Attached is the expression and my solution.
I get a solution of zero, is it correct?
Hi,
If I am not mistaken, this can be solved using hyperbolic functions.
I'll break this problem into many sections so you can see what I am doing
Please follow this closely!
If you consider that the hyperbolic functions are
$\displaystyle \frac{e^{x} - e^{-x}}{2} = sinh(x)$
and that
$\displaystyle \frac{e^{x} + e^{-x}}{2} = cosh(x)$
then we can conclude that
$\displaystyle (e^{x} - e^{-x}) = 2sinh(x)$
$\displaystyle e^{x} + e^{-x} = 2cosh(x)$
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Which means that if you use them in your problem you will get
$\displaystyle (e^{u} + e^{-u})*(e^{u}+e^{-u}) = 4 cosh^{2}(u)$
$\displaystyle (e^{u} - e^{-u})*(e^{u}-e^{-u}) = 4 sinh^{2}(u)$
$\displaystyle (e^{u} - e^{-u})^{2} = 4 cosh^{2}(u)$
$\displaystyle 4 cosh^{2}(u) - 4 sinh^{2}(u) = 4$
$\displaystyle \frac{4}{4 cosh^{2}(u)} = \frac{1}{cosh^{2}(u)} = sech^{2}(u)
$