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CBSE Class 12-science Answered

Integration cosec3 x dx explain in great detail and give full solution
Asked by haroonrashidgkp | 18 Oct, 2018, 04:31: PM
answered-by-expert Expert Answer
let cosec3x=cosec2x cosec x
so integral cosec3x dx= integralcosec2x cosec x dx.
use cosec2x-cot2x=1 
hence cosec2x=1+cot2x
cos e c x space equals space square root of c o t squared plus 1 end root
integralcosec x cosec2x dx
put cot x= t
differentiate w.r.t x
-cosec2x dx =dt
 negative integral square root of t squared plus 1 space end root space d t

minus left square bracket t over 2 square root of t squared plus 1 space end root space plus space 1 half log vertical line t plus square root of t squared plus 1 space end root vertical line plus c
minus left square bracket fraction numerator c o t space x over denominator 2 end fraction square root of c o t squared space x plus 1 space end root space plus space 1 half log vertical line c o t space x plus square root of c o t squared space x plus 1 space end root vertical line plus c
Answered by Ram Singh | 18 Oct, 2018, 07:03: PM
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