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Identical expressions
dx/(sqrt(x)+3sqrt(x))
dx divide by ( square root of (x) plus 3 square root of (x))
dx/(√(x)+3√(x))
dx/sqrtx+3sqrtx
dx divide by (sqrt(x)+3sqrt(x))
Similar expressions
dx/(sqrtx+3sqrtx)
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Solving integrals/ dx/(sqrt(x)+3sqrt(x))

Integral of dx/(sqrt(x)+3sqrt(x)) dx

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = \sqrt{x}$ .

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

$\int \frac{1}{2}\, du$
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: $\frac{u}{2}$
Now substitute $u$ back in:

$\frac{\sqrt{x}}{2}$
Add the constant of integration:

$\frac{\sqrt{x}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\sqrt{x}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \frac{1}{\sqrt{x} + 3 \sqrt{x}}\, dx = C + \frac{\sqrt{x}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Identical expressions

Similar expressions

Integral of dx/(sqrt(x)+3sqrt(x)) dx

Limits of integration:

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Piecewise:

The solution