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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Assertion : The value of the integral ∫ex[tan⁡x+sec⁡2x]dx\int e^x\left[\tan x+\sec ^2 x\right] d x is extan⁡x+C\mathrm{e}^{\mathrm{x}} \tan \mathrm{x}+\mathrm{C}

Reason: The value of the integral ex{f(x)+f′(x)}dxe^x\left\{f(x)+f^{\prime}(x)\right\} d x is exf(x)+C\mathrm{e}^{\mathrm{x}} \mathrm{f}(\mathrm{x})+\mathrm{C}.
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Correct option: A
Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
Option A is correct because the assertion is true, and the reason correctly explains why the assertion is true. The integral of ex[f(x)+f′(x)]dxe^x[f(x) + f'(x)] dx is indeed exf(x)+Ce^x f(x) + C, and this applies to the given assertion with f(x)=tan⁡xf(x) = \tan x.

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