PG entrance exam CUET PG 2025 Mock Test Engineering Mathematics Calculus Theorems of Integral Calculus
The value of \(\smallint \frac{{{{\rm{e}}^{\rm{x}}} + {{\rm{e}}^{ - {\rm{x}}}}}}{{{{\rm{e}}^{\rm{x}}} - {{\rm{e}}^{ - {\rm{x}}}}}}{\rm{\;dx}}\) is equal to –
1
\({\tan ^{ - 1}}\left( {{{\rm{e}}^{\rm{x}}} - {{\rm{e}}^{ - {\rm{x}}}}} \right)\)
2
\(\log \left( {{{\rm{e}}^{\rm{x}}} + {{\rm{e}}^{ - {\rm{x}}}}} \right)\)
3
\(\log \left( {{{\rm{e}}^{ - {\rm{x}}}} - {{\rm{e}}^{\rm{x}}}} \right)\)
4
\(\log \left( {{{\rm{e}}^{\rm{x}}} - {{\rm{e}}^{ - {\rm{x}}}}} \right)\)