∫ 2x dx = ?

**The reasoning** When you integrate 2x, you're finding the *antiderivative* — the function whose derivative gives you 2x back. Using the power rule for integration: ∫xⁿ dx = (xⁿ⁺¹)/(n+1) + C So: ∫2x dx = 2∫x¹ dx = 2 · (x²/2) + C = **x² + C** The "+ C" is crucial! It's called the **constant of integration**. Since the derivative of any constant is zero, when we reverse differentiation, we must account for that "lost" constant. **Why the wrong options tempt you** **A) x²** — You did the math correctly but forgot the constant! In indefinite integrals, C is *always* needed because there are infinitely many antiderivatives (x², x²+5, x²−3, etc. all have derivative 2x). **C) 2** — This treats integration like a simple operation instead of finding the antiderivative. **D) 2x²** — You forgot to divide by the new power (2). **Quick takeaway** Every indefinite integral needs "+ C" — no C, no marks in JAMB!