`int(dx)/(5+4cosx)`का मान ज्ञात कीजिये

1.	`int(dx)/(5+4cosx)`का मान ज्ञात कीजिये ।
Answer» माना ` I = int(dx)/(5+4cosx)` `=int(dx)/(5[sin^(2).(x)/(2) + cos^(2).(x)/(2)] +4[cos^(2).(x)/(2)sin^(2).(x)/(2)])` `= int(dx)/(9cos^(2) x//2 +sin^(2)x//2)` अश व हर को `cos^(2)s//2` से भगा देने पर `I = int (sec^(2)x//2dx)/(9+tan^(2)x//2)=(1)/(9)int(sec^(2)x//2sx)/(1+((tanx//2)/(3)))` माना `(tan x//2)/(3) = t therefore (1)/(6) sec^(2)x//2 dx = dt` `rArr " "sec^(2) x//2 dx = 6dt` `therefore " "I= (6)/(9)int(dt)/(1+t^(2)) = (2)/(3) tan^(-1) t = (2)/(3) tan^(-1)((tanx//2)/(3))`

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