What is the integral of ((9+x)^2)/(x^2) ?

The integral of ((9+x)^2)/(x^2) is -(81)/x+18ln|x|+x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((9+x)^2)/(x^2)

\int \frac{( 9 + x ) ^{2}}{x ^{2}} d x

- \frac{81}{x} + 18 ln ∣ x ∣ + x + C

Solution steps

\int \frac{( 9 + x ) ^{2}}{x ^{2}} d x

Expand

\frac{( 9 + x ) ^{2}}{x ^{2}} : \frac{81}{x ^{2}} + \frac{18}{x} + 1

= \int \frac{81}{x ^{2}} + \frac{18}{x} + 1 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{81}{x ^{2}} d x + \int \frac{18}{x} d x + \int 1 d x

\int \frac{81}{x ^{2}} d x = - \frac{81}{x}

\int \frac{18}{x} d x = 18 ln ∣ x ∣

\int 1 d x = x

= - \frac{81}{x} + 18 ln ∣ x ∣ + x

Add a constant to the solution

= - \frac{81}{x} + 18 ln ∣ x ∣ + x + C

\int ln^{2} (z) d z

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

\int sin (\frac{3}{2}) x sin (\frac{1}{2}) x d x

\int \frac{x}{4 x ^{2} + 4 x + 5} d x

What is the integral of ((9+x)^2)/(x^2) ?
The integral of ((9+x)^2)/(x^2) is -(81)/x+18ln|x|+x+C