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Integrate the function
$\frac{(x-2) e^x}{(x-1)^3}$
$\frac{(x-2) e^x}{(x-1)^3}$
Solution:
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Verified Answer
$I=\int e^x\left[\frac{1}{(x-1)^2}-\frac{2}{(x-1)^3}\right] d x$
Put $\frac{e^x}{(x-1)^2}=t \Rightarrow e^x\left[\frac{1}{(x-1)^2}-\frac{2}{(x-1)^3}\right] d x=d t$
$\therefore I=\int d t=t+C=\frac{e^x}{(x-1)^2}+C$
Put $\frac{e^x}{(x-1)^2}=t \Rightarrow e^x\left[\frac{1}{(x-1)^2}-\frac{2}{(x-1)^3}\right] d x=d t$
$\therefore I=\int d t=t+C=\frac{e^x}{(x-1)^2}+C$
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