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Popular Calculus >

integral of-(x+2)/x

Solution

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

Solution

- x - 2 ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Expand

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

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

\int 1 d x = x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= - (x + 2 ln ∣ x ∣)

Simplify

= - x - 2 ln ∣ x ∣

Add a constant to the solution

= - x - 2 ln ∣ x ∣ + C

Graph

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Frequently Asked Questions (FAQ)

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