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Question-188534




Question Number 188534 by thotasandeep111 last updated on 03/Mar/23
Answered by mr W last updated on 03/Mar/23
∫f(x)dx=f(x)  ⇒f(x)=e^x   ∫(f(x))^2 dx=∫e^(2x) dx=(e^(2x) /2)+C=(((f(x))^2 )/2)+C
$$\int{f}\left({x}\right){dx}={f}\left({x}\right) \\ $$$$\Rightarrow{f}\left({x}\right)={e}^{{x}} \\ $$$$\int\left({f}\left({x}\right)\right)^{\mathrm{2}} {dx}=\int{e}^{\mathrm{2}{x}} {dx}=\frac{{e}^{\mathrm{2}{x}} }{\mathrm{2}}+{C}=\frac{\left({f}\left({x}\right)\right)^{\mathrm{2}} }{\mathrm{2}}+{C} \\ $$

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