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`int((x^(2)+4))/((x^(4)+16))dx` का मान ज्ञात कीजिए ।

Answer» `int((x^(2)+4))/((x^(4)+16))dx=int((1+(4)/(x^(2)))/(x^(2)+(16)/(x^(2))))`
`=int((1+(4)/(x^(2))))/((x-(4)/(x))^(2)+8)dx`
माना `(x-(4)/(x))=t rArr (1+(4)/(x^(2)))dx=dt,` तब
`int((1+(4)/(x^(2))))/((x-(4)/(x))^(2)+8)dx=int(dt)/((t^(2)+8))`
`=int(dt)/(t^(2)+(sqrt8)^(2))=(1)/(sqrt8)tan^(-1)((t)/(sqrt8))+c`
`=(1)/(sqrt8)tan^(-1).((x-(4)/(x)))/(sqrt8)+c`
`=(1)/(2sqrt2)tan^(-1)((x^(2)-4)/(2sqrt2x))+c`


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