Question

Evaluate the definite integral:
\[ \int_{0}^{1} \frac{1}{x^2 + 2x + 3} \, dx \]

Hint:

When completing the square for $x^2 + bx + c$, always rewrite it as $\left(x + \frac{b}{2}\right)^2 + \left(c - \frac{b^2}{4}\right)$. Keeping this mental shortcut handy makes working through algebraic steps much faster during exams.

Answer 1