Integration of x^n = x^(n + 1) / n + 1 is false when then n = ...?

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Answer

n = -1

Explanation

Every one know the basic and fundamental formula of integration
n + 1
/ n x
| x dx = ------- + C ..... (i)
/ n + 1
But if n = -1 we not use the above formula. In such case we use....
/ -1 / 1
| x dx = | --- dx = ln | x | + C ..... (ii)
/ / x

So when n = -1 we never use the formla (i). In such case we use the formula (ii).

In other words the integration of power rule is true for all n ≠ -1 or false for n = -1.

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Note

Always add the condition (n ≠ -1) in front of power rule integration formula.