What is the integral of (x+4)/(sqrt(x)) ?

The integral of (x+4)/(sqrt(x)) is 2/3 x^{3/2}+8sqrt(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+4)/(sqrt(x))

\int \frac{x + 4}{x} d x

\frac{2}{3} x^{\frac{3}{2}} + 8 x + C

Solution steps

\int \frac{x + 4}{x} d x

Expand

\frac{x + 4}{x} : x + \frac{4}{x}

= \int x + \frac{4}{x} 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{4}{x} d x

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

\int \frac{4}{x} d x = 8 x

= \frac{2}{3} x^{\frac{3}{2}} + 8 x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + 8 x + C

f (x) = tan (\frac{π}{3})

\frac{d}{d x} (\frac{e ^{i x} + e ^{- i x}}{2})

\frac{\partial}{\partial y} (\frac{x}{9 + y})

y^{^{'}} + y cos (x) = sin (x) cos (x)

f (x) = (ln (x))^{6}, at x = 4

What is the integral of (x+4)/(sqrt(x)) ?
The integral of (x+4)/(sqrt(x)) is 2/3 x^{3/2}+8sqrt(x)+C