Indefinite Integration
Integration by Substitution
Premium Question
Grade 12
Question:
If $\int \frac{2x + 3}{\sqrt{x^2 + 3x + 1}} \, dx = k\sqrt{x^2 + 3x + 1} + C$, the value of $k$ equals _____.
Step-by-Step Solution
Key Concept: Notice that the numerator $2x + 3$ is exactly the derivative of the expression $x^2 + 3x + 1$ under the square root, and substitute $t = x^2 + 3x + 1$.
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Correct Answer: 2