InterviewSolution
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InterviewSolution
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`int(dx)/(2+cosx)` का मान ज्ञात कीजिए । |
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Answer» `int(1)/(2+cosx)dx` `" "int(1)/(2+2cos^(2).(x)/(2)-1)dx=int(1)/(1+2cos^(2).(x)/(2))dx` `" "=int(1)/(sin^(2).(x)/(2)+cos^(2).(x)/(2)+2cos^(2).(x)/(2))dx` `" "=int(1)/(sin^(2).(x)/(2)+3cos^(2).(x)/(2))dx` `" "=int(sec^(2).(x)/(2))/(tan^(2).(x)/(2)+3)dx" माना "tan.(x)/(2)=t` `=int(2dt)/(t^(2)+3)" "{:(rArr(1)/(2)sec^(2).(x)/(2)=(dt)/(dx)),(rArrsec^(2).(x)/(2)dx=2dt):}` `" "=2int(1)/(t^(2)+(sqrt3)^(2))dt` `" "=(2)/(sqrt3)tan^(-1)((t)/(sqrt3))+c` `" "=(2)/(sqrt3)tan^(-1)((tan.(x)/(2))/(sqrt3))+c` |
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