`int(1)/(5+4 cosx)dx` का मान ज्ञात कीजिए ।

Explanation

`int(1)/(5+4 cosx)dx`
`=int(1)/(5(cos^(2).(x)/(2)+sin^(2).(x)/(2))+4(cos^(2).(x)/(2)-sin^(2).(x)/(2)))dx`
`=int(1)/(9cos^(2).(x)/(2)+sin^(2).(x)/(2))dx`
(अंश और हर को `cos^(2).(x)/(2)` से भाग देने पर )
`=int(sec^(2).(x)/(2)dx)/(9+tan^(2).(x)/(2))`
`=int(2dt)/(9+t^(2))" माना " tan.(x)/(2)=t`
`=2 int(1)/(t^(2)+3^(2))dt" "therefore (1)/(2)sec^(2).(x)/(2)=(dt)/(dx)`
`=(2)/(3) tan^(-1)((t)/(3))+c" "rArr sec^(2).(x)/(2)dx=2dt`
`=(2)/(3)tan^(-1)((tan.(x)/(2))/(3))+c`