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- Integral of d{x}:
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Integral of 1/(1+4x^2)
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Integral of (sec(x))^3
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Integral of sec^3
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Integral of x*3^x
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Identical expressions
- one /(shxch^4x)
- 1 divide by (shxch to the power of 4x)
- one divide by (shxch to the power of 4x)
- 1/(shxch4x)
- 1/shxch4x
- 1/(shxch⁴x)
- 1/shxch^4x
- 1 divide by (shxch^4x)
- 1/(shxch^4x)dx
Integral of 1/(shxch^4x) dx
The solution
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[src]
1 / | | 1 | ---------------- dx | 4 | sinh(x)*cosh (x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\sinh{\left(x \right)} \cosh^{4}{\left(x \right)}}\, dx$$
Integral(1/(sinh(x)*cosh(x)^4), (x, 0, 1))
The answer (Indefinite)
[src]
/ / /x\\ 2/x\ 4/x\ 6/x\ / /x\\ 2/x\ / /x\\ 4/x\ / /x\\ | 3*log|tanh|-|| 12*tanh |-| 12*tanh |-| 3*tanh |-|*log|tanh|-|| 9*tanh |-|*log|tanh|-|| 9*tanh |-|*log|tanh|-|| | 1 8 \ \2// \2/ \2/ \2/ \ \2// \2/ \ \2// \2/ \ \2// | ---------------- dx = C + ---------------------------------------- + ---------------------------------------- + ---------------------------------------- + ---------------------------------------- + ---------------------------------------- + ---------------------------------------- + ---------------------------------------- | 4 6/x\ 2/x\ 4/x\ 6/x\ 2/x\ 4/x\ 6/x\ 2/x\ 4/x\ 6/x\ 2/x\ 4/x\ 6/x\ 2/x\ 4/x\ 6/x\ 2/x\ 4/x\ 6/x\ 2/x\ 4/x\ | sinh(x)*cosh (x) 3 + 3*tanh |-| + 9*tanh |-| + 9*tanh |-| 3 + 3*tanh |-| + 9*tanh |-| + 9*tanh |-| 3 + 3*tanh |-| + 9*tanh |-| + 9*tanh |-| 3 + 3*tanh |-| + 9*tanh |-| + 9*tanh |-| 3 + 3*tanh |-| + 9*tanh |-| + 9*tanh |-| 3 + 3*tanh |-| + 9*tanh |-| + 9*tanh |-| 3 + 3*tanh |-| + 9*tanh |-| + 9*tanh |-| | \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{1}{\sinh{\left(x \right)} \cosh^{4}{\left(x \right)}}\, dx = C + \frac{3 \log{\left(\tanh{\left(\frac{x}{2} \right)} \right)} \tanh^{6}{\left(\frac{x}{2} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{9 \log{\left(\tanh{\left(\frac{x}{2} \right)} \right)} \tanh^{4}{\left(\frac{x}{2} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{9 \log{\left(\tanh{\left(\frac{x}{2} \right)} \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{3 \log{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{12 \tanh^{4}{\left(\frac{x}{2} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{12 \tanh^{2}{\left(\frac{x}{2} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{8}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3}$$
The graph
Use the examples entering the upper and lower limits of integration.