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Question
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Solution
`int ("e"^x - "e"^-x)/("e"^x + "e"^-x) * "d"x`
Put ex + e–x = u
(ex – e–x) = du
`int ("e"^x - "e"^-x)/("e"^x + "e"^-x) * "d"x = int "du"/"u"`
= `log |"u"| + "c"`
`int ("e"^x - "e"^-x)/("e"^x + "e"^-x) * "d"x = log |"e"^x + "e"^-x| + "c"`
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