Discussion
The integral \( \displaystyle\int x^{n}\,dx \) for \( n \neq -1 \) equals
Answer: A
Raising the index and dividing by the new index reverses the power rule:
\[ \frac{d}{dx}\left(\frac{x^{n+1}}{n+1}\right) \;=\; \frac{(n+1)x^{n}}{n+1} \;=\; x^{n}. \]
The exclusion \( n = -1 \) is needed because the divisor would vanish; that case integrates to \( \ln|x| \) instead. Lowering the index is differentiation, not integration
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