Integral of 1/(shxch^4x) dx
The solution
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/
/
$$\int \frac{1}{\sinh{\left(x \right)} \cosh^{4}{\left(x \right)}}\, dx = C + \frac{3 \log{\left(\tanh{\left(\frac{x}{2} \right)} \right)} \tanh^{6}{\left(\frac{x}{2} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{9 \log{\left(\tanh{\left(\frac{x}{2} \right)} \right)} \tanh^{4}{\left(\frac{x}{2} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{9 \log{\left(\tanh{\left(\frac{x}{2} \right)} \right)} \tanh^{2}{\left(\frac{x}{2} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{3 \log{\left(\tanh{\left(\frac{x}{2} \right)} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{12 \tanh^{4}{\left(\frac{x}{2} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{12 \tanh^{2}{\left(\frac{x}{2} \right)}}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3} + \frac{8}{3 \tanh^{6}{\left(\frac{x}{2} \right)} + 9 \tanh^{4}{\left(\frac{x}{2} \right)} + 9 \tanh^{2}{\left(\frac{x}{2} \right)} + 3}$$
Use the examples entering the upper and lower limits of integration.