Evaluate ∫(2x + 3) dx.

**The reasoning** Integration is the reverse of differentiation. We use the power rule: ∫xⁿ dx = (xⁿ⁺¹)/(n+1) + c For ∫(2x + 3) dx, integrate each term separately: - ∫2x dx = 2 · (x²/2) = x² - ∫3 dx = 3x (because 3 is just 3x⁰, so we get 3x¹) Therefore: ∫(2x + 3) dx = **x² + 3x + c** This is called **integration by the power rule**. Always add the constant c because there are infinitely many antiderivatives. **Why the wrong options tempt you** **Option B (2x² + 3x + c)**: You forgot to divide by 2 after raising x to power 2. The coefficient 2 doesn't just carry forward—you must divide by the new power! **Option C (x² + 3 + c)**: You treated the constant 3 incorrectly. The integral of 3 is 3x, not just 3. **Option D**: Completely mixed up the terms and coefficients. **Quick takeaway** When integrating xⁿ, increase the power by 1, then divide by that new power—and don't forget: the integral of a constant k is kx, not k!