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Question
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Solution
Let `I = int (e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))` dx
Put e2x + e-2x = t
2e2x - 2e-2x dx = dt
⇒ 2(e2x - e-2x) dx = `dt/2`
Hence, `I = 1/2 int 1/t` dt
`= 1/2 log t + C`
`= 1/2 log (e^(2x) + e^(-2x)) + C`
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