Integral of sinx/(2cosx)/2 dx

The solution

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

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

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

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{\sin{\left(x \right)}}{2 \cdot 2 \cos{\left(x \right)}}\, dx = \frac{\int \frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)}}\, dx}{2}$
1. Let $u = 2 \cos{\left(x \right)}$ .
  
  Then let $du = - 2 \sin{\left(x \right)} dx$ and substitute $- \frac{du}{2}$ :
  
  $\int \frac{1}{4 u}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{1}{2 u}\right)\, du = - \frac{\int \frac{1}{u}\, du}{2}$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    So, the result is: $- \frac{\log{\left(u \right)}}{2}$
  Now substitute $u$ back in:
  
  $- \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{2}$
So, the result is: $- \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{4}$
Add the constant of integration:

$- \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{4}+ \mathrm{constant}$

The answer is:

$- \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                                  
 |   sin(x)            log(2*cos(x))
 | ---------- dx = C - -------------
 | 2*cos(x)*2                4      
 |                                  
/

$$-{{\log \cos x}\over{4}}$$

Simplify

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Plot the graph f(x)

The answer [src]

-log(cos(1)) 
-------------
      4

$$-{{\log \cos 1}\over{4}}$$

-log(cos(1)) 
-------------
      4

$$- \frac{\log{\left(\cos{\left(1 \right)} \right)}}{4}$$

Упростить

Numerical answer [src]

0.153906617596504

0.153906617596504

The graph

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

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Integral of sinx/(2cosx)/2 dx

Limits of integration:

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The solution