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Identical expressions
dx/(five *x+ three)
dx divide by (5 multiply by x plus 3)
dx divide by (five multiply by x plus three)
dx/(5x+3)
dx/5x+3
dx divide by (5*x+3)
Similar expressions
dx/(5x+3)^3
dx/(5*x-3)

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

The solution

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 oo           
  /           
 |            
 |     1      
 |  ------- dx
 |  5*x + 3   
 |            
/             
2

$$\int\limits_{2}^{\infty} \frac{1}{5 x + 3}\, dx$$

Integral(1/(5*x + 3), (x, 2, oo))

Detail solution

Let $u = 5 x + 3$ .

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:

$\frac{\log{\left(5 x + 3 \right)}}{5}$
Now simplify:

$\frac{\log{\left(5 x + 3 \right)}}{5}$
Add the constant of integration:

$\frac{\log{\left(5 x + 3 \right)}}{5}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(5 x + 3 \right)}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                              
 |    1             log(5*x + 3)
 | ------- dx = C + ------------
 | 5*x + 3               5      
 |                              
/

$$\int \frac{1}{5 x + 3}\, dx = C + \frac{\log{\left(5 x + 3 \right)}}{5}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

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$$\infty$$

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

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Identical expressions

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

Limits of integration:

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Piecewise:

The solution