What is the integral of ((x+6)/(sqrt(x))) ?

The integral of ((x+6)/(sqrt(x))) is 2/3 x^{3/2}+12sqrt(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+6)/(sqrt(x)))

\int (\frac{x + 6}{x}) d x

\frac{2}{3} x^{\frac{3}{2}} + 12 x + C

Solution steps

\int \frac{x + 6}{x} d x

Expand

\frac{x + 6}{x} : x + \frac{6}{x}

= \int x + \frac{6}{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{6}{x} d x

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

\int \frac{6}{x} d x = 12 x

= \frac{2}{3} x^{\frac{3}{2}} + 12 x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + 12 x + C

\frac{d}{d x} (\frac{2 x + x ^{4}}{( 1 - x ^{3} ) ^{2}})

\int ln (sin (x)) d x

\frac{\partial}{\partial y} (2 e^{- l n (y)} y)

\frac{d ^{2}}{d x ^{2}} (cos (- 1.5 x))

\int 25 - t^{2} d t

What is the integral of ((x+6)/(sqrt(x))) ?
The integral of ((x+6)/(sqrt(x))) is 2/3 x^{3/2}+12sqrt(x)+C