What is the integral of (6sqrt(x)-4x^{-3}+5) ?

The integral of (6sqrt(x)-4x^{-3}+5) is 4x^{3/2}+2/(x^2)+5x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (6sqrt(x)-4x^{-3}+5)

\int (6 x - 4 x^{- 3} + 5) d x

4 x^{\frac{3}{2}} + \frac{2}{x ^{2}} + 5 x + C

Solution steps

\int 6 x - 4 x^{- 3} + 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 6 x d x - \int 4 x^{- 3} d x + \int 5 d x

\int 6 x d x = 4 x^{\frac{3}{2}}

\int 4 x^{- 3} d x = - \frac{2}{x ^{2}}

\int 5 d x = 5 x

= 4 x^{\frac{3}{2}} - (- \frac{2}{x ^{2}}) + 5 x

Simplify

= 4 x^{\frac{3}{2}} + \frac{2}{x ^{2}} + 5 x

Add a constant to the solution

= 4 x^{\frac{3}{2}} + \frac{2}{x ^{2}} + 5 x + C

What is the integral of (6sqrt(x)-4x^{-3}+5) ?
The integral of (6sqrt(x)-4x^{-3}+5) is 4x^{3/2}+2/(x^2)+5x+C