Q. $\int_{}^{}{e^{x}(1 - \cot{x + \cot^{2}{x)dx}}}$ equals
A) $e^{x}\cot{x + c}$
B) $e^{x}cosec\ x + c$
C) $- e^{x}\cot{x + c}$
D) $- e^{x}cosec\ x + c$
Explanation
(c)
$\int_{}^{}{e^{x}(1 - \cot{x + \cot^{2}{x)dx}}}$
$= \int_{}^{}{e^{x}( - \cot{x + cosec^{2}x)dx}}$
$= - \int_{}^{}{e^{x}\cot{x\ dx + \int_{}^{}{e^{x}cosec^{2}x\ \ }}}dx$
$= - e^{x}\cot{x - \int_{}^{}{e^{x}cosec^{2}x\ \ }}dx\int_{}^{}{e^{x}cosec^{2}xdx\ }$
$= e^{x}( - \cot{x) + c = -}e^{x}\cot{x + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.