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

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

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

x - \frac{4}{x} + C

Solution steps

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

Expand

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

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

\int 1 d x = x

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

= x - \frac{4}{x}

Add a constant to the solution

= x - \frac{4}{x} + C

\int x arctan (x^{2} - 1) d x

\int \frac{x - 1}{x + 1} d x

e^{- x}

5 cos (π x)

\frac{d}{d x} (- \frac{2 x}{( - x ^{2} + 1 ) ^{2}})

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