Mathematics · 2022
JEE Main · 27 June 2022, Shift 1 · Q9
If ∫ ((x^2+1) e^x)/((x+1)^2) d x=f(x) e^x+ C, where C is a constant, then (d^3 f)/(d x^3) at x=1 is equal to:
If $\displaystyle \int \frac{\left(x^2+1\right) \mathrm{e}^x}{(x+1)^2} \mathrm{~d} x=f(x) \mathrm{e}^x+\mathrm{C}$, where C is a constant, then $\displaystyle \frac{\mathrm{d}^3 f}{\mathrm{~d} x^3}$ at $\displaystyle x=1$ is equal to:
Official answer
(2)
$\displaystyle \frac{3}{4}$
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.