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Question Number 35238 by abdo.msup.com last updated on 17/May/18

$$studytheconvergenceof$$$${\int }_1^{+\mathrm{\infty }}\frac{e^{-3x}-e^{-2x}}{x^2}dx$$

Commented by prof Abdo imad last updated on 20/May/18

$$thefunctionf\left(x\right)=\frac{e^{-3x}-e^{-2x}}{x}iscontinueon$$$$[1,+\mathrm{\infty }[so{\int }_1^{A}f\left(x\right)dxisconvergentforallA>1$$$$wehavealso{lim}_{x\to +\mathrm{\infty }}{x}^{2}f\left(x\right)=$$$${lim}_{x\to +\mathrm{\infty }}(e^{-3x}-e^{-2x})=0sotheintegralis$$$$convergent.$$

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