`int(1)/(sqrt(1-x-x^(2)))dx` का मान ज्ञात कीजिए ।

Explanation

`int(1)/(sqrt(1-x-x^(2)))dx=int(dx)/(sqrt(1-(x+x^(2)))`
`=int(dx)/(sqrt((1+(1)/(4))-(x^(2)+x+(1)/(4))))`
`=int(dx)/(sqrt[((sqrt5)/(2))^(2)-(x+(1)/(2))^(2)])`
`=int(dx)/(sqrt([((sqrt5)/(2))^(2)-t^(2)]))" जहाँ "x+(1)/(2)= t rArr dx=dt`
`=sin^(-1)((t)/(sqrt5//2))+c=sin^(-1)[(2(x+(1)/(2)))/(sqrt5)]+c`
`=sin^(-1)((2x+1)/(sqrt5))+c`