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(two *sqrt(x)-sqrt(2x)+ five)
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Similar expressions
(2*sqrt(x)+sqrt(2x)+5)
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Solving integrals/ (2*sqrt(x)-sqrt(2x)+5)

Integral of (2*sqrt(x)-sqrt(2x)+5) dx

The solution

You have entered [src]

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

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

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

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 \sqrt{x}\, dx = 2 \int \sqrt{x}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
    So, the result is: $\frac{4 x^{\frac{3}{2}}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \sqrt{2 x}\right)\, dx = - \int \sqrt{2 x}\, dx$
    1. Don't know the steps in finding this integral.
      
      But the integral is
      
      $\frac{2 \sqrt{2} x^{\frac{3}{2}}}{3}$
    So, the result is: $- \frac{2 \sqrt{2} x^{\frac{3}{2}}}{3}$
  The result is: $- \frac{2 \sqrt{2} x^{\frac{3}{2}}}{3} + \frac{4 x^{\frac{3}{2}}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 5\, dx = 5 x$
The result is: $- \frac{2 \sqrt{2} x^{\frac{3}{2}}}{3} + \frac{4 x^{\frac{3}{2}}}{3} + 5 x$
Add the constant of integration:

$- \frac{2 \sqrt{2} x^{\frac{3}{2}}}{3} + \frac{4 x^{\frac{3}{2}}}{3} + 5 x+ \mathrm{constant}$

The answer is:

$- \frac{2 \sqrt{2} x^{\frac{3}{2}}}{3} + \frac{4 x^{\frac{3}{2}}}{3} + 5 x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                            
 |                                           3/2       ___  3/2
 | /    ___     _____    \                4*x      2*\/ 2 *x   
 | \2*\/ x  - \/ 2*x  + 5/ dx = C + 5*x + ------ - ------------
 |                                          3           3      
/

$$\int \left(\left(2 \sqrt{x} - \sqrt{2 x}\right) + 5\right)\, dx = C - \frac{2 \sqrt{2} x^{\frac{3}{2}}}{3} + \frac{4 x^{\frac{3}{2}}}{3} + 5 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         ___
19   2*\/ 2 
-- - -------
3       3

$$\frac{19}{3} - \frac{2 \sqrt{2}}{3}$$

         ___
19   2*\/ 2 
-- - -------
3       3

$$\frac{19}{3} - \frac{2 \sqrt{2}}{3}$$

19/3 - 2*sqrt(2)/3

Numerical answer [src]

5.39052429175127

5.39052429175127

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

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Integral of (2*sqrt(x)-sqrt(2x)+5) dx

Limits of integration:

The graph:

Piecewise:

The solution