∫cosec4xdx=
cotx+cot3x3+C
tanx+tan3x3+C
-cotx-cot3x3+C
-tanx-tan3x3+C
Explanation for Correct answer:
Finding the value for the given function:
∫cosec4xdx=∫cosec2x.cosec2xdx=∫cosec2x.1+cot2xdx∵cosec2x=1+cot2x=∫cosec2x.dx+∫cosec2xcot2xdx∵∫cosec2x.dx=-cotx=-cotx-∫t2dt[lett=cotx⇒dt=-cosec2xdx]=-cotx-t33+C=-cotx-cot3x3+C
Hence, option (C) is the correct answer.