Integral of 1/√(x+1) dx

The solution

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  1             
  /             
 |              
 |      1       
 |  --------- dx
 |    _______   
 |  \/ x + 1    
 |              
/               
0

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

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

Detail solution

Let $u = \sqrt{x + 1}$ .

Then let $du = \frac{dx}{2 \sqrt{x + 1}}$ and substitute $2 du$ :

$\int 2\, du$
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: $2 u$
Now substitute $u$ back in:

$2 \sqrt{x + 1}$
Now simplify:

$2 \sqrt{x + 1}$
Add the constant of integration:

$2 \sqrt{x + 1}+ \mathrm{constant}$

The answer is:

$2 \sqrt{x + 1}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

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

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

Other calculators

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Identical expressions

Similar expressions

Integral of 1/√(x+1) dx

Limits of integration:

The graph:

Piecewise:

The solution