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tanx/(2secx+1)
Solving integrals/ tanx/(2secx+1)

Integral of tanx/(2secx+1) dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |     tan(x)      
 |  ------------ dx
 |  2*sec(x) + 1   
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{\tan{\left(x \right)}}{2 \sec{\left(x \right)} + 1}\, dx$$
Simplify
The answer (Indefinite) [src] 
  /                                                          
 |                          /       2   \                    
 |    tan(x)             log\1 + tan (x)/                    
 | ------------ dx = C + ---------------- - log(1 + 2*sec(x))
 | 2*sec(x) + 1                 2                            
 |                                                           
/
$$-\log \left(\cos x+2\right)$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   /       2   \                             
log\1 + tan (1)/                             
---------------- - log(1 + 2*sec(1)) + log(3)
       2
$$\log 3-\log \left(\cos 1+2\right)$$ 
=
= 
   /       2   \                             
log\1 + tan (1)/                             
---------------- - log(1 + 2*sec(1)) + log(3)
       2
$$- \log{\left(1 + 2 \sec{\left(1 \right)} \right)} + \frac{\log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{2} + \log{\left(3 \right)}$$
Simplify
Numerical answer [src] 
0.166329196661429
0.166329196661429
The graph
Integral of tanx/(2secx+1) dx

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

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