Q. $\int_{}^{}{e^{x}\left\lbrack f(x) + f^{'}(x) \right\rbrack dx}$ is equal to
A) $e^{x}f(x) + c$
B) $e^{x} + c$
C) $e^{x}f^{'}(x) + c$
D) None of these
Explanation
(a)
$\int_{}^{}{\left\lbrack e^{x}f(x) + f^{'}(x)e^{x} \right\rbrack dx}$
$= e^{x}f(x) - \int_{}^{}{e^{x}f^{'}(x)dx + \int_{}^{}{e^{x}f^{'}(x)dx}}$
$= e^{x}\ f(x) + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.