`(1)/(xsqrt(ax-x^(2)))` [संकेत : `x=(a)/(t)` रखिए]

Explanation

माना`" "I=int(1)/(xsqrt(ax-x^(2)))dx`
माना `x=(a)/(t)" "rArr" "dx=-(1)/(t^(2))dt`
`therefore" "I=int(1)/((a)/(t)sqrt(a((a)/(t))-(a^(2))/(t^(2))))((-a)/(t^(2)))dt`
`" "=int(-a)/(a.asqrt(t-1))dt=-(1)/(a)int(t-1)^(-1//2)dt`
`" "=-(1)/(a).((t-1)^((-1//2)+1))/(-(1//2)+1)+C=-(2)/(a)sqrt(t-1)+C`
`" "=-(2)/(a)sqrt((a)/(x)-1)+C=-(2)/(a)sqrt((a-x)/(x))+C`