Question:
Evaluate the following integrals:
$\int \frac{2-x}{(1-x)^{2}} e^{x} d x$
Solution:
Let I $=\int \frac{2-x}{(1-x)^{2}} e^{x} d x$
$=\int e^{x}\left\{\frac{(1-x)+1}{(1-x)^{2}}\right\} d x$
$=\int e^{x}\left\{\frac{1}{1-x}+\frac{1}{(1-x)^{2}}\right\}$
$\frac{1}{1-x}=f(x) \frac{1}{(1-x)^{2}}=f^{\prime}(x)$
$=e^{x} \frac{1}{1-x}+c$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.