Integrals — Maths STD 12 Science — Question

$\left[ {\int {{e^x}\left\{ {f\left( x \right) + f'\left( x \right)} \right\}dx} } \right]$

It is in the form of ${\int {{e^x}\left\{ {f\left( x \right) + f'\left( x \right)} \right\}dx} }$, Here $f\left( x \right) = \frac{1}{x} = {x^{ - 1}}$ and $f'\left( x \right) = \frac{{ - 1}}{{{x^2}}}$

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

$= \frac{{{e^x}}}{x} + c$ ...$\left[ {\because \int {{e^x}\left\{ {f\left( x \right) + f'\left( x \right)} \right\}} dx = {e^x}f\left( x \right) + c} \right]$