Mister Exam

Other calculators

Solving integrals/ 1/(sh(t)+1)

Integral of 1/(sh(t)+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 3/4              
  /               
 |                
 |       1        
 |  ----------- dt
 |  sinh(t) + 1   
 |                
/                 
0
$$\int\limits_{0}^{\frac{3}{4}} \frac{1}{\sinh{\left(t \right)} + 1}\, dt$$ 
Integral(1/(sinh(t) + 1), (t, 0, 3/4))
The answer (Indefinite) [src] 
  /                       ___    /       ___       /t\\     ___    /       ___       /t\\
 |                      \/ 2 *log|-1 + \/ 2  + tanh|-||   \/ 2 *log|-1 - \/ 2  + tanh|-||
 |      1                        \                 \2//            \                 \2//
 | ----------- dt = C + ------------------------------- - -------------------------------
 | sinh(t) + 1                         2                                 2               
 |                                                                                       
/
$$\int \frac{1}{\sinh{\left(t \right)} + 1}\, dt = C + \frac{\sqrt{2} \log{\left(\tanh{\left(\frac{t}{2} \right)} - 1 + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \log{\left(\tanh{\left(\frac{t}{2} \right)} - \sqrt{2} - 1 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___ /          /      ___\\     ___    /       ___            \     ___ /          /      ___            \\     ___    /       ___\
\/ 2 *\pi*I + log\1 + \/ 2 //   \/ 2 *log\-1 + \/ 2  + tanh(3/8)/   \/ 2 *\pi*I + log\1 + \/ 2  - tanh(3/8)//   \/ 2 *log\-1 + \/ 2 /
----------------------------- + --------------------------------- - ----------------------------------------- - ---------------------
              2                                 2                                       2                                 2
$$\frac{\sqrt{2} \log{\left(-1 + \tanh{\left(\frac{3}{8} \right)} + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \log{\left(-1 + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \left(\log{\left(- \tanh{\left(\frac{3}{8} \right)} + 1 + \sqrt{2} \right)} + i \pi\right)}{2} + \frac{\sqrt{2} \left(\log{\left(1 + \sqrt{2} \right)} + i \pi\right)}{2}$$ 
=
= 
  ___ /          /      ___\\     ___    /       ___            \     ___ /          /      ___            \\     ___    /       ___\
\/ 2 *\pi*I + log\1 + \/ 2 //   \/ 2 *log\-1 + \/ 2  + tanh(3/8)/   \/ 2 *\pi*I + log\1 + \/ 2  - tanh(3/8)//   \/ 2 *log\-1 + \/ 2 /
----------------------------- + --------------------------------- - ----------------------------------------- - ---------------------
              2                                 2                                       2                                 2
$$\frac{\sqrt{2} \log{\left(-1 + \tanh{\left(\frac{3}{8} \right)} + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \log{\left(-1 + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \left(\log{\left(- \tanh{\left(\frac{3}{8} \right)} + 1 + \sqrt{2} \right)} + i \pi\right)}{2} + \frac{\sqrt{2} \left(\log{\left(1 + \sqrt{2} \right)} + i \pi\right)}{2}$$ 
sqrt(2)*(pi*i + log(1 + sqrt(2)))/2 + sqrt(2)*log(-1 + sqrt(2) + tanh(3/8))/2 - sqrt(2)*(pi*i + log(1 + sqrt(2) - tanh(3/8)))/2 - sqrt(2)*log(-1 + sqrt(2))/2
Numerical answer [src] 
0.554388243048801
0.554388243048801

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

    © Mister Exam – Calculator