Integral of cosx/sqrt(sinx) dx

The solution

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  1              
  /              
 |               
 |    cos(x)     
 |  ---------- dx
 |    ________   
 |  \/ sin(x)    
 |               
/                
0

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

Integral(cos(x)/(sqrt(sin(x))), (x, 0, 1))

Detail solution

Let $u = \sqrt{\sin{\left(x \right)}}$ .

Then let $du = \frac{\cos{\left(x \right)} dx}{2 \sqrt{\sin{\left(x \right)}}}$ and substitute $2 du$ :

$\int 4\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2\, du = 2 \int 1\, du$
  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:

$2 \sqrt{\sin{\left(x \right)}}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$2\,\sqrt{\sin x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    ________
2*\/ sin(1)

$$2\,\sqrt{\sin 1}$$

    ________
2*\/ sin(1)

$$2 \sqrt{\sin{\left(1 \right)}}$$

Simplify

Numerical answer [src]

1.83463455128634

1.83463455128634

The graph

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

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Integral of cosx/sqrt(sinx) dx

Limits of integration:

The graph:

Piecewise:

The solution