1.

फलनों का x के सापेक्ष समाकलन कीजिए - `(1)/(a+b sinx)`

Answer» Correct Answer - `(2)/sqrt((a^(2)-b^(2)))tan^(-1)[(a tan x//2+b)/(sqrt((a^(2)-b^(2))))]`
`int(dx)/(a+b sinx)=int(dx)/(a+b((2tanx//2)/(1+tan^(2)x//2)))`
`=int(1+tan^(2)x//2)/(a(1+tan^(2)x//2)+b(2tanx//2)).dx`
`=int(sec^(2)x//2)/(a tan^(2)x//2+2b tanx//2+a)`
अब माना `tan.(x)/(2)=t rArr sec^(2).(x)/(2)dx=2dt`


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