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Identical expressions
2x- one /(2sqrt(x))
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2x-1/(2sqrt(x))dx
Similar expressions
2x+1/(2sqrt(x))
2*x-1/(2*sqrt(x))

Integral of 2x-1/(2sqrt(x)) dx

The solution

You have entered [src]

  4                   
  /                   
 |                    
 |  /         1   \   
 |  |2*x - -------| dx
 |  |          ___|   
 |  \      2*\/ x /   
 |                    
/                     
1

$$\int\limits_{1}^{4} \left(2 x - \frac{1}{2 \sqrt{x}}\right)\, dx$$

Integral(2*x - 1/(2*sqrt(x)), (x, 1, 4))

Detail solution

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

$- \sqrt{x} + x^{2}+ \mathrm{constant}$

The answer is:

$- \sqrt{x} + x^{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                                    
 | /         1   \           2     ___
 | |2*x - -------| dx = C + x  - \/ x 
 | |          ___|                    
 | \      2*\/ x /                    
 |                                    
/

$$\int \left(2 x - \frac{1}{2 \sqrt{x}}\right)\, dx = C - \sqrt{x} + x^{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$14$$

Numerical answer [src]

14.0

14.0

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

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Integral of 2x-1/(2sqrt(x)) dx

Limits of integration:

The graph:

Piecewise:

The solution