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Identical expressions
dx/(four *x+ eleven)
dx divide by (4 multiply by x plus 11)
dx divide by (four multiply by x plus eleven)
dx/(4x+11)
dx/4x+11
dx divide by (4*x+11)
Similar expressions
dx/(4*x-11)

Integral of dx/(4*x+11) dx

The solution

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 oo            
  /            
 |             
 |     1       
 |  -------- dx
 |  4*x + 11   
 |             
/              
2

$$\int\limits_{2}^{\infty} \frac{1}{4 x + 11}\, dx$$

Integral(1/(4*x + 11), (x, 2, oo))

Detail solution

Let $u = 4 x + 11$ .

Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :

$\int \frac{1}{4 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{4}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\log{\left(u \right)}}{4}$
Now substitute $u$ back in:

$\frac{\log{\left(4 x + 11 \right)}}{4}$
Now simplify:

$\frac{\log{\left(4 x + 11 \right)}}{4}$
Add the constant of integration:

$\frac{\log{\left(4 x + 11 \right)}}{4}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(4 x + 11 \right)}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 |    1              log(4*x + 11)
 | -------- dx = C + -------------
 | 4*x + 11                4      
 |                                
/

$$\int \frac{1}{4 x + 11}\, dx = C + \frac{\log{\left(4 x + 11 \right)}}{4}$$

Simplify

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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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Identical expressions

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Integral of dx/(4*x+11) dx

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Piecewise:

The solution