Integral of tgx/sin2x dx

The solution

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

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

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

Detail solution

Rewrite the integrand:

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

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

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

$\frac{\tan{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\tan{\left(x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

 sin(1) 
--------
2*cos(1)

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

 sin(1) 
--------
2*cos(1)

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

sin(1)/(2*cos(1))

Numerical answer [src]

0.778703862327451

0.778703862327451

The graph

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

Other calculators

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Identical expressions

Similar expressions

Integral of tgx/sin2x dx

Limits of integration:

The graph:

Piecewise:

The solution