What is the integral of x+x^5+x^{-5} ?

The integral of x+x^5+x^{-5} is (x^2)/2+(x^6)/6-1/(4x^4)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x+x^5+x^{-5}

\int x + x^{5} + x^{- 5} d x

\frac{x ^{2}}{2} + \frac{x ^{6}}{6} - \frac{1}{4 x ^{4}} + C

Solution steps

\int x + x^{5} + x^{- 5} 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 x^{5} d x + \int x^{- 5} d x

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

\int x^{5} d x = \frac{x ^{6}}{6}

\int x^{- 5} d x = - \frac{1}{4 x ^{4}}

= \frac{x ^{2}}{2} + \frac{x ^{6}}{6} - \frac{1}{4 x ^{4}}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{x ^{6}}{6} - \frac{1}{4 x ^{4}} + C

\int \frac{8}{( 1 - 7 x ) ^{4}} d x

\int 2 x (x^{2} + 1)^{7} d x

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

\int \frac{1}{4 - v ^{2}} d v

\int \frac{3}{x + 1} d x

What is the integral of x+x^5+x^{-5} ?
The integral of x+x^5+x^{-5} is (x^2)/2+(x^6)/6-1/(4x^4)+C