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sin(x)/(cos(x)+2)

Integral of sin(x)/(cos(x)+2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |    sin(x)     
 |  ---------- dx
 |  cos(x) + 2   
 |               
/                
0                
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 2}\, dx$$
Integral(sin(x)/(cos(x) + 2), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

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

      1. The integral of is .

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                   
 |                                    
 |   sin(x)                           
 | ---------- dx = C - log(cos(x) + 2)
 | cos(x) + 2                         
 |                                    
/                                     
$$\int \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 2}\, dx = C - \log{\left(\cos{\left(x \right)} + 2 \right)}$$
The graph
The answer [src]
-log(2 + cos(1)) + log(3)
$$- \log{\left(\cos{\left(1 \right)} + 2 \right)} + \log{\left(3 \right)}$$
=
=
-log(2 + cos(1)) + log(3)
$$- \log{\left(\cos{\left(1 \right)} + 2 \right)} + \log{\left(3 \right)}$$
-log(2 + cos(1)) + log(3)
Numerical answer [src]
0.166329196661429
0.166329196661429
The graph
Integral of sin(x)/(cos(x)+2) dx

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