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

The integral of (3/x+2/(x^3)) is 3ln|x|-1/(x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

3 ln ∣ x ∣ - \frac{1}{x ^{2}} + C

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= 3 ln ∣ x ∣ - \frac{1}{x ^{2}}

Add a constant to the solution

= 3 ln ∣ x ∣ - \frac{1}{x ^{2}} + C

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

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

x \to \infty lim (π^{\infty})

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

2 x^{3} + 3 x^{2} - 12 x + 6

What is the integral of (3/x+2/(x^3)) ?
The integral of (3/x+2/(x^3)) is 3ln|x|-1/(x^2)+C