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Identical expressions
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cosx/(5sinx)^(1/2)dx

Solving integrals/ cosx/(5sinx)^(1/2)

Integral of cosx/(5sinx)^(1/2) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |     cos(x)      
 |  ------------ dx
 |    __________   
 |  \/ 5*sin(x)    
 |                 
/                  
0

$$\int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{\sqrt{5 \sin{\left(x \right)}}}\, dx$$

Integral(cos(x)/(sqrt(5*sin(x))), (x, 0, 1))

Detail solution

Let $u = \sqrt{5 \sin{\left(x \right)}}$ .

Then let $du = \frac{\sqrt{5} \cos{\left(x \right)} dx}{2 \sqrt{\sin{\left(x \right)}}}$ and substitute $\frac{2 du}{5}$ :

$\int \frac{4}{25}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{2}{5}\, du = \frac{2 \int 1\, du}{5}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, du = u$
  So, the result is: $\frac{2 u}{5}$
Now substitute $u$ back in:

$\frac{2 \sqrt{5} \sqrt{\sin{\left(x \right)}}}{5}$
Now simplify:

$\frac{2 \sqrt{5} \sqrt{\sin{\left(x \right)}}}{5}$
Add the constant of integration:

$\frac{2 \sqrt{5} \sqrt{\sin{\left(x \right)}}}{5}+ \mathrm{constant}$

The answer is:

$\frac{2 \sqrt{5} \sqrt{\sin{\left(x \right)}}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                        
 |                           ___   ________
 |    cos(x)             2*\/ 5 *\/ sin(x) 
 | ------------ dx = C + ------------------
 |   __________                  5         
 | \/ 5*sin(x)                             
 |                                         
/

$${{2\,\sqrt{\sin x}}\over{\sqrt{5}}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    ___   ________
2*\/ 5 *\/ sin(1) 
------------------
        5

$${{2\,\sqrt{\sin 1}}\over{\sqrt{5}}}$$

    ___   ________
2*\/ 5 *\/ sin(1) 
------------------
        5

$$\frac{2 \sqrt{5} \sqrt{\sin{\left(1 \right)}}}{5}$$

Упростить

Numerical answer [src]

0.820473514109217

0.820473514109217

The graph

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

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Identical expressions

Integral of cosx/(5sinx)^(1/2) dx

Limits of integration:

The graph:

Piecewise:

The solution