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Integration of x^n = x^(n + 1) / n + 1 is use only when = ...?

____________________________________

Answer

x^a

Explanation
We know the famous power formula is 

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

This formula will use when we have to find integration of any power function type question and its exponent value also should not be equal to -1.


                     x
Given option (a) is a

is an exponential form so we cant apply the above power formula of integration


                     x
Given option (b) is x 

is has also variable power x so we cant apply the above power formula of integration


                     -1
Given option (c) is x 

is in power form but its power is -1 so we cant apply the above power formula of integration


                     a
Given option (d) is x 

is in power form and its power is also not equal to -1. So only here we can apply the above formula.

                  a + 1 
    /  a         x
    | x  dx = ------- + C    
    /          a + 1

    a
so x  is only true for apply above formula.

____________________________________

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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