{dx}{e^x+e^{-x}} is equal to - NCERT Class XII Mathematics ...

NCERT Class XII Mathematics Chapter - - Solutions

Choose the correct answers in Exercises 269 to 272.

Question : 269 of 271

Marks: +1, -0

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

is equal to

Solution:

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

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

\Rightarrow I=\int \frac{e^x dx}{(e^x)^2+1}

Put

e^x = t

\Rightarrow e^x dx = dt

\therefore I=\int \frac{dt}{t^2+1}

=\tan^{-1}t+C

=\tan^{-1}(e^x)+C

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