Mathematics

The value of $$\int {\left( {x - 1} \right){e^{ - x}}} $$ is equal to 


ANSWER

$$ - x{e^{ - x}} + C$$


SOLUTION
$$ \int (x-1) e^{-x} \ dx$$.
$$-x = t - dx= dt$$
$$= \int (t+1) e^{t} \ dt$$
$$= (t+1 )e^{t} - \int e^{t} \ dt$$ [Integration by  parts].
$$= (t+1) e^{t} - e^{t} +c$$
$$= te^{t} + c$$
$$= - xe^{-x}+ c$$.
$$C$$ is correct.
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Single Correct Medium Published on 17th 09, 2020
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