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Solving integrals/ (1/(5+3cosx))

Integral of (1/(5+3cosx)) dx

Limits of integration:

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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
∫0113cos⁡(x)+5 dx\int\limits_{0}^{1} \frac{1}{3 \cos{\left(x \right)} + 5}\, dx 
Integral(1/(5 + 3*cos(x)), (x, 0, 1))
The answer (Indefinite) [src] 
                             /   /x\\           /x   pi\
                             |tan|-||           |- - --|
  /                          |   \2/|           |2   2 |
 |                       atan|------|   pi*floor|------|
 |      1                    \  2   /           \  pi  /
 | ------------ dx = C + ------------ + ----------------
 | 5 + 3*cos(x)               2                2        
 |                                                      
/
∫13cos⁡(x)+5 dx=C+atan⁡(tan⁡(x2)2)2+π⌊x2−π2π⌋2\int \frac{1}{3 \cos{\left(x \right)} + 5}\, dx = C + \frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{2} \right)}}{2} + \frac{\pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
    /tan(1/2)\
atan|--------|
    \   2    /
--------------
      2
atan⁡(tan⁡(12)2)2\frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{2} \right)}}{2} 
=
= 
    /tan(1/2)\
atan|--------|
    \   2    /
--------------
      2
atan⁡(tan⁡(12)2)2\frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{2} \right)}}{2} 
atan(tan(1/2)/2)/2
Numerical answer [src] 
0.133323313468988
0.133323313468988

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

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