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1/(1+5x)
Solving integrals/ 1/(1+5x)

Integral of 1/(1+5x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     1      
 |  ------- dx
 |  1 + 5*x   
 |            
/             
0
$$\int\limits_{0}^{1} \frac{1}{5 x + 1}\, dx$$ 
Integral(1/(1 + 5*x), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of is .

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                             
 |                              
 |    1             log(1 + 5*x)
 | ------- dx = C + ------------
 | 1 + 5*x               5      
 |                              
/
$$\int \frac{1}{5 x + 1}\, dx = C + \frac{\log{\left(5 x + 1 \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
log(6)
------
  5
$$\frac{\log{\left(6 \right)}}{5}$$ 
=
= 
log(6)
------
  5
$$\frac{\log{\left(6 \right)}}{5}$$ 
log(6)/5
Numerical answer [src] 
0.358351893845611
0.358351893845611
The graph
Integral of 1/(1+5x) dx

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

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