Q. The value of $\int_{}^{}{e^{x}(x^{5} + 5x^{4} + 1)dx}$ is
A) $e^{x}.x^{5} + c$
B) $e^{x}.x^{5} + e^{x} + c$
C) $e^{x + 1}.x^{5} + c$
D) $5x^{4}.e^{x} + c$
Explanation
(b)
Let $I = \int_{}^{}{e^{x}(x^{5} + 5x^{4} + 1)dx}$
$= \int_{}^{}{e^{x}x^{5}dx + 5\int_{}^{}e^{x}x^{4}dx + \int_{}^{}e^{x}}dx$
$= x^{5}e^{x} - \int_{}^{}{5x^{4}e^{x}dx + 5\int_{}^{}{e^{x}x^{4}dx + e^{x}}}$
$= x^{5}e^{x} + e^{x} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.