JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

The value of

\int {\frac{{dx}}{{\left( {{e^x} + 1} \right)\left( {2{e^x} + 3} \right)}}}

is equal to

View answer and explanation

Correct option: B

\frac{1}{3}x - \ln \left( {{e^x} + 1} \right) + \frac{2}{3}\ln \left( {2{e^x} + 3} \right) + c

Option B (

\frac{1}{3}x - \ln \left( {{e^x} + 1} \right) + \frac{2}{3}\ln \left( {2{e^x} + 3} \right) + c

) is correct because after using partial fractions and substituting

e^x = t

, the integral evaluates to this expression.

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