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Identical expressions
x/(raiz(2x- five))
x divide by (raiz(2x minus 5))
x divide by (raiz(2x minus five))
x/raiz2x-5
x divide by (raiz(2x-5))
x/(raiz(2x-5))dx
Similar expressions
x/(raiz(2x+5))

Solving integrals/ x/(raiz(2x-5))

Integral of x/(raiz(2x-5)) dx

The solution

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  1               
  /               
 |                
 |       x        
 |  ----------- dx
 |    _________   
 |  \/ 2*x - 5    
 |                
/                 
0

$$\int\limits_{0}^{1} \frac{x}{\sqrt{2 x - 5}}\, dx$$

Integral(x/sqrt(2*x - 5), (x, 0, 1))

Detail solution

Let $u = \sqrt{2 x - 5}$ .

Then let $du = \frac{dx}{\sqrt{2 x - 5}}$ and substitute $du$ :

$\int \left(\frac{u^{2}}{2} + \frac{5}{2}\right)\, du$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{u^{2}}{2}\, du = \frac{\int u^{2}\, du}{2}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u^{2}\, du = \frac{u^{3}}{3}$
    So, the result is: $\frac{u^{3}}{6}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \frac{5}{2}\, du = \frac{5 u}{2}$
  The result is: $\frac{u^{3}}{6} + \frac{5 u}{2}$
Now substitute $u$ back in:

$\frac{\left(2 x - 5\right)^{\frac{3}{2}}}{6} + \frac{5 \sqrt{2 x - 5}}{2}$
Now simplify:

$\frac{\left(x + 5\right) \sqrt{2 x - 5}}{3}$
Add the constant of integration:

$\frac{\left(x + 5\right) \sqrt{2 x - 5}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\left(x + 5\right) \sqrt{2 x - 5}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                 
 |                               3/2       _________
 |      x               (2*x - 5)      5*\/ 2*x - 5 
 | ----------- dx = C + ------------ + -------------
 |   _________               6               2      
 | \/ 2*x - 5                                       
 |                                                  
/

$$\int \frac{x}{\sqrt{2 x - 5}}\, dx = C + \frac{\left(2 x - 5\right)^{\frac{3}{2}}}{6} + \frac{5 \sqrt{2 x - 5}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                  ___
      ___   5*I*\/ 5 
2*I*\/ 3  - ---------
                3

$$- \frac{5 \sqrt{5} i}{3} + 2 \sqrt{3} i$$

                  ___
      ___   5*I*\/ 5 
2*I*\/ 3  - ---------
                3

$$- \frac{5 \sqrt{5} i}{3} + 2 \sqrt{3} i$$

2*i*sqrt(3) - 5*i*sqrt(5)/3

Numerical answer [src]

(0.0 - 0.262678347361895j)

(0.0 - 0.262678347361895j)

The graph

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

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Identical expressions

Similar expressions

Integral of x/(raiz(2x-5)) dx

Limits of integration:

The graph:

Piecewise:

The solution