What is the integral from 2 to 6 of (8x^3-6x^{-2}) ?

The integral from 2 to 6 of (8x^3-6x^{-2}) is 2558

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 6 of (8x^3-6x^{-2})

\int_{2}^{6} (8 x^{3} - 6 x^{- 2}) d x

2558

Solution steps

\int_{2}^{6} 8 x^{3} - 6 x^{- 2} d x

6 x^{- 2} = \frac{6}{x ^{2}}

= \int_{2}^{6} 8 x^{3} - \frac{6}{x ^{2}} 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_{2}^{6} 8 x^{3} d x - \int_{2}^{6} \frac{6}{x ^{2}} d x

\int_{2}^{6} 8 x^{3} d x = 2560

\int_{2}^{6} \frac{6}{x ^{2}} d x = 2

= 2560 - 2

Simplify

= 2558

\int_{- 2}^{2} x^{2} + 4 d x

\int_{0}^{6} 6 d x

\int_{1}^{3} x^{2} - x + 6 d x

\int_{1}^{4} (3 x + x) d x

\int_{0}^{4} (6 x + x) d x

What is the integral from 2 to 6 of (8x^3-6x^{-2}) ?
The integral from 2 to 6 of (8x^3-6x^{-2}) is 2558