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

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

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

- \frac{81}{x} + 18 ln ∣ x ∣ + x + C

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \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 - csc (2 x) cot (2 x) d x

(2, 3), (- 4, - 3)

h \to 0 lim (\frac{( 5 + h ) ^{4} - 625}{h})

y = ln (5) x^{3}

3 e^{3 t}

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