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- Integral of d{x}:
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Integral of e^(2*x+1)
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Integral of e^x²
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Integral of (-x)/(1+x^2)
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Integral of sqrt(x^2+4)/x^2
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Identical expressions
- one /ch(x)^ three
- 1 divide by ch(x) cubed
- one divide by ch(x) to the power of three
- 1/ch(x)3
- 1/chx3
- 1/ch(x)³
- 1/ch(x) to the power of 3
- 1/chx^3
- 1 divide by ch(x)^3
- 1/ch(x)^3dx
Integral of 1/ch(x)^3 dx
The solution
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[src]
oo / | | 1 | -------- dx | 3 | cosh (x) | / 0
$$\int\limits_{0}^{\infty} \frac{1}{\cosh^{3}{\left(x \right)}}\, dx$$
Integral(1/(cosh(x)^3), (x, 0, oo))
The answer (Indefinite)
[src]
/ / /x\\ /x\ 3/x\ 4/x\ / /x\\ 2/x\ / /x\\ | atan|tanh|-|| tanh|-| tanh |-| tanh |-|*atan|tanh|-|| 2*tanh |-|*atan|tanh|-|| | 1 \ \2// \2/ \2/ \2/ \ \2// \2/ \ \2// | -------- dx = C + ------------------------- + ------------------------- - ------------------------- + ------------------------- + ------------------------- | 3 4/x\ 2/x\ 4/x\ 2/x\ 4/x\ 2/x\ 4/x\ 2/x\ 4/x\ 2/x\ | cosh (x) 1 + tanh |-| + 2*tanh |-| 1 + tanh |-| + 2*tanh |-| 1 + tanh |-| + 2*tanh |-| 1 + tanh |-| + 2*tanh |-| 1 + tanh |-| + 2*tanh |-| | \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{1}{\cosh^{3}{\left(x \right)}}\, dx = C + \frac{\tanh^{4}{\left(\frac{x}{2} \right)} \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{\tanh^{3}{\left(\frac{x}{2} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2 \tanh^{2}{\left(\frac{x}{2} \right)} \operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\tanh{\left(\frac{x}{2} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\operatorname{atan}{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{\tanh^{4}{\left(\frac{x}{2} \right)} + 2 \tanh^{2}{\left(\frac{x}{2} \right)} + 1}$$
The graph
Use the examples entering the upper and lower limits of integration.