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प्रश्न
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
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उत्तर
Let `I = int (e^(2x) - 1)/(e^(2x) + 1)` dx
On dividing the numerator and denominator by ex
`= int (e^x - e^(-x))/(e^x + e^(-x))` dx
Put ex + e-x = t
Then, ex - e-x dx = dt
Hence, `I = int 1/t` dt
= log t + C
= log (ex + e-x) + C
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