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sqrt(tanhx)
Solving integrals/ sqrt(tanhx)

Integral of sqrt(tanhx) dx

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |    _________   
 |  \/ tanh(x)  dx
 |                
/                 
0
$$\int\limits_{0}^{1} \sqrt{\tanh{\left(x \right)}}\, dx$$ 
Integral(sqrt(tanh(x)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                     
 |                         /      _________\                          /       _________\
 |   _________          log\1 + \/ tanh(x) /       /  _________\   log\-1 + \/ tanh(x) /
 | \/ tanh(x)  dx = C + -------------------- - atan\\/ tanh(x) / - ---------------------
 |                               2                                           2          
/
$$\int {\sqrt{\tanh x}}{\;dx}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   /      _________\                          /      _________\
log\1 + \/ tanh(1) /       /  _________\   log\1 - \/ tanh(1) /
-------------------- - atan\\/ tanh(1) / - --------------------
         2                                          2
$$\int_{0}^{1}{\sqrt{\tanh x}\;dx}$$ 
=
= 
   /      _________\                          /      _________\
log\1 + \/ tanh(1) /       /  _________\   log\1 - \/ tanh(1) /
-------------------- - atan\\/ tanh(1) / - --------------------
         2                                          2
$$- \operatorname{atan}{\left(\sqrt{\tanh{\left(1 \right)}} \right)} + \frac{\log{\left(\sqrt{\tanh{\left(1 \right)}} + 1 \right)}}{2} - \frac{\log{\left(- \sqrt{\tanh{\left(1 \right)}} + 1 \right)}}{2}$$
Simplify
Numerical answer [src] 
0.626746010848783
0.626746010848783
The graph
Integral of sqrt(tanhx) dx

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

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