CBSE Class 12-science Answered
Integration cosec3 x dx explain in great detail and give full solution
Asked by haroonrashidgkp | 18 Oct, 2018, 16:31: PM
let cosec3x=cosec2x cosec x
so
cosec3x dx=
cosec2x cosec x dx.
![integral](https://images.topperlearning.com/topper/tinymce/cache/b90ca9885076e9e59645a0870bea4bda.png)
![integral](https://images.topperlearning.com/topper/tinymce/cache/b90ca9885076e9e59645a0870bea4bda.png)
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](https://images.topperlearning.com/topper/tinymce/cache/5e421bff19406d7c7daf1c06f0ea06a8.png)
![integral](https://images.topperlearning.com/topper/tinymce/cache/b90ca9885076e9e59645a0870bea4bda.png)
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](https://images.topperlearning.com/topper/tinymce/cache/6fa18bc8039d3a9cf058bb31e2a32854.png)
Answered by Ram Singh | 18 Oct, 2018, 19:03: PM
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