Integral of 3/sqrt(x) dx

The solution

You have entered [src]

  1         
  /         
 |          
 |    3     
 |  ----- dx
 |    ___   
 |  \/ x    
 |          
/           
0

$$\int\limits_{0}^{1} \frac{3}{\sqrt{x}}\, dx$$

Integral(3/sqrt(x), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{3}{\sqrt{x}}\, dx = 3 \int \frac{1}{\sqrt{x}}\, dx$
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:
  
  $2 \sqrt{x}$
So, the result is: $6 \sqrt{x}$
Add the constant of integration:

$6 \sqrt{x}+ \mathrm{constant}$

The answer is:

$6 \sqrt{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |   3                ___
 | ----- dx = C + 6*\/ x 
 |   ___                 
 | \/ x                  
 |                       
/

$$\int \frac{3}{\sqrt{x}}\, dx = C + 6 \sqrt{x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$6$$

Numerical answer [src]

5.99999999840825

5.99999999840825

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 3/sqrt(x) dx

Limits of integration:

The graph:

Piecewise:

The solution