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Integral of ((2/x)+4x^(-3/2)) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  3              
  /              
 |               
 |  /2    4  \   
 |  |- + ----| dx
 |  |x    3/2|   
 |  \    x   /   
 |               
/                
2                
$$\int\limits_{2}^{3} \left(\frac{2}{x} + \frac{4}{x^{\frac{3}{2}}}\right)\, dx$$
Integral(2/x + 4/x^(3/2), (x, 2, 3))
Detail solution
  1. Integrate term-by-term:

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

      1. The integral of is .

      So, the result is:

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

      1. The integral of is when :

      So, the result is:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                    
 |                                     
 | /2    4  \            8             
 | |- + ----| dx = C - ----- + 2*log(x)
 | |x    3/2|            ___           
 | \    x   /          \/ x            
 |                                     
/                                      
$$\int \left(\frac{2}{x} + \frac{4}{x^{\frac{3}{2}}}\right)\, dx = C + 2 \log{\left(x \right)} - \frac{8}{\sqrt{x}}$$
The graph
The answer [src]
                                     ___
                           ___   8*\/ 3 
-2*log(2) + 2*log(3) + 4*\/ 2  - -------
                                    3   
$$- \frac{8 \sqrt{3}}{3} - 2 \log{\left(2 \right)} + 2 \log{\left(3 \right)} + 4 \sqrt{2}$$
=
=
                                     ___
                           ___   8*\/ 3 
-2*log(2) + 2*log(3) + 4*\/ 2  - -------
                                    3   
$$- \frac{8 \sqrt{3}}{3} - 2 \log{\left(2 \right)} + 2 \log{\left(3 \right)} + 4 \sqrt{2}$$
-2*log(2) + 2*log(3) + 4*sqrt(2) - 8*sqrt(3)/3
Numerical answer [src]
1.8489823121917
1.8489823121917

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