What is the integral of ((x+3))/(x^2) ?

The integral of ((x+3))/(x^2) is ln|x|-3/x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((x+3))/(x^2)

\int \frac{( x + 3 )}{x ^{2}} d x

ln ∣ x ∣ - \frac{3}{x} + C

Solution steps

\int \frac{x + 3}{x ^{2}} d x

Expand

\frac{x + 3}{x ^{2}} : \frac{1}{x} + \frac{3}{x ^{2}}

= \int \frac{1}{x} + \frac{3}{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{3}{x ^{2}} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{3}{x ^{2}} d x = - \frac{3}{x}

= ln ∣ x ∣ - \frac{3}{x}

Add a constant to the solution

= ln ∣ x ∣ - \frac{3}{x} + C

x \to \frac{π}{3} lim (tan (x))

\frac{d}{d x} (a x e^{x} + a e^{x})

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

\int 3 e^{- s t} d t

\int - 3 cos (5 x) d x

What is the integral of ((x+3))/(x^2) ?
The integral of ((x+3))/(x^2) is ln|x|-3/x+C