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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫ex(1+ex)(2+ex)dx=\int \frac{e^x}{\left(1+e^x\right)\left(2+e^x\right)} d x=
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Correct option: B
log⁡[1+ex2+ex]+c\log \left[\frac{1+e^x}{2+e^x}\right]+c
Option B is correct because the integral is solved by substituting ex=te^x = t and using partial fraction decomposition.

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