Integral of 1/(x+4) dx

The solution

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 oo         
  /         
 |          
 |    1     
 |  ----- dx
 |  x + 4   
 |          
/           
2

$$\int\limits_{2}^{\infty} \frac{1}{x + 4}\, dx$$

Integral(1/(x + 4), (x, 2, oo))

Detail solution

Let $u = x + 4$ .

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

$\int \frac{1}{u}\, du$
1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
Now substitute $u$ back in:

$\log{\left(x + 4 \right)}$
Now simplify:

$\log{\left(x + 4 \right)}$
Add the constant of integration:

$\log{\left(x + 4 \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(x + 4 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                          
 |   1                      
 | ----- dx = C + log(x + 4)
 | x + 4                    
 |                          
/

$$\int \frac{1}{x + 4}\, dx = C + \log{\left(x + 4 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$\infty$$

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$$\infty$$

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

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Integral of 1/(x+4) dx

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The solution