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Solving integrals/ 1/(shxch^4x)

Integral of 1/(shxch^4x) dx

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  1                    
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 |         1           
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 |              4      
 |  sinh(x)*cosh (x)   
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∫011sinh⁡(x)cosh⁡4(x) dx\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/
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∫1sinh⁡(x)cosh⁡4(x) dx=C+3log⁡(tanh⁡(x2))tanh⁡6(x2)3tanh⁡6(x2)+9tanh⁡4(x2)+9tanh⁡2(x2)+3+9log⁡(tanh⁡(x2))tanh⁡4(x2)3tanh⁡6(x2)+9tanh⁡4(x2)+9tanh⁡2(x2)+3+9log⁡(tanh⁡(x2))tanh⁡2(x2)3tanh⁡6(x2)+9tanh⁡4(x2)+9tanh⁡2(x2)+3+3log⁡(tanh⁡(x2))3tanh⁡6(x2)+9tanh⁡4(x2)+9tanh⁡2(x2)+3+12tanh⁡4(x2)3tanh⁡6(x2)+9tanh⁡4(x2)+9tanh⁡2(x2)+3+12tanh⁡2(x2)3tanh⁡6(x2)+9tanh⁡4(x2)+9tanh⁡2(x2)+3+83tanh⁡6(x2)+9tanh⁡4(x2)+9tanh⁡2(x2)+3\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}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1000010000
Plot the graph f(x)
The answer [src] 
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∞\infty 
=
= 
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∞\infty 
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Numerical answer [src] 
43.4170994776155
43.4170994776155

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