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1/(5+3*cos(x))
Solving integrals/ 1/(5+3*cos(x))

Integral of 1/(5+3*cos(x)) dx

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The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |         1         
 |  1*------------ dx
 |    5 + 3*cos(x)   
 |                   
/                    
0
∫011⋅13cos⁡(x)+5 dx\int\limits_{0}^{1} 1 \cdot \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  /
 | 1*------------ dx = C + ------------ + ----------------
 |   5 + 3*cos(x)               2                2        
 |                                                        
/
∫1⋅13cos⁡(x)+5 dx=C+atan⁡(tan⁡(x2)2)2+π⌊x2−π2π⌋2\int 1 \cdot \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}
Упростить
Numerical answer [src] 
0.133323313468988
0.133323313468988
The graph
Integral of 1/(5+3*cos(x)) dx

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

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