Integral of sqrt(x+5) dx

The solution

You have entered [src]

  1             
  /             
 |              
 |    _______   
 |  \/ x + 5  dx
 |              
/               
0

$$\int\limits_{0}^{1} \sqrt{x + 5}\, dx$$

Integral(sqrt(x + 5), (x, 0, 1))

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:

$\frac{2 \left(x + 5\right)^{\frac{3}{2}}}{3}$
Now simplify:

$\frac{2 \left(x + 5\right)^{\frac{3}{2}}}{3}$
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*(x + 5)   
 | \/ x + 5  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]

               ___
    ___   10*\/ 5 
4*\/ 6  - --------
             3

$$- \frac{10 \sqrt{5}}{3} + 4 \sqrt{6}$$

               ___
    ___   10*\/ 5 
4*\/ 6  - --------
             3

$$- \frac{10 \sqrt{5}}{3} + 4 \sqrt{6}$$

4*sqrt(6) - 10*sqrt(5)/3

Numerical answer [src]

2.34439904613341

2.34439904613341

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sqrt(x+5) dx

Limits of integration:

The graph:

Piecewise:

The solution