$\smallint \,\,\frac{{{e^x}}}{{\left( {2 + {e^x}} \right)\,\,\left( {{e^x} + 1} \right)}}\,\,dx$ is equal to

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

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{{e^x}}}{{\left( {2 + {e^x}} \right)\,\,\left( {{e^x} + 1} \right)}}\,\,dx

is equal to

View answer and explanation

Correct option: A

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

Option A (

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

) is correct because the integral is solved using substitution and partial fraction decomposition.