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1/(1+tg(x))
Solving integrals/ 1/(1+tg(x))

Integral of 1/(1+tg(x)) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |      1        
 |  ---------- dx
 |  1 + tan(x)   
 |               
/                
0
$$\int\limits_{0}^{1} \frac{1}{\tan{\left(x \right)} + 1}\, dx$$ 
Integral(1/(1 + tan(x)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                          
 |                                              /       2   \
 |     1               x   log(1 + tan(x))   log\1 + tan (x)/
 | ---------- dx = C + - + --------------- - ----------------
 | 1 + tan(x)          2          2                 4        
 |                                                           
/
$$\int \frac{1}{\tan{\left(x \right)} + 1}\, dx = C + \frac{x}{2} + \frac{\log{\left(\tan{\left(x \right)} + 1 \right)}}{2} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                         /       2   \
1   log(1 + tan(1))   log\1 + tan (1)/
- + --------------- - ----------------
2          2                 4
$$- \frac{\log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{4} + \frac{\log{\left(1 + \tan{\left(1 \right)} \right)}}{2} + \frac{1}{2}$$ 
=
= 
                         /       2   \
1   log(1 + tan(1))   log\1 + tan (1)/
- + --------------- - ----------------
2          2                 4
$$- \frac{\log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{4} + \frac{\log{\left(1 + \tan{\left(1 \right)} \right)}}{2} + \frac{1}{2}$$ 
1/2 + log(1 + tan(1))/2 - log(1 + tan(1)^2)/4
Numerical answer [src] 
0.661683833757691
0.661683833757691
The graph
Integral of 1/(1+tg(x)) dx

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

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