Mister Exam

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Identical expressions
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(1/x^1/2)+sinxdx
Similar expressions
(1/x^1/2)-sinx

Integral of (1/x^1/2)+sinx dx

The solution

You have entered [src]

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

$$\int\limits_{0}^{\pi} \left(\sin{\left(x \right)} + \frac{1}{\sqrt{x}}\right)\, dx$$

Integral(1/(sqrt(x)) + sin(x), (x, 0, pi))

Detail solution

Integrate term-by-term:
1. The integral of sine is negative cosine:
  
  $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
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:
  
  $2 \sqrt{x}$
The result is: $2 \sqrt{x} - \cos{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

        ____
2 + 2*\/ pi

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

        ____
2 + 2*\/ pi

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

2 + 2*sqrt(pi)

Numerical answer [src]

5.54490770087063

5.54490770087063

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

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Identical expressions

Similar expressions

Integral of (1/x^1/2)+sinx dx

Limits of integration:

The graph:

Piecewise:

The solution