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Similar expressions
(4*1)/(3x-2)

Solving integrals/ (4*1)/(3x+2)

Integral of (4*1)/(3x+2) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |         1      
 |  4*1*------- dx
 |      3*x + 2   
 |                
/                 
0

$$\int\limits_{0}^{1} 4 \cdot 1 \cdot \frac{1}{3 x + 2}\, dx$$

Integral(4*1/(3*x + 2), (x, 0, 1))

Detail solution

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

$\int 4 \cdot 1 \cdot \frac{1}{3 x + 2}\, dx = 4 \int \frac{1}{3 x + 2}\, dx$
1. Let $u = 3 x + 2$ .
  
  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:
  
  $\frac{\log{\left(3 x + 2 \right)}}{3}$
So, the result is: $\frac{4 \log{\left(3 x + 2 \right)}}{3}$
Now simplify:

$\frac{4 \log{\left(3 x + 2 \right)}}{3}$
Add the constant of integration:

$\frac{4 \log{\left(3 x + 2 \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{4 \log{\left(3 x + 2 \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                                    
 |        1             4*log(3*x + 2)
 | 4*1*------- dx = C + --------------
 |     3*x + 2                3       
 |                                    
/

$${{4\,\log \left(3\,x+2\right)}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  4*log(2)   4*log(5)
- -------- + --------
     3          3

$$4\,\left({{\log 5}\over{3}}-{{\log 2}\over{3}}\right)$$

  4*log(2)   4*log(5)
- -------- + --------
     3          3

$$- \frac{4 \log{\left(2 \right)}}{3} + \frac{4 \log{\left(5 \right)}}{3}$$

Упростить

Numerical answer [src]

1.22172097583221

1.22172097583221

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 (4*1)/(3x+2) dx

Limits of integration:

The graph:

Piecewise:

The solution