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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
- Integral of sin^-1(x)
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Integral of 1/x(x+1)
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Integral of x(x^2+1)^3
- Integral of e^(1/x)
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Identical expressions
- x/(cosh(x))^ two
- x divide by ( hyperbolic co sinus of e of ine of (x)) squared
- x divide by ( hyperbolic co sinus of e of ine of (x)) to the power of two
- x/(cosh(x))2
- x/coshx2
- x/(cosh(x))²
- x/(cosh(x)) to the power of 2
- x/coshx^2
- x divide by (cosh(x))^2
- x/(cosh(x))^2dx
Integral of x/(cosh(x))^2 dx
The solution
You have entered
[src]
1 / | | x | -------- dx | 2 | cosh (x) | / 0
$$\int\limits_{0}^{1} \frac{x}{\cosh^{2}{\left(x \right)}}\, dx$$
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/ /
$$4\,\left({{x\,e^{2\,x}}\over{2\,e^{2\,x}+2}}-{{\log \left(e^{2\,x}+
1\right)}\over{4}}\right)$$
The graph
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)
$$\log 2-{{\left(e^2+1\right)\,\log \left(e^2+1\right)-2\,e^2}\over{e
^2+1}}$$
=
=
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)
$$- \frac{1}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{\tanh^{2}{\left(\frac{1}{2} \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{\log{\left(\tanh^{2}{\left(\frac{1}{2} \right)} + 1 \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{\log{\left(\tanh^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tanh^{2}{\left(\frac{1}{2} \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} + \frac{2 \log{\left(\tanh{\left(\frac{1}{2} \right)} + 1 \right)} \tanh^{2}{\left(\frac{1}{2} \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} + \frac{2 \log{\left(\tanh{\left(\frac{1}{2} \right)} + 1 \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1} + \frac{2 \tanh{\left(\frac{1}{2} \right)}}{\tanh^{2}{\left(\frac{1}{2} \right)} + 1}$$
The graph
Use the examples entering the upper and lower limits of integration.