What is the integral of (2x+4)/(x^2) ?

The integral of (2x+4)/(x^2) is 2ln|x|-4/x+C

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integral of (2x+4)/(x^2)

\int \frac{2 x + 4}{x ^{2}} d x

2 ln ∣ x ∣ - \frac{4}{x} + C

Solution steps

\int \frac{2 x + 4}{x ^{2}} d x

Expand

\frac{2 x + 4}{x ^{2}} : \frac{2}{x} + \frac{4}{x ^{2}}

= \int \frac{2}{x} + \frac{4}{x ^{2}} 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 \frac{4}{x ^{2}} d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{4}{x ^{2}} d x = - \frac{4}{x}

= 2 ln ∣ x ∣ - \frac{4}{x}

Add a constant to the solution

= 2 ln ∣ x ∣ - \frac{4}{x} + C

n = 0 \sum \infty \frac{1}{( 2 ^{n} )}

P - P^{2} = \frac{d P}{d t}

\frac{\partial}{\partial x} (e^{\frac{- y}{x}})

x^{2} y^{^{'}} - 2 x y = 3 y^{4}

\int \frac{x}{8} 64 + x^{2} d x

What is the integral of (2x+4)/(x^2) ?
The integral of (2x+4)/(x^2) is 2ln|x|-4/x+C