for the second one
int (1/(e^(-x) + e^x)) dx
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multiply numerator and denominator by ex
=int exdx / (1 + e2x )
now you look at the table of standard integrals and you use the tan-1 one. I'l take out ex as it is a constant.
= ex int dx / (1 + (ex )2)
= ex x...