{e²x}-e^{-2x}}{e²x}+e^{-2x}} - NCERT Class XII Mathematics ...

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.2
Integrate the functions in Exercises 23 to 59.

Question : 42 of 271

Marks: +1, -0

\frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}

Solution:

Let

I=\int \frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}

Put

e^{2x}+e^{-2x}=t

\Rightarrow (2e^{2x}-2e^{-2x})dx=dt

\Rightarrow (e^{2x}-e^{-2x})dx=\frac{dt}{2}

\therefore I=\frac{1}{2}\int \frac{1}{t}dt = \frac{1}{2}\log|t|+C

=\frac{1}{2}\log|e^{2x}+e^{-2x}|+C

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