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Integrate the functions: e2x-1e2x+1

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प्रश्न

Integrate the functions:

`(e^(2x) - 1)/(e^(2x) + 1)`

योग
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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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अध्याय 7: Integrals - Exercise 7.2 [पृष्ठ ३०५]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 7 Integrals
Exercise 7.2 | Q 19 | पृष्ठ ३०५

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