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(6*sqrt(x))/sqrt(x)dx

Integral of (6*sqrt(x))/sqrt(x) dx

The solution

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  1           
  /           
 |            
 |      ___   
 |  6*\/ x    
 |  ------- dx
 |     ___    
 |   \/ x     
 |            
/             
0

$$\int\limits_{0}^{1} \frac{6 \sqrt{x}}{\sqrt{x}}\, dx$$

Integral((6*sqrt(x))/sqrt(x), (x, 0, 1))

Detail solution

Let $u = \sqrt{x}$ .

Then let $du = \frac{dx}{2 \sqrt{x}}$ and substitute $12 du$ :

$\int 12 u\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int u\, du = 12 \int u\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int u\, du = \frac{u^{2}}{2}$
  So, the result is: $6 u^{2}$
Now substitute $u$ back in:

$6 x$
Add the constant of integration:

$6 x+ \mathrm{constant}$

The answer is:

$6 x+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$6$$

Numerical answer [src]

6.0

6.0

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

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Identical expressions

Integral of (6*sqrt(x))/sqrt(x) dx

Limits of integration:

The graph:

Piecewise:

The solution