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Let \(f(x)=\int_0^x e^t f(t) d t+e^x\) be a differentiable function for all \(x \in R\). Then \(f(x)\) equals: [JEE Main…

Q1

Let \(f(x)=\int_0^x e^t f(t) d t+e^x\) be a differentiable function for all \(x \in R\). Then \(f(x)\) equals:

[JEE Main 2021, 26 Feb (Shift 2)]

a

\(2 e^{\left(e^x-1\right)}-1\)

b

\(2 e^{e^x}-1\)

c

\(e^{e^x}-1\)

d

\(\mathrm{e}^{\left(\mathrm{e}^{\mathrm{x}-1}\right)}\)

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