Question

What happens when you apply the power rule for integration to the function f(x)=1/x?

Answer 1

The power rule that applies to
`f(x)= (1)/(x)` is
`f(x)= x^(-1)`

Integrating
`\int\ {x^(-1) } \, dx` will give the effect of

`(x^(-1+1) )/(-1+1) = ( x^(0) )/(0)`, which is undefined since we cannot divide by '0'

The conclusion is that to integrate
`f(x)= (1)/(x)` we don't use the power rule. We use instead

`\int\ { (1)/(x) } \, dx =ln(x)`