Question

Evaluate the integral: \[ \int \frac{x^2 + 2x}{\sqrt{x^2 + 1}} \, dx \]

• A. \( \frac{1}{3} \left( x^2 + 1 \right)^{3/2} \)
• B. \( \frac{1}{2} \left( x^2 + 1 \right)^{3/2} \)
• C. \( \frac{1}{2} \left( x^2 + 1 \right)^{5/2} \)
• D. \( \frac{1}{3} \left( x^2 + 1 \right)^{5/2} \)

Hint:

Remember: For integrals involving square roots, substitution can simplify the process significantly.