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

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

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

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

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

Solution steps

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

Expand

\frac{x + 1}{x} : x + \frac{1}{x}

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

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

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

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

Add a constant to the solution

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

\int \frac{1}{2} x^{5} d x

x \to \frac{π}{2} + lim (2 e^{t a n (x)})

t an g e n t f (x) = 3 x^{4} - 8 x^{2}, (- 1, 5)

\frac{\partial}{\partial x} (- 3 x y ln (x y))

\frac{\partial}{\partial x} (\frac{x y ^{2}}{z ^{3}})

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