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Integral of (2tanx)/(1-tanx^2) dx

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The solution

You have entered [src]
  1               
  /               
 |                
 |    2*tan(x)    
 |  ----------- dx
 |         2      
 |  1 - tan (x)   
 |                
/                 
0                 
$$\int\limits_{0}^{1} \frac{2 \tan{\left(x \right)}}{1 - \tan^{2}{\left(x \right)}}\, dx$$
Integral((2*tan(x))/(1 - tan(x)^2), (x, 0, 1))
The answer (Indefinite) [src]
  /                                                        
 |                      //      /   2   \         4       \
 |   2*tan(x)           ||-acoth\tan (x)/  for tan (x) > 1|
 | ----------- dx = C - |<                                |
 |        2             ||      /   2   \         4       |
 | 1 - tan (x)          \\-atanh\tan (x)/  for tan (x) < 1/
 |                                                         
/                                                          
$$\int \frac{2 \tan{\left(x \right)}}{1 - \tan^{2}{\left(x \right)}}\, dx = C - \begin{cases} - \operatorname{acoth}{\left(\tan^{2}{\left(x \right)} \right)} & \text{for}\: \tan^{4}{\left(x \right)} > 1 \\- \operatorname{atanh}{\left(\tan^{2}{\left(x \right)} \right)} & \text{for}\: \tan^{4}{\left(x \right)} < 1 \end{cases}$$
The graph
The answer [src]
nan
$$\text{NaN}$$
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nan
$$\text{NaN}$$
nan
Numerical answer [src]
-0.96117546625349
-0.96117546625349

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