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

____________________________________

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.

____________________________________

Note

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

                n + 1 
    /  n       x
    | x  dx = ------- + C         (n ≠ -1)      
    /          n + 1
 
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