Indefinite Integral of x²
∫ x² dx = x³/3 + C.
Problem
Answer
Step-by-step solution
Step 1: Raise the power
x² becomes x³.
Step 2: Divide by the new exponent
Divide by 3.
Step 3: Add C
An indefinite integral is a family of antiderivatives.
Why this works
Integration reverses differentiation. The power rule for n ≠ −1 is ∫ xⁿ dx = xⁿ⁺¹/(n+1) + C. Differentiating x³/3 recovers x², which verifies the result.
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Frequently asked questions
Why is C required?
Any constant has derivative 0, so infinitely many antiderivatives differ only by C.