`int(sqrt(x^2+1){log(x^2+1)-2logx})/x^4dx` का मान ज्ञात कीजिए ।

Explanation

दिया है - `int(sqrt(x^2+1){log(x^2+1)-22logx})/x^4dx`
`=intsqrt(x^2+1)/x^4log((x^2+1)/x^2)dx`
`=intsqrt(1+1/x^2). 1/x^3log(1+1/x^2)dx`
यदि `(1+1/x^2)=t` व `-2/x^3dx=dt`
`rArr1/x^3dx=-(dt)/2,` तब
`=-1/2int(logt)sqrtt dt`
`=-1/2{2/3(logt)t^(3//2)-int(1/txxt^(3//2))dt}`
`=-1/3t^(3//2)(logt)+1/2int t^(1//2)dt`
`=-1/3t^(3//2)(logt)+2/9t^(3//2)+c`
`=-1/3t^(3//2){logt-2/3}+c`
`=-1/3(1+1/x^2)^(3//2){log(1+1/x^2-2/3}+c`