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Identical expressions
one /(4x- twelve)
1 divide by (4x minus 12)
one divide by (4x minus twelve)
1/4x-12
1 divide by (4x-12)
1/(4x-12)dx
Similar expressions
(1/(4(x+1))+1/(4(x+1)^2)-1/(4(x-1))+1/(4(x-1)^2))
1/(4x+12)

Integral of 1/(4x-12) dx

The solution

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  3            
  /            
 |             
 |     1       
 |  -------- dx
 |  4*x - 12   
 |             
/              
-1

$$\int\limits_{-1}^{3} \frac{1}{4 x - 12}\, dx$$

Integral(1/(4*x - 12), (x, -1, 3))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = 4 x - 12$ .
  
  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:
  
  $\frac{\log{\left(4 x - 12 \right)}}{4}$
Method #2
1. Rewrite the integrand:
  
  $\frac{1}{4 x - 12} = \frac{1}{4 \left(x - 3\right)}$
2. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{4 \left(x - 3\right)}\, dx = \frac{\int \frac{1}{x - 3}\, dx}{4}$
  1. Let $u = x - 3$ .
    
    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:
    
    $\log{\left(x - 3 \right)}$
  So, the result is: $\frac{\log{\left(x - 3 \right)}}{4}$
Now simplify:

$\frac{\log{\left(4 x - 12 \right)}}{4}$
Add the constant of integration:

$\frac{\log{\left(4 x - 12 \right)}}{4}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(4 x - 12 \right)}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 |    1              log(4*x - 12)
 | -------- dx = C + -------------
 | 4*x - 12                4      
 |                                
/

$$\int \frac{1}{4 x - 12}\, dx = C + \frac{\log{\left(4 x - 12 \right)}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      pi*I
-oo - ----
       4

$$-\infty - \frac{i \pi}{4}$$

      pi*I
-oo - ----
       4

$$-\infty - \frac{i \pi}{4}$$

-oo - pi*i/4

Numerical answer [src]

-11.0227391965549

-11.0227391965549

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

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Identical expressions

Similar expressions

Integral of 1/(4x-12) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2