The value of the integral $\smallint \frac{{dx}}{{{{\left( {{e^x}\,\, + \,\,{e^{ - x}}} \right)}^2}}}$ is

$\frac{1}{2}\,\,\left( {{e^{2x}} + \,\,1} \right)\,\, + \,\,c$

$\frac{1}{2}\,\,\left( {{e^{ - 2x}} + \,\,1} \right)\,\, + \,\,c$

$\frac{1}{4}\,\,\left( {{e^{2x}} - \,\,1} \right)\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of the integral

\int \frac{{dx}}{{{{\left( {{e^x}\,\, + \,\,{e^{ - x}}} \right)}^2}}}

View answer and explanation

Correct option: C

- \frac{1}{2}\,\,{\left( {{e^{2x}} + \,\,1} \right)^{ - 1}}\,\, + \,\,c

Option C (

- \frac{1}{2}\,{\left( {{e^{2x}} + \,1} \right)^{ - 1}}\, + \,c

) is correct because it is the result of integrating the given expression using substitution.