Mathematics

Evaluate : $$\displaystyle \int{\dfrac{x-3}{(x-1)^{3}}e^{x}}dx$$.


SOLUTION
We have
$$\int {\frac{{x - 3}}{{{{\left( {x - 1} \right)}^3}}}{e^x}dx} $$

$$ = \int {{e^x}\frac{{x - 3}}{{{{\left( {x - 1} \right)}^3}}}dx} $$

$$ = \int {{e^x}\left( {\frac{1}{{{{\left( {x - 1} \right)}^2}}} - \frac{2}{{{{\left( {x - 1} \right)}^3}}}} \right)} $$

$$ = \frac{{{e^x}}}{{{{\left( {x - 1} \right)}^2}}} + c$$
Hence, which is the required answer.
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Subjective Medium Published on 17th 09, 2020
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