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Solving integrals/ 1/sqrt(x+2+3)

Integral of 1/sqrt(x+2+3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |    ___________   
 |  \/ x + 2 + 3    
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{\left(x + 2\right) + 3}}\, dx$$ 
Integral(1/(sqrt(x + 2 + 3)), (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. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                      
 |                                       
 |       1                    ___________
 | ------------- dx = C + 2*\/ x + 2 + 3 
 |   ___________                         
 | \/ x + 2 + 3                          
 |                                       
/
$$\int \frac{1}{\sqrt{\left(x + 2\right) + 3}}\, dx = C + 2 \sqrt{\left(x + 2\right) + 3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
      ___       ___
- 2*\/ 5  + 2*\/ 6
$$- 2 \sqrt{5} + 2 \sqrt{6}$$ 
=
= 
      ___       ___
- 2*\/ 5  + 2*\/ 6
$$- 2 \sqrt{5} + 2 \sqrt{6}$$ 
-2*sqrt(5) + 2*sqrt(6)
Numerical answer [src] 
0.426843530566777
0.426843530566777

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

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