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Identical expressions
dx/(five + three *x)
dx divide by (5 plus 3 multiply by x)
dx divide by (five plus three multiply by x)
dx/(5+3x)
dx/5+3x
dx divide by (5+3*x)
Similar expressions
dx/((5+3x+4sqrt(1-x^2))*sqrt(1-x^2))
dx/(5-3*x)

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

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

The solution

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  1             
  /             
 |              
 |       1      
 |  1*------- dx
 |    5 + 3*x   
 |              
/               
0

$$\int\limits_{0}^{1} 1 \cdot \frac{1}{3 x + 5}\, dx$$

Integral(1/(5 + 3*x), (x, 0, 1))

Detail solution

Let $u = 3 x + 5$ .

Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :

$\int \frac{1}{9 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{3 u}\, du = \frac{\int \frac{1}{u}\, du}{3}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\log{\left(u \right)}}{3}$
Now substitute $u$ back in:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$${{\log \left(3\,x+5\right)}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  log(5)   log(8)
- ------ + ------
    3        3

$${{\log 8}\over{3}}-{{\log 5}\over{3}}$$

  log(5)   log(8)
- ------ + ------
    3        3

$$- \frac{\log{\left(5 \right)}}{3} + \frac{\log{\left(8 \right)}}{3}$$

Упростить

Numerical answer [src]

0.156667876415245

0.156667876415245

The graph

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+3*x) dx

Limits of integration:

The graph:

Piecewise:

The solution