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Identical expressions
3dx/sqrt2x- five
3dx divide by square root of 2x minus 5
3dx divide by square root of 2x minus five
3dx/√2x-5
3dx divide by sqrt2x-5
Similar expressions
3dx/sqrt2x+5

Integral of 3dx/sqrt2x-5 dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |  /   3       \   
 |  |------- - 5| dx
 |  |  _____    |   
 |  \\/ 2*x     /   
 |                  
/                   
0

$$\int\limits_{0}^{1} \left(-5 + \frac{3}{\sqrt{2 x}}\right)\, dx$$

Integral(3/sqrt(2*x) - 5, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-5\right)\, dx = - 5 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{3}{\sqrt{2 x}}\, dx = 3 \int \frac{1}{\sqrt{2 x}}\, dx$
  1. Let $u = \sqrt{2 x}$ .
    
    Then let $du = \frac{\sqrt{2} dx}{2 \sqrt{x}}$ and substitute $du$ :
    
    $\int 1\, du$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    Now substitute $u$ back in:
    
    $\sqrt{2 x}$
  So, the result is: $3 \sqrt{2} \sqrt{x}$
The result is: $3 \sqrt{2} \sqrt{x} - 5 x$
Add the constant of integration:

$3 \sqrt{2} \sqrt{x} - 5 x+ \mathrm{constant}$

The answer is:

$3 \sqrt{2} \sqrt{x} - 5 x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                          
 |                                           
 | /   3       \                    ___   ___
 | |------- - 5| dx = C - 5*x + 3*\/ 2 *\/ x 
 | |  _____    |                             
 | \\/ 2*x     /                             
 |                                           
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

         ___
-5 + 3*\/ 2

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

         ___
-5 + 3*\/ 2

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

-5 + 3*sqrt(2)

Numerical answer [src]

-0.757359314006251

-0.757359314006251

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

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Integral of 3dx/sqrt2x-5 dx

Limits of integration:

The graph:

Piecewise:

The solution