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Integral of e^x sqrt(e^x - 1)/(e^x + 3) from 0 to log 5

The same question, asked 3 times: 15 Apr 2026 S1*, 16 Apr 2026 S1, 18 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    15 Apr 2026 S1

    81
    ∫0log⁡10[exex−1ex+8]dx=\displaystyle\int_0^{\log 10}\left[\dfrac{e^x\sqrt{e^x - 1}}{e^x + 8}\right]dx =

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  2. Question 2

    16 Apr 2026 S1

    80
    ∫0log⁡5exex−1ex+3 dx=\displaystyle\int_0^{\log 5}\dfrac{e^x\sqrt{e^x - 1}}{e^x + 3}\,dx =

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  3. Question 3

    18 Apr 2026 S1

    82
    The value of the definite integral ∫0log⁡e5exex−1ex+3 dx\int_0^{\log_e 5}\dfrac{e^x\sqrt{e^x - 1}}{e^x + 3}\,dx is equal to...

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