing each term by $$t^4$$: $$\frac{t^2}{t^4} - \frac{2t^4}{t^4} = t^{2-4} - 2 = t^{-2} - 2$$. 3. **Integral formula:** Recall that $$\int t^n dt = \frac{t^{n+1}}{n+1} + C$$ for $$n \neq -1$$. 4. **Integrate term-by-term:** - For $$t^{-2}$$, $$n = -2$$, so $$\int t^{-2} dt = \frac{t^{-2+1}}{-2+1} + C = \frac{t^{-1}}{-1} + C = -t^{-1} + C$$. - For $$-2$$, treat as constant: $$\int -2 dt = -2t + C$$. 5. **Combine results:** $$\int \left(t^{-2} - 2\right) dt = -t^{-1} - 2t + C = -\frac{1}{t} - 2t + C$$. **Final answer:** $$\boxed{-\frac{1}{t} - 2t + C}$$