Integral of sqrt(5+x) dx

The solution

You have entered [src]

 -2             
  /             
 |              
 |    _______   
 |  \/ 5 + x  dx
 |              
/               
-5

$$\int\limits_{-5}^{-2} \sqrt{x + 5}\, dx$$

Integral(sqrt(5 + x), (x, -5, -2))

Detail solution

Let $u = x + 5$ .

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:

$\frac{2 \left(x + 5\right)^{\frac{3}{2}}}{3}$
Add the constant of integration:

$\frac{2 \left(x + 5\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer is:

$\frac{2 \left(x + 5\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                             3/2
 |   _______          2*(5 + x)   
 | \/ 5 + x  dx = C + ------------
 |                         3      
/

$$\int \sqrt{x + 5}\, dx = C + \frac{2 \left(x + 5\right)^{\frac{3}{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    ___
2*\/ 3

$$2 \sqrt{3}$$

    ___
2*\/ 3

$$2 \sqrt{3}$$

2*sqrt(3)

Numerical answer [src]

3.46410161513775

3.46410161513775

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sqrt(5+x) dx

Limits of integration:

The graph:

Piecewise:

The solution