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Identical expressions
dx/(seven *x- eight)
dx divide by (7 multiply by x minus 8)
dx divide by (seven multiply by x minus eight)
dx/(7x-8)
dx/7x-8
dx divide by (7*x-8)
Similar expressions
dx/(7*x+8)

Solving integrals/ dx/(7*x-8)

Integral of dx/(7*x-8) dx

The solution

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  1           
  /           
 |            
 |     1      
 |  ------- dx
 |  7*x - 8   
 |            
/             
0

$$\int\limits_{0}^{1} \frac{1}{7 x - 8}\, dx$$

Integral(1/(7*x - 8), (x, 0, 1))

Detail solution

Let $u = 7 x - 8$ .

Then let $du = 7 dx$ and substitute $\frac{du}{7}$ :

$\int \frac{1}{7 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{7}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\log{\left(u \right)}}{7}$
Now substitute $u$ back in:

$\frac{\log{\left(7 x - 8 \right)}}{7}$
Now simplify:

$\frac{\log{\left(7 x - 8 \right)}}{7}$
Add the constant of integration:

$\frac{\log{\left(7 x - 8 \right)}}{7}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(7 x - 8 \right)}}{7}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                              
 |    1             log(7*x - 8)
 | ------- dx = C + ------------
 | 7*x - 8               7      
 |                              
/

$$\int \frac{1}{7 x - 8}\, dx = C + \frac{\log{\left(7 x - 8 \right)}}{7}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(8) 
--------
   7

$$- \frac{\log{\left(8 \right)}}{7}$$

-log(8) 
--------
   7

$$- \frac{\log{\left(8 \right)}}{7}$$

-log(8)/7

Numerical answer [src]

-0.297063077382834

-0.297063077382834

The graph

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

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Identical expressions

Similar expressions

Integral of dx/(7*x-8) dx

Limits of integration:

The graph:

Piecewise:

The solution