{e²x}-1}{e²x}+1} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 41 of 271

Marks: +1, -0

\frac{e^{2x}-1}{e^{2x}+1}

Solution:

Let

I=\int\frac{e^{2x}-1}{e^{2x}+1}dx

=\int\frac{e^x(e^x-e^{-x})}{e^x(e^x+e^{-x})}dx

=\int\frac{e^x-e^{-x}}{e^x+e^{-x}}dx

Put

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

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

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

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

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