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Integral of xdx/sqrt(5+4x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 -1               
  /               
 |                
 |       x        
 |  ----------- dx
 |    _________   
 |  \/ 5 + 4*x    
 |                
/                 
-2                
$$\int\limits_{-2}^{-1} \frac{x}{\sqrt{4 x + 5}}\, dx$$
Integral(x/sqrt(5 + 4*x), (x, -2, -1))
Detail solution
  1. Let .

    Then let and substitute :

    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 when :

        So, the result is:

      1. The integral of a constant is the constant times the variable of integration:

      The result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                 
 |                          _________            3/2
 |      x               5*\/ 5 + 4*x    (5 + 4*x)   
 | ----------- dx = C - ------------- + ------------
 |   _________                8              24     
 | \/ 5 + 4*x                                       
 |                                                  
/                                                   
$$\int \frac{x}{\sqrt{4 x + 5}}\, dx = C + \frac{\left(4 x + 5\right)^{\frac{3}{2}}}{24} - \frac{5 \sqrt{4 x + 5}}{8}$$
The graph
The answer [src]
             ___
  7    3*I*\/ 3 
- -- + ---------
  12       4    
$$- \frac{7}{12} + \frac{3 \sqrt{3} i}{4}$$
=
=
             ___
  7    3*I*\/ 3 
- -- + ---------
  12       4    
$$- \frac{7}{12} + \frac{3 \sqrt{3} i}{4}$$
-7/12 + 3*i*sqrt(3)/4
Numerical answer [src]
(-0.759777064460204 + 1.21294360408918j)
(-0.759777064460204 + 1.21294360408918j)

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