积分 dx/sqrt(5+x) dx

解答

You have entered [src]

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

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

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

Detail solution

Let $u = \sqrt{x + 5}$ .

Then let $du = \frac{dx}{2 \sqrt{x + 5}}$ 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:

$2 \sqrt{x + 5}$
Add the constant of integration:

$2 \sqrt{x + 5}+ \mathrm{constant}$

The answer is:

$2 \sqrt{x + 5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                               
 |     1                  _______
 | --------- dx = C + 2*\/ 5 + x 
 |   _______                     
 | \/ 5 + x                      
 |                               
/

$$\int \frac{1}{\sqrt{x + 5}}\, dx = C + 2 \sqrt{x + 5}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      ___       ___
- 2*\/ 5  + 2*\/ 6

$$- 2 \sqrt{5} + 2 \sqrt{6}$$

      ___       ___
- 2*\/ 5  + 2*\/ 6

$$- 2 \sqrt{5} + 2 \sqrt{6}$$

-2*sqrt(5) + 2*sqrt(6)

Numerical answer [src]

0.426843530566777

0.426843530566777

这些示例也可用于输入定积分的上下限.

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积分 dx/sqrt(5+x) dx

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