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