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x/(cosh(x))^2
Solving integrals/ x/(cosh(x))^2

Integral of x/(cosh(x))^2 dx

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The solution

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  1            
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 |     x       
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 |      2      
 |  cosh (x)   
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0
∫01xcosh⁡2(x) dx\int\limits_{0}^{1} \frac{x}{\cosh^{2}{\left(x \right)}}\, dx 
Integral(x/(cosh(x)^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                    /        2/x\\        /        /x\\          2/x\        2/x\    /        2/x\\           /x\          2/x\    /        /x\\
 |                                  log|1 + tanh |-||   2*log|1 + tanh|-||    x*tanh |-|    tanh |-|*log|1 + tanh |-||   2*x*tanh|-|    2*tanh |-|*log|1 + tanh|-||
 |    x                   x            \         \2//        \        \2//           \2/         \2/    \         \2//           \2/           \2/    \        \2//
 | -------- dx = C - ------------ - ----------------- + ------------------ - ------------ - -------------------------- + ------------ + ---------------------------
 |     2                     2/x\              2/x\                2/x\              2/x\                  2/x\                  2/x\                   2/x\       
 | cosh (x)          1 + tanh |-|      1 + tanh |-|        1 + tanh |-|      1 + tanh |-|          1 + tanh |-|          1 + tanh |-|           1 + tanh |-|       
 |                            \2/               \2/                 \2/               \2/                   \2/                   \2/                    \2/       
/
4 (x e2 x2 e2 x+2−log⁡(e2 x+1)4)4\,\left({{x\,e^{2\,x}}\over{2\,e^{2\,x}+2}}-{{\log \left(e^{2\,x}+ 1\right)}\over{4}}\right)
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.00.5
Plot the graph f(x)
The answer [src] 
                         2             /        2     \                                               2         /        2     \         2                        
        1            tanh (1/2)     log\1 + tanh (1/2)/   2*log(1 + tanh(1/2))    2*tanh(1/2)     tanh (1/2)*log\1 + tanh (1/2)/   2*tanh (1/2)*log(1 + tanh(1/2))
- -------------- - -------------- - ------------------- + -------------------- + -------------- - ------------------------------ + -------------------------------
          2                2                   2                     2                   2                        2                                 2             
  1 + tanh (1/2)   1 + tanh (1/2)      1 + tanh (1/2)        1 + tanh (1/2)      1 + tanh (1/2)           1 + tanh (1/2)                    1 + tanh (1/2)
log⁡2−(e2+1) log⁡(e2+1)−2 e2e2+1\log 2-{{\left(e^2+1\right)\,\log \left(e^2+1\right)-2\,e^2}\over{e ^2+1}} 
=
= 
                         2             /        2     \                                               2         /        2     \         2                        
        1            tanh (1/2)     log\1 + tanh (1/2)/   2*log(1 + tanh(1/2))    2*tanh(1/2)     tanh (1/2)*log\1 + tanh (1/2)/   2*tanh (1/2)*log(1 + tanh(1/2))
- -------------- - -------------- - ------------------- + -------------------- + -------------- - ------------------------------ + -------------------------------
          2                2                   2                     2                   2                        2                                 2             
  1 + tanh (1/2)   1 + tanh (1/2)      1 + tanh (1/2)        1 + tanh (1/2)      1 + tanh (1/2)           1 + tanh (1/2)                    1 + tanh (1/2)
−1tanh⁡2(12)+1−tanh⁡2(12)tanh⁡2(12)+1−log⁡(tanh⁡2(12)+1)tanh⁡2(12)+1−log⁡(tanh⁡2(12)+1)tanh⁡2(12)tanh⁡2(12)+1+2log⁡(tanh⁡(12)+1)tanh⁡2(12)tanh⁡2(12)+1+2log⁡(tanh⁡(12)+1)tanh⁡2(12)+1+2tanh⁡(12)tanh⁡2(12)+1- \frac{1}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{\tanh^{2}{\left(\frac{1}{2} \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{\log{\left(\tanh^{2}{\left(\frac{1}{2} \right)} + 1 \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{\log{\left(\tanh^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tanh^{2}{\left(\frac{1}{2} \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} + \frac{2 \log{\left(\tanh{\left(\frac{1}{2} \right)} + 1 \right)} \tanh^{2}{\left(\frac{1}{2} \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} + \frac{2 \log{\left(\tanh{\left(\frac{1}{2} \right)} + 1 \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} + \frac{2 \tanh{\left(\frac{1}{2} \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1}
Simplify
Numerical answer [src] 
0.327813325472738
0.327813325472738
The graph
Integral of x/(cosh(x))^2 dx

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

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