1. **State the problem:** We are given that $$\int \frac{t(x)}{x^2 + 3x + 5} \, dx = \ln |x^2 + 3x + 5| + c.$$ We need to determine which function $t(x)$ satisfies this integral equation. 2. **Recall the formula for integration:** If $$\int \frac{f'(x)}{f(x)} \, dx = \ln |f(x)| + c,$$ then the numerator must be the derivative of the denominator. 3. **Identify $f(x)$ and find its derivative:** Here, $f(x) = x^2 + 3x + 5$. Calculate $$f'(x) = \frac{d}{dx}(x^2 + 3x + 5) = 2x + 3.$$ 4. **Compare $t(x)$ with $f'(x)$:** Since the integral equals $\ln |f(x)| + c$, the numerator $t(x)$ must be equal to $f'(x) = 2x + 3$. 5. **Conclusion:** The function $t(x)$ must be $$t(x) = 2x + 3.$$