Question

What is the anti derivative of x^-1 and why?

Answer 1

Answer:

∫$\frac{dx}{x}$ = ㏑|x| +c

Proof:

let x = $e^{u}$   take derivative for both sides

so dx = $e^{u}$ * du

substitute in the original function

∫du = u + C

u = ㏑|x|