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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫ex(1+tan⁡x+tan⁡2x)dx=\int e^x\left(1+\tan x+\tan ^2 x\right) d x=
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Correct option: C
extan⁡x+ce^x \tan x+c
Option C is correct because the integral simplifies to extan⁡x+ce^x \tan x + c by recognizing the form ∫ex[f(x)+f′(x)]dx=exf(x)+c\int e^x [f(x) + f'(x)] dx = e^x f(x) + c.

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