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

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

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

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

ln ∣ x ∣ + \frac{4}{x} + C

Solution steps

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

Expand

\frac{x - 4}{x ^{2}} : \frac{1}{x} - \frac{4}{x ^{2}}

= \int \frac{1}{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{1}{x} d x - \int \frac{4}{x ^{2}} d x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - (- \frac{4}{x})

Simplify

= ln ∣ x ∣ + \frac{4}{x}

Add a constant to the solution

= ln ∣ x ∣ + \frac{4}{x} + C

f (x) = 6 e^{x} (cos (x) - sin (x))

3 t^{7} + 4 t^{5} - t

\frac{d}{d x} (ln (\frac{4 x ^{2} - 9}{2 x - 3}))

x \to 1 + lim (x^{2} - x)

\frac{\partial}{\partial y} (x^{3} - 3 x y + y^{3})

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