फलन `int(dx)/(xsqrt(x^(2)-a^(2)))` का x के सापेक्ष समाकलन कीजिए।

Explanation

माना `" "I=int(dx)/(xsqrt(x^(2)-a^(2)))=int(xdx)/(x^(2)sqrt(x^(2)-a^(2)))`
माना `" "x^(2)-a^(2)=t^(2)" "therefore" "2xdx=2t dt`
या `" "xdx=t dt`
तथा `" "x^(2)=t^(2)+a^(2)`
अतः `" "I=int(tdt)/((t^(2)+a^(2))t)=int(dt)/(a^(2)+t^(2))`
`=(1)/(a) tan^(-1)((t)/(a))=(1)/(a)tan^(-1)[(sqrt(x^(2)-a^(2)))/(a)]`