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Solving integrals/ 1/(sqrt(x)+3sqrt(x))

Integral of 1/(sqrt(x)+3sqrt(x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |    ___       ___   
 |  \/ x  + 3*\/ x    
 |                    
/                     
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{x} + 3 \sqrt{x}}\, dx$$ 
Integral(1/(sqrt(x) + 3*sqrt(x)), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of a constant is the constant times the variable of integration:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

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] 
1/2
$$\frac{1}{2}$$ 
=
= 
1/2
$$\frac{1}{2}$$ 
1/2
Numerical answer [src] 
0.499999999867354
0.499999999867354

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

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