Question Find the values of $a$, $b$, and $c$ such that the integral $\int_{0}^{1}(x+3) e^{x^{2}+6 x+5} d x$ can be expressed as $\int_{a}^{b} c e^{u} d u$.

Studdy Solution
The transformed integral is:
$$\int_{0}^{1}(x+3) e^{x^{2}+6 x+5} d x = \int_{5}^{12} e^{u} du$$
Therefore, the exact values of the constants are $a = 5$, $b = 12$, and $c = 1$.