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Identical expressions
sqrt(tgx)/sin2x
square root of (tgx) divide by sinus of 2x
√(tgx)/sin2x
sqrttgx/sin2x
sqrt(tgx) divide by sin2x
sqrt(tgx)/sin2xdx

Integral of sqrt(tgx)/sin2x dx

The solution

You have entered [src]

  1              
  /              
 |               
 |    ________   
 |  \/ tan(x)    
 |  ---------- dx
 |   sin(2*x)    
 |               
/                
0

$$\int\limits_{0}^{1} \frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(2 x \right)}}\, dx$$

Integral(sqrt(tan(x))/sin(2*x), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(2 x \right)}} = \frac{\sqrt{\tan{\left(x \right)}}}{2 \sin{\left(x \right)} \cos{\left(x \right)}}$
The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{\sqrt{\tan{\left(x \right)}}}{2 \sin{\left(x \right)} \cos{\left(x \right)}}\, dx = \frac{\int \frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(x \right)} \cos{\left(x \right)}}\, dx}{2}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int \frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(x \right)} \cos{\left(x \right)}}\, dx$
So, the result is: $\frac{\int \frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(x \right)} \cos{\left(x \right)}}\, dx}{2}$
Now simplify:

$\int \frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(2 x \right)}}\, dx$
Add the constant of integration:

$\int \frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(2 x \right)}}\, dx+ \mathrm{constant}$

The answer is:

$\int \frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(2 x \right)}}\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

  1              
  /              
 |               
 |    ________   
 |  \/ tan(x)    
 |  ---------- dx
 |   sin(2*x)    
 |               
/                
0

$$\int\limits_{0}^{1} \frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(2 x \right)}}\, dx$$

  1              
  /              
 |               
 |    ________   
 |  \/ tan(x)    
 |  ---------- dx
 |   sin(2*x)    
 |               
/                
0

$$\int\limits_{0}^{1} \frac{\sqrt{\tan{\left(x \right)}}}{\sin{\left(2 x \right)}}\, dx$$

Упростить

Numerical answer [src]

1.24796142721597

1.24796142721597

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

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Identical expressions

Integral of sqrt(tgx)/sin2x dx

Limits of integration:

The graph:

Piecewise:

The solution