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1/(5-3cosx)

Integral of 1/(5-3cosx) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |  5 - 3*cos(x)   
 |                 
/                  
0                  
$$\int\limits_{0}^{1} \frac{1}{5 - 3 \cos{\left(x \right)}}\, dx$$
Integral(1/(5 - 3*cos(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]
                                                  /x   pi\
                                                  |- - --|
  /                          /     /x\\           |2   2 |
 |                       atan|2*tan|-||   pi*floor|------|
 |      1                    \     \2//           \  pi  /
 | ------------ dx = C + -------------- + ----------------
 | 5 - 3*cos(x)                2                 2        
 |                                                        
/                                                         
$$\int \frac{1}{5 - 3 \cos{\left(x \right)}}\, dx = C + \frac{\operatorname{atan}{\left(2 \tan{\left(\frac{x}{2} \right)} \right)}}{2} + \frac{\pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{2}$$
The graph
The answer [src]
atan(2*tan(1/2))
----------------
       2        
$$\frac{\operatorname{atan}{\left(2 \tan{\left(\frac{1}{2} \right)} \right)}}{2}$$
=
=
atan(2*tan(1/2))
----------------
       2        
$$\frac{\operatorname{atan}{\left(2 \tan{\left(\frac{1}{2} \right)} \right)}}{2}$$
atan(2*tan(1/2))/2
Numerical answer [src]
0.414811377137613
0.414811377137613
The graph
Integral of 1/(5-3cosx) dx

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