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Integral of e^x [f(x) + f'(x)] equals e^x f(x)

This type of question, asked 3 times: 19 Apr 2025 S1, 11 Apr 2026 S2, 15 May 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    19 Apr 2025 S1

    124
    ∫1eexx(1+xlogx)dx=\int_{1}^{e} \frac{e^{x}}{x}(1 +xlogx)dx=

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  2. Question 2

    11 Apr 2026 S2

    81
    If ∫2e[1log⁡x−1(log⁡x)2]dx=a+blog⁡2\displaystyle\int_2^e\left[\dfrac{1}{\log x} - \dfrac{1}{(\log x)^2}\right]dx = a + \dfrac{b}{\log 2}, then values of aa and bb are

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  3. Question 3

    15 May 2026 S2

    84
    The value of I=∫13ex(x+2)2(x+4)2 dxI = \int_1^3 e^x\dfrac{(x + 2)^2}{(x + 4)^2}\, dx is:

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