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Question-129378




Question Number 129378 by BHOOPENDRA last updated on 15/Jan/21
Answered by Dwaipayan Shikari last updated on 15/Jan/21
L(ut^2 e^(−2t) −ute^(−2t) )=u∫_0 ^∞ t^2 e^(−(s+2)t) −u∫_0 ^∞ te^(−(s+2)t) dt  =((2u)/((s+2)^3 ))−(u/((s+2)^2 ))
$$\mathscr{L}\left({ut}^{\mathrm{2}} {e}^{−\mathrm{2}{t}} −{ute}^{−\mathrm{2}{t}} \right)={u}\int_{\mathrm{0}} ^{\infty} {t}^{\mathrm{2}} {e}^{−\left({s}+\mathrm{2}\right){t}} −{u}\int_{\mathrm{0}} ^{\infty} {te}^{−\left({s}+\mathrm{2}\right){t}} {dt} \\ $$$$=\frac{\mathrm{2}{u}}{\left({s}+\mathrm{2}\right)^{\mathrm{3}} }−\frac{{u}}{\left({s}+\mathrm{2}\right)^{\mathrm{2}} } \\ $$

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