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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