Question

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

Answer 1

`f'(x)=-1/x^2`

Explanation:

We know that : `f(x)=1/x=x^(-1)` so now we can use the power rule.

`f(x)=x^(-1)=>f'(x)=-1x^(-1-1)=-x^(-2)=-1/x^2`

Answer 2

`"see explanation"`

Explanation:

`"the power rule does not work for this function"`

`int(ax^n)=a/(n+1)x^(n+1)color(white)(x)n!=-1`

`"as" int1/xdx=intx^-1dx != 1/0x^0" undefined"`

`"instead know the standard result"`

`int1/xdx=lnx+c`