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`int(1)/(x^(2)+x+1)` का मान ज्ञात कीजिए ।

Answer» हम जानते हैं कि `x^(2)+x+1=x^(2)+x+(1)/(4)+(1-(1)/(4))=(x+(1)/(2))^(2)+(x+(1)/(2))^(2)+((sqrt3)/(2))^(2)`
`therefore (1)/(x^(2)+x+1)dx=int(1)/((x+(1)/(2))^(2)+((sqrt3)/(2))^(2))dx`
`=int(1)/(t^(2)+((sqrt3)/(2))^(2))dt" "` जहाँ `x+(1)/(2)=t rArr dx=dt`
`=(1)/(sqrt3//2)tn^(-1)((t)/(sqrt3//2))+c`
`=(2)/(sqrt3)tan^(-1)[(2)/(sqrt3)(x+(1)/(2))]+c`
`=(2)/(sqrt3)tam^(-1)((2x+1)/(sqrt3))+c`


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