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Identical expressions
one /(8x- one)
1 divide by (8x minus 1)
one divide by (8x minus one)
1/8x-1
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1/(8x-1)dx
Similar expressions
1/(8x+1)

Integral of 1/(8x-1) dx

The solution

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 oo           
  /           
 |            
 |     1      
 |  ------- dx
 |  8*x - 1   
 |            
/             
-oo

$$\int\limits_{-\infty}^{\infty} \frac{1}{8 x - 1}\, dx$$

Integral(1/(8*x - 1), (x, -oo, oo))

Detail solution

Let $u = 8 x - 1$ .

Then let $du = 8 dx$ and substitute $\frac{du}{8}$ :

$\int \frac{1}{8 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{8}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\log{\left(u \right)}}{8}$
Now substitute $u$ back in:

$\frac{\log{\left(8 x - 1 \right)}}{8}$
Now simplify:

$\frac{\log{\left(8 x - 1 \right)}}{8}$
Add the constant of integration:

$\frac{\log{\left(8 x - 1 \right)}}{8}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(8 x - 1 \right)}}{8}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                              
 |    1             log(8*x - 1)
 | ------- dx = C + ------------
 | 8*x - 1               8      
 |                              
/

$$\int \frac{1}{8 x - 1}\, dx = C + \frac{\log{\left(8 x - 1 \right)}}{8}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$$\text{NaN}$$

nan

$$\text{NaN}$$

nan

Numerical answer [src]

-0.406613215878135

-0.406613215878135

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

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Identical expressions

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Integral of 1/(8x-1) dx

Limits of integration:

The graph:

Piecewise:

The solution