Laplace transform of $t²+2t+3$ is
- A. $\frac{-2}{s³}-\frac{2}{s²}-\frac{3}{s}$
- B. $\frac{2}{s³}+\frac{2}{s²}-\frac{3}{s}$
- C. $\frac{2}{s³}+\frac{2}{s²}+\frac{3}{s}$
- D. $\frac{-2}{s³}+\frac{2}{s²}-\frac{3}{s}$
Answer: C. $\frac{2}{s³}+\frac{2}{s²}+\frac{3}{s}$
Explanation: Using the standard formula for Laplace transform: $L\{t^n\} = \frac{n!}{s^{n+1}}$. For $t²+2t+3$, $L\{t²+2t+3\} = \frac{2!}{s³}+\frac{2 \cdot 1!}{s²}+\frac{3}{s} = \frac{2}{s³}+\frac{2}{s²}+\frac{3}{s}$.