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Identical expressions
(sqrt(x)+ one /sqrt(x))dx
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( square root of (x) plus one divide by square root of (x))dx
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Similar expressions
(sqrt(x)-1/sqrt(x))dx

Solving integrals/ (sqrt(x)+1/sqrt(x))dx

Integral of (sqrt(x)+1/sqrt(x))dx dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  /  ___     1  \   
 |  |\/ x  + -----| dx
 |  |          ___|   
 |  \        \/ x /   
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)\, dx$$

Integral(sqrt(x) + 1/(sqrt(x)), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
1. Let $u = \sqrt{x}$ .
  
  Then let $du = \frac{dx}{2 \sqrt{x}}$ and substitute $2 du$ :
  
  $\int 2\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\text{False}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    So, the result is: $2 u$
  Now substitute $u$ back in:
  
  $2 \sqrt{x}$
The result is: $\frac{2 x^{\frac{3}{2}}}{3} + 2 \sqrt{x}$
Now simplify:

$\frac{2 \sqrt{x} \left(x + 3\right)}{3}$
Add the constant of integration:

$\frac{2 \sqrt{x} \left(x + 3\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{2 \sqrt{x} \left(x + 3\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                       3/2
 | /  ___     1  \              ___   2*x   
 | |\/ x  + -----| dx = C + 2*\/ x  + ------
 | |          ___|                      3   
 | \        \/ x /                          
 |                                          
/

$$\int \left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)\, dx = C + \frac{2 x^{\frac{3}{2}}}{3} + 2 \sqrt{x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

8/3

$$\frac{8}{3}$$

8/3

$$\frac{8}{3}$$

8/3

Numerical answer [src]

2.66666666613608

2.66666666613608

Use the examples entering the upper and lower limits of integration.

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Identical expressions

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Integral of (sqrt(x)+1/sqrt(x))dx dx

Limits of integration:

The graph:

Piecewise:

The solution