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Solving integrals/ dx/(4+5sin2x)

Integral of dx/(4+5sin2x) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  x                    
  /                    
 |                     
 |          1          
 |  1*-------------- dx
 |    4 + 5*sin(2*x)   
 |                     
/                      
0
$$\int\limits_{0}^{x} 1 \cdot \frac{1}{5 \sin{\left(2 x \right)} + 4}\, dx$$ 
Integral(1/(4 + 5*sin(2*x)), (x, 0, x))
The answer (Indefinite) [src] 
  /                                                             
 |                                                              
 |         1                 log(2 + tan(x))   log(1 + 2*tan(x))
 | 1*-------------- dx = C - --------------- + -----------------
 |   4 + 5*sin(2*x)                 6                  6        
 |                                                              
/
$${{\log \left({{2\,\sin \left(2\,x\right)}\over{\cos \left(2\,x \right)+1}}+1\right)}\over{6}}-{{\log \left({{\sin \left(2\,x\right) }\over{\cos \left(2\,x\right)+1}}+2\right)}\over{6}}$$
Simplify
The answer [src] 
  log(2 + tan(x))   log(2)   log(1 + 2*tan(x))
- --------------- + ------ + -----------------
         6            6              6
$$- \frac{\log{\left(\tan{\left(x \right)} + 2 \right)}}{6} + \frac{\log{\left(2 \tan{\left(x \right)} + 1 \right)}}{6} + \frac{\log{\left(2 \right)}}{6}$$ 
=
= 
  log(2 + tan(x))   log(2)   log(1 + 2*tan(x))
- --------------- + ------ + -----------------
         6            6              6
$$- \frac{\log{\left(\tan{\left(x \right)} + 2 \right)}}{6} + \frac{\log{\left(2 \tan{\left(x \right)} + 1 \right)}}{6} + \frac{\log{\left(2 \right)}}{6}$$
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    Use the examples entering the upper and lower limits of integration.

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