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The power rule says d/dx (a·xᵖ) = a·p·x^(p−1), reducing the exponent by one and multiplying by the old exponent. Reversing it gives the antiderivative a·x^(p+1)/(p+1), valid whenever p ≠ −1.
Power rule
d/dx (a·xᵖ) = a·p·x^(p−1)
Reverse power rule
∫a·xᵖ dx = a·x^(p+1)/(p+1) + C, for p ≠ −1
20x³ = 20 × 8 = 160.
The antiderivative becomes a·ln|x| rather than a power, which is where the natural logarithm enters calculus.