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Integral of x^n e^x written as e^x f(x)

This type of question, asked 3 times: 13 Apr 2026 S2, 12 May 2026 S2, 14 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    13 Apr 2026 S2

    77
    If ∫x2⋅ex dx=exf(x)+c\displaystyle\int x^2 \cdot e^x\,dx = e^x f(x) + c, then the minimum value of f(x)f(x) is ...

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  2. Question 2

    12 May 2026 S2

    77
    If ∫x7ex dx=exf(x)+c\displaystyle\int x^7e^x\,dx = e^xf(x) + c, then f(x)f(x) is equal to...

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  3. Question 3

    14 May 2026 S1

    80
    If ∫x3ex dx=ex(px3+qx2+rx+s)+c\displaystyle\int x^3e^x\,dx = e^x(px^3 + qx^2 + rx + s) + c, then the value of p+q+r+sp + q + r + s is

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