1. **Stating the problem:** Solve a linear equation using the DI (Derivative-Integral) method or tabular method. Since the user did not specify the exact equation, I will demonstrate the DI method for integration by parts, which is commonly solved using the tabular method. 2. **Formula used:** Integration by parts formula is $$\int u\,dv = uv - \int v\,du$$ where $u$ and $dv$ are parts of the integrand. 3. **Tabular method explanation:** - Choose $u$ to differentiate repeatedly until it becomes zero. - Choose $dv$ to integrate repeatedly. - Alternate signs starting with positive. - Multiply diagonally and sum the results. 4. **Example:** Solve $$\int x e^x dx$$ using the tabular method. | Derivative of $u=x$ | Integral of $dv=e^x dx$ | |---------------------|-------------------------| | $x$ | $e^x$ | | $1$ | $e^x$ | | $0$ | | 5. **Applying signs and multiplying diagonally:** $$+ x \cdot e^x - 1 \cdot e^x = x e^x - e^x + C$$ 6. **Final answer:** $$\int x e^x dx = e^x (x - 1) + C$$ This method simplifies integration by parts by organizing derivatives and integrals in a table and applying alternating signs.