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

Integral of 1/sqrt(1+x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |      1       
 |  --------- dx
 |    _______   
 |  \/ 1 + x    
 |              
/               
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{x + 1}}\, dx$$ 
Integral(1/(sqrt(1 + 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                  _______
 | --------- dx = C + 2*\/ 1 + x 
 |   _______                     
 | \/ 1 + x                      
 |                               
/
$$\int \frac{1}{\sqrt{x + 1}}\, dx = C + 2 \sqrt{x + 1}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
         ___
-2 + 2*\/ 2
$$-2 + 2 \sqrt{2}$$ 
=
= 
         ___
-2 + 2*\/ 2
$$-2 + 2 \sqrt{2}$$ 
-2 + 2*sqrt(2)
Numerical answer [src] 
0.82842712474619
0.82842712474619
The graph
Integral of 1/sqrt(1+x) dx

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

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