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sech

eq1:sech(x);

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sech

e^(sech(A*x)^4);

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sech

f: sech(a*x);

int(f^2,x);

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sech

e^(sech(x)^4);

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sech

sech(A*x)^4;

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sech

f: sech(a*x);

integral(f^2,x);

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sech-trigexpand

trigexpand(sech(x)^4);

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sech

D(t):= (1/(4*a))*sech...

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sech

Run Example
(%i1)f(x):=diff(sech(A*x)^4, x, 2);
                                         4
(%o1)                   f(x) := diff(sech (A x), x, 2)
(%i2) f(x);
                     2     4          2           2     6
(%o2)            16 A  sech (x A) tanh (x A) - 4 A  sech (x A)
(%i3) g(x):=sech(A*x)^4;
                                          4
(%o3)                         g(x) := sech (A x)
(%i4) h(x):=1/sqrt(1.0-g(x));
                                          1
(%o4)                      h(x) := ----------------
                                   sqrt(1.0 - g(x))
(%i5) 
Run Example
asech(0.980);
(%o1)                          0.20168848779884
(%i2) 
Run Example
asech(0.935);
(%o1)                          0.37075017946602
(%i2) 

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