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Question
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Solution
Let I = `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Put aex − be−x = t
∴ `["ae"^("x") − "be"^(−"x") .(-1)] "dx" = "dt"`
∴ `("ae"^("x") + "be"^(−"x")) "dx" = "dt"`
∴ I = `int "dt"/"t"`
∴ I = `int 1/"t" "dt"`
∴ I = log | t | + c
∴ I = log | aex − be−x | + c
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