What is the integral of (x^6-3x)/(x^4) ?

The integral of (x^6-3x)/(x^4) is (x^3)/3+3/(2x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^6-3x)/(x^4)

\int \frac{x ^{6} - 3 x}{x ^{4}} d x

\frac{x ^{3}}{3} + \frac{3}{2 x ^{2}} + C

Solution steps

\int \frac{x ^{6} - 3 x}{x ^{4}} d x

Expand

\frac{x ^{6} - 3 x}{x ^{4}} : x^{2} - \frac{3}{x ^{3}}

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

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

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

= \frac{x ^{3}}{3} - (- \frac{3}{2 x ^{2}})

Simplify

= \frac{x ^{3}}{3} + \frac{3}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{3}{2 x ^{2}} + C

\frac{y ^{4}}{8} + \frac{1}{4 y ^{2}}

\frac{d}{d x} (- \frac{6 x}{1 - 3 x ^{2}})

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

\int sin (2 y) d y

x \to 2 lim (x + \frac{1}{x - 2})

What is the integral of (x^6-3x)/(x^4) ?
The integral of (x^6-3x)/(x^4) is (x^3)/3+3/(2x^2)+C