Indefinite Integration of 1/x

Indefinite Integration of 1/x

How to solve the indefinite integration of 1/x problems: formula, example, and its solution.

Formula

(integral of 1/x dx) = ln |x| + C

∫ 1/x dx = ln |x| + C

This is true because
[ln |x| + C]' = 1/x.

Derivative of ln |x|

Example

Find the given indefinite integral. The integral of (x^2 - x + 2)/x dx

Split the fraction into three parts.

∫ 1/x dx = ln |x|

So (given) = (1/2)x2 - x + 2 ln |x| + C.

Indefinite integration of polynomials