EXPONENTIAL FUNCTIONS
24.109
24.111
207
24.110 Find f jc tanh x
2 dx.
Find
Find
Moreover, by Problems 24.102 and 24.101,
Thus,
Let M = tanh(x/2); by Problems 24.99 and 24.101,
Let M = 1+ cosh x, du = sinh x dx. Then
Let M = x
2
, du = 2x dx. Then
f x tanh x
2 dx
J tanh u du
In icosh u\ + C =
In (cosh x
2 ) + C.
dw = In |M| + C = In (1 + cosh x) + C.