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dx/(5+4cos2x)
Solving integrals/ dx/(5+4cos2x)

Integral of dx/(5+4cos2x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                    
  /                    
 |                     
 |          1          
 |  1*-------------- dx
 |    5 + 4*cos(2*x)   
 |                     
/                      
0
∫011⋅14cos⁡(2x)+5 dx\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))
The answer (Indefinite) [src] 
                                                    /    pi\
                                                    |x - --|
  /                              /tan(x)\           |    2 |
 |                           atan|------|   pi*floor|------|
 |         1                     \  3   /           \  pi  /
 | 1*-------------- dx = C + ------------ + ----------------
 |   5 + 4*cos(2*x)               3                3        
 |                                                          
/
arctan⁡(sin⁡(2 x)3 (cos⁡(2 x)+1))3{{\arctan \left({{\sin \left(2\,x\right)}\over{3\,\left(\cos \left( 2\,x\right)+1\right)}}\right)}\over{3}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.901-2
Plot the graph f(x)
The answer [src] 
    /tan(1)\
atan|------|
    \  3   /
------------
     3
arctan⁡(sin⁡23 cos⁡2+3)3{{\arctan \left({{\sin 2}\over{3\,\cos 2+3}}\right)}\over{3}} 
=
= 
    /tan(1)\
atan|------|
    \  3   /
------------
     3
atan⁡(tan⁡(1)3)3\frac{\operatorname{atan}{\left(\frac{\tan{\left(1 \right)}}{3} \right)}}{3}
Simplify
Numerical answer [src] 
0.15961295948005
0.15961295948005
The graph
Integral of dx/(5+4cos2x) dx

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

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