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

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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} (x cos (x) + x^{2} sin (x))

\int 3 x + 1 d x

\int_{0}^{1} x e^{1 - x^{2}} d x

(3 x - 1 + 4 5 - x)^{^{'}}

\int \frac{1}{5 x} d x

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