Evaluate the following integrals:

Question:

Evaluate the following integrals:

$\int \frac{2-x}{(1-x)^{2}} e^{x} d x$

Solution:

Let I $=\int \frac{2-x}{(1-x)^{2}} e^{x} d x$

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

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

$\frac{1}{1-x}=f(x) \frac{1}{(1-x)^{2}}=f^{\prime}(x)$

$=e^{x} \frac{1}{1-x}+c$

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