Integral of sqrt(2+x) dx

The solution

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  7             
  /             
 |              
 |    _______   
 |  \/ 2 + x  dx
 |              
/               
-1

$$\int\limits_{-1}^{7} \sqrt{x + 2}\, dx$$

Integral(sqrt(2 + x), (x, -1, 7))

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:

$\frac{2 \left(x + 2\right)^{\frac{3}{2}}}{3}$
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*(2 + x)   
 | \/ 2 + x  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]

52/3

$$\frac{52}{3}$$

52/3

$$\frac{52}{3}$$

52/3

Numerical answer [src]

17.3333333333333

17.3333333333333

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

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Integral of sqrt(2+x) dx

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The solution