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Let \(f(x)={\int }_{0}^{x}{e}^{t}f(t)dt+{e}^{x}\) be a differentiable function for all \(x\in R\). Then \(f(x)\) equals:…

Q1

Let \(f(x)={\int }_{0}^{x}{e}^{t}f(t)dt+{e}^{x}\) 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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