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

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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((e^x + 1)/(e^x + 2)) + c) is correct because by using substitution and partial fraction decomposition, the integral can be solved to obtain the given result.

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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