Express $\displaystyle\int_{1}^{\infty }{x{{e}^{-2x}}\,\mathrm{d}x} $ in the form of \(a+b{{e}^{-2

Question

Express $\displaystyle\int_{1}^{\infty }{x{{e}^{-2x}}\,\mathrm{d}x} $ in the form of $a+b{{e}^{-2}}$ where $a$ and $b$ are constants to be determined.

Accepted Answer

$\int_1^\infty xe^{-2x}\,\mathrm dx=\frac34e^{-2}$, so $a=0$ and $b=\frac34$.

Techniques of Integration - Integration by Parts

Techniques of Integration - Integration by Parts

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