What is the integral of x^{-7}(x+1) ?

The integral of x^{-7}(x+1) is -1/(5x^5)-1/(6x^6)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^{-7}(x+1)

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

- \frac{1}{5 x ^{5}} - \frac{1}{6 x ^{6}} + C

Solution steps

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

Simplify

x^{- 7} (x + 1) : \frac{x + 1}{x ^{7}}

= \int \frac{x + 1}{x ^{7}} d x

Expand

\frac{x + 1}{x ^{7}} : \frac{1}{x ^{6}} + \frac{1}{x ^{7}}

= \int \frac{1}{x ^{6}} + \frac{1}{x ^{7}} 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{1}{x ^{6}} d x + \int \frac{1}{x ^{7}} d x

\int \frac{1}{x ^{6}} d x = - \frac{1}{5 x ^{5}}

\int \frac{1}{x ^{7}} d x = - \frac{1}{6 x ^{6}}

= - \frac{1}{5 x ^{5}} - \frac{1}{6 x ^{6}}

Add a constant to the solution

= - \frac{1}{5 x ^{5}} - \frac{1}{6 x ^{6}} + C

What is the integral of x^{-7}(x+1) ?
The integral of x^{-7}(x+1) is -1/(5x^5)-1/(6x^6)+C