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Solving integrals/ 1/(2x+5)

Integral of 1/(2x+5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2           
  /           
 |            
 |     1      
 |  ------- dx
 |  2*x + 5   
 |            
/             
0
$$\int\limits_{0}^{2} \frac{1}{2 x + 5}\, dx$$ 
Integral(1/(2*x + 5), (x, 0, 2))
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. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                             
 |                              
 |    1             log(2*x + 5)
 | ------- dx = C + ------------
 | 2*x + 5               2      
 |                              
/
$$\int \frac{1}{2 x + 5}\, dx = C + \frac{\log{\left(2 x + 5 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
log(9)   log(5)
------ - ------
  2        2
$$- \frac{\log{\left(5 \right)}}{2} + \frac{\log{\left(9 \right)}}{2}$$ 
=
= 
log(9)   log(5)
------ - ------
  2        2
$$- \frac{\log{\left(5 \right)}}{2} + \frac{\log{\left(9 \right)}}{2}$$ 
log(9)/2 - log(5)/2
Numerical answer [src] 
0.29389333245106
0.29389333245106

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

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