What is the integral of (sqrt(x)+1/(9sqrt(x))) ?

The integral of (sqrt(x)+1/(9sqrt(x))) is 2/3 x^{3/2}+2/9 sqrt(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sqrt(x)+1/(9sqrt(x)))

\int (x + \frac{1}{9 x}) d x

\frac{2}{3} x^{\frac{3}{2}} + \frac{2}{9} x + C

Solution steps

\int x + \frac{1}{9 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{1}{9 x} d x

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

\int \frac{1}{9 x} d x = \frac{2}{9} x

= \frac{2}{3} x^{\frac{3}{2}} + \frac{2}{9} x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + \frac{2}{9} x + C

\int ln (1 + x^{3}) d x

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 4, y^{^{'}} (0) = 7

\frac{\partial}{\partial z} (x^{2} + y^{2} + z^{2})

y^{^{'}} + 9 x e^{y} = 0

\int (x - 1)^{2} (e^{x + 1} - 1) d x

What is the integral of (sqrt(x)+1/(9sqrt(x))) ?
The integral of (sqrt(x)+1/(9sqrt(x))) is 2/3 x^{3/2}+2/9 sqrt(x)+C