⇒∫sec2xcosec2xdx=∫1cos2xsin2xdx=∫sin2x+cos2xcos2xsin2xdx=∫sin2xcos2xsin2xdx+∫cos2xcos2xsin2xdx=∫sec2x dx+∫cosec2x dx=tanx-cotx+c

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

$\int \sec^{2} x {cosec}^{2} xdx =$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

tan x - cot x - 4x + c

tan x + x + c

tan x - cot x + c

tan x - x + c

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\Rightarrow \int \sec^{2} x {cosec}^{2} xdx = \int \frac{1}{\cos^{2} {xsin}^{2} x} dx = \int \frac{\sin^{2} x + \cos^{2} x}{\cos^{2} {xsin}^{2} x} dx$

$= \int \frac{\sin^{2} x}{\cos^{2} {xsin}^{2} x} dx + \int \frac{\cos^{2} x}{\cos^{2} {xsin}^{2} x} dx = \int \sec^{2} x dx + \int {cosec}^{2} x dx = tanx - cotx + c$