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Popular Calculus >

integral of (2-x)/x

Solution

\int \frac{2 - x}{x} d x

Solution

2 ln ∣ x ∣ - x + C

Solution steps

\int \frac{2 - x}{x} d x

Expand

\frac{2 - x}{x} : \frac{2}{x} - 1

= \int \frac{2}{x} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2}{x} d x - \int 1 d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 1 d x = x

= 2 ln ∣ x ∣ - x

Add a constant to the solution

= 2 ln ∣ x ∣ - x + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (2-x)/x ?
The integral of (2-x)/x is 2ln|x|-x+C