Integrate the following integrals
`(i) int(dx)/(sqrt(5x^(2)-2x))` `(ii) int(1)/(sqrt(2ax-x^(2)))dx`

Explanation

`(i) l=int(dx)/(sqrt(5x^(2)-2x))=int(dx)/(sqrt(5{x^(2)-(2x)/(5)}))`
`:.l=(1)/(sqrt(5))int(dx)/(sqrt((x-(1)/(5))^(2)-((1)/(5))^(2)))`
put `x-(1)/(5)=timpliesdx=dt`
`:.l=(1)/(sqrt(5))int(dt)/(sqrt(t^(2)-((1)/(5))^(2)))=(1)/(sqrt(5))log|t+sqrt(t^(2)-((1)/(5))^(2))|+C`
`:.l=(1)/(sqrt(5))log|x-(1)/(5)+sqrt(x^(2)-(2x)/(5))|+C`
`(ii) l=int(dx)/(sqrt(2ax-x^(2)))=int(dx)/(sqrt(a^(2)-(x-a)^(2)))` put `x-a=t`
`impliesdx=dt`
`:.l=int(dt)/(sqrt(a^(2)-t^(2)))=sin^(-1){(1)/(a)}+C`
`:.l=sin^(-1){(x-a)/(a)}+C`