Question

integral and derivative of 1/x
please fast

Answer 1

$\int { \frac{1}{x} } \, dx=log\ x+c\\ \\ \frac{d}{dx}( \frac{1}{x} )= -\frac{1}{ x^{2} }$

Answer 2

DEAR STUDENT,

Kindly check the attached papers to bring out the solutions for same expressions in a step by step manner with great elaborations to finally reach our conclusion or the desired or required answer that is,

FOR INTEGRAL:

$\boxed{\bf{\underline{\int \: \dfrac{1}{x} \: dx = In|x| + C}}}$

OR,

$\boxed{\bf{\underline{\int \: \dfrac{1}{x} \: dx = log (x) + C}}}$

FOR DERIVATIVE:

$\boxed{\bf{\underline{\dfrac{d}{dx} \: (\dfrac{1}{x}) = - \dfrac{1}{x^2}}}}$

Which are the required solutions for these types of queries.

Hope this helps you and gives you the idea how it's derived and solves the doubts for integration and differentiation!!!!!