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Solving integrals/ dx/sqrt(4+3*x)

Integral of dx/sqrt(4+3*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |    _________   
 |  \/ 4 + 3*x    
 |                
/                 
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{3 x + 4}}\, dx$$ 
Integral(1/(sqrt(4 + 3*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               2*\/ 4 + 3*x 
 | ----------- dx = C + -------------
 |   _________                3      
 | \/ 4 + 3*x                        
 |                                   
/
$$\int \frac{1}{\sqrt{3 x + 4}}\, dx = C + \frac{2 \sqrt{3 x + 4}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
          ___
  4   2*\/ 7 
- - + -------
  3      3
$$- \frac{4}{3} + \frac{2 \sqrt{7}}{3}$$ 
=
= 
          ___
  4   2*\/ 7 
- - + -------
  3      3
$$- \frac{4}{3} + \frac{2 \sqrt{7}}{3}$$ 
-4/3 + 2*sqrt(7)/3
Numerical answer [src] 
0.43050087404306
0.43050087404306

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

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