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

2 Answers
Jul 25, 2017

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

Jul 25, 2017

"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