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(- one /sqrt(x))+cos(x)
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( minus one divide by square root of (x)) plus co sinus of e of (x)
(-1/√(x))+cos(x)
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Similar expressions
(-1/sqrt(x))-cos(x)
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Integral of (-1/sqrt(x))+cos(x) dx

The solution

You have entered [src]

  0                      
  /                      
 |                       
 |  /    1           \   
 |  |- ----- + cos(x)| dx
 |  |    ___         |   
 |  \  \/ x          /   
 |                       
/                        
pi                       
--                       
2

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

Integral(-1/sqrt(x) + cos(x), (x, pi/2, 0))

Detail solution

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

$- 2 \sqrt{x} + \sin{\left(x \right)}+ \mathrm{constant}$

The answer is:

$- 2 \sqrt{x} + \sin{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                            
 |                                             
 | /    1           \              ___         
 | |- ----- + cos(x)| dx = C - 2*\/ x  + sin(x)
 | |    ___         |                          
 | \  \/ x          /                          
 |                                             
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

       ___   ____
-1 + \/ 2 *\/ pi

$$-1 + \sqrt{2} \sqrt{\pi}$$

       ___   ____
-1 + \/ 2 *\/ pi

$$-1 + \sqrt{2} \sqrt{\pi}$$

-1 + sqrt(2)*sqrt(pi)

Numerical answer [src]

1.50662827379146

1.50662827379146

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

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Identical expressions

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Integral of (-1/sqrt(x))+cos(x) dx

Limits of integration:

The graph:

Piecewise:

The solution