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1/(1+tgx)
Solving integrals/ 1/(1+tgx)

Integral of 1/(1+tgx) dx

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The solution

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

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

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