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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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$\int {{e^x}\left( {\cos x - \sin x} \right)dx}$

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If $\displaystyle I_{n}=\int_{-\pi }^{\pi }\frac{\sin nx}{(1+\pi ^{x})\cdot \sin x}dx,n=0,1,2,...,$then
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Q4 Subjective Medium
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