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Solving integrals/ (1/(3+2*cos(3x)))

Integral of (1/(3+2*cos(3x))) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                  
 --                  
 3                   
  /                  
 |                   
 |        1          
 |  -------------- dx
 |  3 + 2*cos(3*x)   
 |                   
/                    
0
∫0π312cos⁡(3x)+3 dx\int\limits_{0}^{\frac{\pi}{3}} \frac{1}{2 \cos{\left(3 x \right)} + 3}\, dx 
Integral(1/(3 + 2*cos(3*x)), (x, 0, pi/3))
The answer (Indefinite) [src] 
                                   /        /  pi   3*x\       /  ___    /3*x\\\
                                   |        |- -- + ---|       |\/ 5 *tan|---|||
  /                            ___ |        |  2     2 |       |         \ 2 /||
 |                         2*\/ 5 *|pi*floor|----------| + atan|--------------||
 |       1                         \        \    pi    /       \      5       //
 | -------------- dx = C + -----------------------------------------------------
 | 3 + 2*cos(3*x)                                    15                         
 |                                                                              
/
∫12cos⁡(3x)+3 dx=C+25(atan⁡(5tan⁡(3x2)5)+π⌊3x2−π2π⌋)15\int \frac{1}{2 \cos{\left(3 x \right)} + 3}\, dx = C + \frac{2 \sqrt{5} \left(\operatorname{atan}{\left(\frac{\sqrt{5} \tan{\left(\frac{3 x}{2} \right)}}{5} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{15}
Simplify
The graph
0.000.100.200.300.400.500.600.700.800.901.002-2
Plot the graph f(x)
The answer [src] 
     ___
pi*\/ 5 
--------
   15
5π15\frac{\sqrt{5} \pi}{15} 
=
= 
     ___
pi*\/ 5 
--------
   15
5π15\frac{\sqrt{5} \pi}{15} 
pi*sqrt(5)/15
Numerical answer [src] 
0.468320982069382
0.468320982069382

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

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