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Integral of d{x}:
Integral of e^(x^2)
Integral of sin(x)^3
Integral of √(x^2+1)
Integral of cos(5x)
Derivative of:
(x+2)^(1/2)
Graphing y =:
(x+2)^(1/2)
Identical expressions
(x+ two)^(one / two)
(x plus 2) to the power of (1 divide by 2)
(x plus two) to the power of (one divide by two)
(x+2)(1/2)
x+21/2
x+2^1/2
(x+2)^(1 divide by 2)
(x+2)^(1/2)dx
Similar expressions
(x-2)^(1/2)

Integral of (x+2)^(1/2) dx

The solution

You have entered [src]

  2             
  /             
 |              
 |    _______   
 |  \/ x + 2  dx
 |              
/               
0

$$\int\limits_{0}^{2} \sqrt{x + 2}\, dx$$

Integral(sqrt(x + 2), (x, 0, 2))

Detail solution

Let $u = x + 2$ .

Then let $du = dx$ and substitute $du$ :

$\int \sqrt{u}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
Now substitute $u$ back in:

$\frac{2 \left(x + 2\right)^{\frac{3}{2}}}{3}$
Now simplify:

$\frac{2 \left(x + 2\right)^{\frac{3}{2}}}{3}$
Add the constant of integration:

$\frac{2 \left(x + 2\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer is:

$\frac{2 \left(x + 2\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                             3/2
 |   _______          2*(x + 2)   
 | \/ x + 2  dx = C + ------------
 |                         3      
/

$$\int \sqrt{x + 2}\, dx = C + \frac{2 \left(x + 2\right)^{\frac{3}{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         ___
16   4*\/ 2 
-- - -------
3       3

$$\frac{16}{3} - \frac{4 \sqrt{2}}{3}$$

         ___
16   4*\/ 2 
-- - -------
3       3

$$\frac{16}{3} - \frac{4 \sqrt{2}}{3}$$

16/3 - 4*sqrt(2)/3

Numerical answer [src]

3.44771525016921

3.44771525016921

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

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Identical expressions

Similar expressions

Integral of (x+2)^(1/2) dx

Limits of integration:

The graph:

Piecewise:

The solution