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Question : 70 of 160
Marks:
+1,
-0
Solution:
Let
I=∫√1+2‌cot‌x(cot‌x+cosec‌x‌dx ‌=∫√cosec2x−cot2x+2cot2x+2‌cot‌x‌cosec‌x‌dx‌=∫√cosec2x+cot2x+2‌cot‌x‌cosec‌xdy‌=∫(cosec‌x+cot‌x)‌dx‌=log|cosec‌x−cot‌x|+log|sin‌x|+C‌=log‌|‌×sin‌x|+C ‌=log‌|2sin‌2‌|+C‌=log‌2+log‌s‌i‌n‌2‌+C‌=2‌log‌|sin‌‌|+C 
[∵log‌2+C=C]
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