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Identical expressions
8dx/(2x+ three) three
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8dx/(2x-3)3
What you mean?
8*dx/((2*x + 3)^3)

You entered:

8dx/(2x+3)3

What you mean?

8*dx/((2*x + 3)^3)

Integral of 8dx/(2x+3)3 dx

The solution

You have entered [src]

  -2                 
   /                 
  |                  
  |         1        
  |  8*1*-------*3 dx
  |      2*x + 3     
  |                  
 /                   
-5/2

$$\int\limits_{- \frac{5}{2}}^{-2} 8 \cdot 1 \cdot \frac{1}{2 x + 3} \cdot 3\, dx$$

Integral(8*1*3/(2*x + 3), (x, -5/2, -2))

Detail solution

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

$\int 8 \cdot 1 \cdot \frac{1}{2 x + 3} \cdot 3\, dx = 24 \int \frac{1}{2 x + 3}\, dx$
1. Let $u = 2 x + 3$ .
  
  Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :
  
  $\int \frac{1}{4 u}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{1}{2 u}\, du = \frac{\int \frac{1}{u}\, du}{2}$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    So, the result is: $\frac{\log{\left(u \right)}}{2}$
  Now substitute $u$ back in:
  
  $\frac{\log{\left(2 x + 3 \right)}}{2}$
So, the result is: $12 \log{\left(2 x + 3 \right)}$
Now simplify:

$12 \log{\left(2 x + 3 \right)}$
Add the constant of integration:

$12 \log{\left(2 x + 3 \right)}+ \mathrm{constant}$

The answer is:

$12 \log{\left(2 x + 3 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                      
 |                                       
 |        1                              
 | 8*1*-------*3 dx = C + 12*log(2*x + 3)
 |     2*x + 3                           
 |                                       
/

$$12\,\log \left(2\,x+3\right)$$

Simplify

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Plot the graph f(x)

The answer [src]

-12*log(2)

$$-12\,\log 2$$

-12*log(2)

$$- 12 \log{\left(2 \right)}$$

Упростить

Numerical answer [src]

-8.31776616671934

-8.31776616671934

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

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What you mean?

Integral of 8dx/(2x+3)3 dx

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The solution