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Identical expressions
twelve /(sqrt(3x- two))
12 divide by ( square root of (3x minus 2))
twelve divide by ( square root of (3x minus two))
12/(√(3x-2))
12/sqrt3x-2
12 divide by (sqrt(3x-2))
12/(sqrt(3x-2))dx
Similar expressions
12/(sqrt(3x+2))

Integral of 12/(sqrt(3x-2)) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |       12       
 |  ----------- dx
 |    _________   
 |  \/ 3*x - 2    
 |                
/                 
0

$$\int\limits_{0}^{1} \frac{12}{\sqrt{3 x - 2}}\, dx$$

Integral(12/sqrt(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:

$\int \frac{12}{\sqrt{3 x - 2}}\, dx = 12 \int \frac{1}{\sqrt{3 x - 2}}\, dx$
1. Let $u = \sqrt{3 x - 2}$ .
  
  Then let $du = \frac{3 dx}{2 \sqrt{3 x - 2}}$ and substitute $\frac{2 du}{3}$ :
  
  $\int \frac{2}{3}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\text{False}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    So, the result is: $\frac{2 u}{3}$
  Now substitute $u$ back in:
  
  $\frac{2 \sqrt{3 x - 2}}{3}$
So, the result is: $8 \sqrt{3 x - 2}$
Now simplify:

$8 \sqrt{3 x - 2}$
Add the constant of integration:

$8 \sqrt{3 x - 2}+ \mathrm{constant}$

The answer is:

$8 \sqrt{3 x - 2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                                   
 |      12                  _________
 | ----------- dx = C + 8*\/ 3*x - 2 
 |   _________                       
 | \/ 3*x - 2                        
 |                                   
/

$$\int \frac{12}{\sqrt{3 x - 2}}\, dx = C + 8 \sqrt{3 x - 2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

          ___
8 - 8*I*\/ 2

$$8 - 8 \sqrt{2} i$$

          ___
8 - 8*I*\/ 2

$$8 - 8 \sqrt{2} i$$

8 - 8*i*sqrt(2)

Numerical answer [src]

(6.94034900092999 - 18.1536245172787j)

(6.94034900092999 - 18.1536245172787j)

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

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Integral of 12/(sqrt(3x-2)) dx

Limits of integration:

The graph:

Piecewise:

The solution