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1/(5-4cos(2x))

Integral of 1/(5-4cos(2x)) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                    
  /                    
 |                     
 |          1          
 |  1*-------------- dx
 |    5 - 4*cos(2*x)   
 |                     
/                      
0                      
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{- 4 \cos{\left(2 x \right)} + 5}\, dx$$
Integral(1/(5 - 4*cos(2*x)), (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

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

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  3. Now simplify:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
                                                      /    pi\
                                                      |x - --|
  /                                                   |    2 |
 |                                            pi*floor|------|
 |         1                 atan(3*tan(x))           \  pi  /
 | 1*-------------- dx = C + -------------- + ----------------
 |   5 - 4*cos(2*x)                3                 3        
 |                                                            
/                                                             
$${{\arctan \left({{3\,\sin \left(2\,x\right)}\over{\cos \left(2\,x \right)+1}}\right)}\over{3}}$$
The graph
The answer [src]
atan(3*tan(1))
--------------
      3       
$${{\arctan \left({{3\,\sin 2}\over{\cos 2+1}}\right)}\over{3}}$$
=
=
atan(3*tan(1))
--------------
      3       
$$\frac{\operatorname{atan}{\left(3 \tan{\left(1 \right)} \right)}}{3}$$
Numerical answer [src]
0.453315553466098
0.453315553466098
The graph
Integral of 1/(5-4cos(2x)) dx

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