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Similar expressions
(3x-2)/(3sqrt^3x)

Integral of (3x+2)/(3sqrt^3x) dx

The solution

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  1            
  /            
 |             
 |  3*x + 2    
 |  -------- dx
 |         3   
 |      ___    
 |  3*\/ x     
 |             
/              
0

$$\int\limits_{0}^{1} \frac{3 x + 2}{3 \left(\sqrt{x}\right)^{3}}\, dx$$

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

Detail solution

Rewrite the integrand:

$\frac{3 x + 2}{3 \left(\sqrt{x}\right)^{3}} = \frac{1}{\sqrt{x}} + \frac{2}{3 x^{\frac{3}{2}}}$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \frac{1}{\sqrt{x}}\, dx = 2 \sqrt{x}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{2}{3 x^{\frac{3}{2}}}\, dx = \frac{2 \int \frac{1}{x^{\frac{3}{2}}}\, dx}{3}$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{x^{\frac{3}{2}}}\, dx = - \frac{2}{\sqrt{x}}$
  So, the result is: $- \frac{4}{3 \sqrt{x}}$
The result is: $2 \sqrt{x} - \frac{4}{3 \sqrt{x}}$
Now simplify:

$\frac{2 \left(3 x - 2\right)}{3 \sqrt{x}}$
Add the constant of integration:

$\frac{2 \left(3 x - 2\right)}{3 \sqrt{x}}+ \mathrm{constant}$

The answer is:

$\frac{2 \left(3 x - 2\right)}{3 \sqrt{x}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                                    
 | 3*x + 2               ___      4   
 | -------- dx = C + 2*\/ x  - -------
 |        3                        ___
 |     ___                     3*\/ x 
 | 3*\/ x                             
 |                                    
/

$$\int \frac{3 x + 2}{3 \left(\sqrt{x}\right)^{3}}\, dx = C + 2 \sqrt{x} - \frac{4}{3 \sqrt{x}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$\infty$$

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$$\infty$$

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Numerical answer [src]

4976299067.10433

4976299067.10433

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

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Similar expressions

Integral of (3x+2)/(3sqrt^3x) dx

Limits of integration:

The graph:

Piecewise:

The solution