Integral of 7/(5x-1) dx

The solution

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  1           
  /           
 |            
 |     7      
 |  ------- dx
 |  5*x - 1   
 |            
/             
0

$$\int\limits_{0}^{1} \frac{7}{5 x - 1}\, dx$$

Integral(7/(5*x - 1), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{7}{5 x - 1}\, dx = 7 \int \frac{1}{5 x - 1}\, dx$
1. Let $u = 5 x - 1$ .
  
  Then let $du = 5 dx$ and substitute $\frac{du}{5}$ :
  
  $\int \frac{1}{5 u}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{5}$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    So, the result is: $\frac{\log{\left(u \right)}}{5}$
  Now substitute $u$ back in:
  
  $\frac{\log{\left(5 x - 1 \right)}}{5}$
So, the result is: $\frac{7 \log{\left(5 x - 1 \right)}}{5}$
Now simplify:

$\frac{7 \log{\left(5 x - 1 \right)}}{5}$
Add the constant of integration:

$\frac{7 \log{\left(5 x - 1 \right)}}{5}+ \mathrm{constant}$

The answer is:

$\frac{7 \log{\left(5 x - 1 \right)}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 |    7             7*log(5*x - 1)
 | ------- dx = C + --------------
 | 5*x - 1                5       
 |                                
/

$$\int \frac{7}{5 x - 1}\, dx = C + \frac{7 \log{\left(5 x - 1 \right)}}{5}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$$\text{NaN}$$

nan

$$\text{NaN}$$

nan

Numerical answer [src]

3.41722666995898

3.41722666995898

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

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Integral of 7/(5x-1) dx

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