Integrals of form $\int (\sqrt{ax^2 + bx + c}) dx$
General
Grade 12
Question:
Evaluate $\int \sqrt{x^2 + 3} dx$
Step-by-Step Solution
Key Concept: General
Using the formula $$\int \sqrt{x^2 + a^2} dx = \frac{x}{2} \sqrt{x^2 + a^2} + \frac{a^2}{2} \ln |x + \sqrt{x^2 + a^2}| + C$$, we get $$\int \sqrt{x^2 + 3} dx = \frac{x}{2} \sqrt{x^2 + 3} + \frac{3}{2} \ln |x + \sqrt{x^2 + 3}| + C$$
Correct Answer: A