What is the integral of (x^5-5x)/(x^4) ?

The integral of (x^5-5x)/(x^4) is (x^2)/2+5/(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^5-5x)/(x^4)

\int \frac{x ^{5} - 5 x}{x ^{4}} d x

\frac{x ^{2}}{2} + \frac{5}{2 x ^{2}} + C

Solution steps

\int \frac{x ^{5} - 5 x}{x ^{4}} d x

Expand

\frac{x ^{5} - 5 x}{x ^{4}} : x - \frac{5}{x ^{3}}

= \int x - \frac{5}{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 d x - \int \frac{5}{x ^{3}} d x

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

\int \frac{5}{x ^{3}} d x = - \frac{5}{2 x ^{2}}

= \frac{x ^{2}}{2} - (- \frac{5}{2 x ^{2}})

Simplify

= \frac{x ^{2}}{2} + \frac{5}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{5}{2 x ^{2}} + C

- sin (x)

\int sec^{2} (10 x) d x

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

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

\int x^{3} + 4 x d x

What is the integral of (x^5-5x)/(x^4) ?
The integral of (x^5-5x)/(x^4) is (x^2)/2+5/(2x^2)+C