Q. $\int_{}^{}{cosec^{4}\ }x\ dx$ is equal to
A) $\cot{x + \frac{\cot^{3}x}{3} + c}$
B) $\tan{x + \frac{\tan^{3}x}{3} + c}$
C) $- \cot{x - \frac{\cot^{3}x}{3} + c}$
D) $- \tan{x - \frac{\tan^{3}x}{3} + c}$
Explanation
(c)
$\int_{}^{}{cosec^{4}\ }x\ dx = \int_{}^{}{cosec^{2}}x \bullet cosec^{2}x\ dx$
$= \int_{}^{}{cosec^{2}}x(1 + \cot^{2}{x)dx}$
$= \int_{}^{}{cosec^{2}}x\ dx + \int_{}^{}{\cot^{2}{x \bullet cosec^{2}}}x\ dx$
$= - \cot{x - \frac{\cot^{3}x}{3} + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.