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Solving integrals/ 5*dx/(2*x+3)

Integral of 5*dx/(2*x+3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo           
  /           
 |            
 |     5      
 |  ------- dx
 |  2*x + 3   
 |            
/             
1
$$\int\limits_{1}^{\infty} \frac{5}{2 x + 3}\, dx$$ 
Integral(5/(2*x + 3), (x, 1, oo))
Detail solution

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

    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:

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                               
 |                                
 |    5             5*log(2*x + 3)
 | ------- dx = C + --------------
 | 2*x + 3                2       
 |                                
/
$$\int \frac{5}{2 x + 3}\, dx = C + \frac{5 \log{\left(2 x + 3 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
oo
$$\infty$$ 
=
= 
oo
$$\infty$$ 
oo

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

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