Evaluate: (i) `int(e^x)/(sqrt(4-e^(2x)))\ dx`
(ii) `int(x^2)/(sqrt(1-x^6))\ dx`
Text Solution
Verified by Experts
`I=int(e^(x))/(sqrt(4-e^(2x)))dx=int(e^(x))/(sqrt(2^(2)-(e^(x))^(2)))dx` Let `e^(x)=t " or " e^(x)dx=dt` `:. I=int(dt)/(sqrt(4-t^(2)))=int(dt)/(sqrt(2^(2)-t^(2)))` `=sin^(-1)((t)/(2))+C=sin^(-1)((e^(x))/(2))+C`
