(Step-by-Step) For each x >0, let G(x)=∫_0^∞ e^-xtdt. Prove that xG(x)=1, for each x


Question: For each x >0, let \(G\left( x \right)=\int\limits_{0}^{\infty }{{{e}^{-xt}}dt}\). Prove that \(xG\left( x \right)=1\), for each x >0.

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