Evaluate: `int(x^(5/2))/(sqrt(1+x^7))dx`

Answer

`(2)/(7)log(x^(7//2)+sqrt(1+x^(7)))+C`

Explanation

` "Put "x^(7//2)=t`
` :. (7)/(2)x^(5//2)dx=dt`
` :. I=int(2)/(7)(dt)/(sqrt(1+t^(2)))=(2)/(7)log(t+sqrt(1+t^(2)))+C`
`=(2)/(7)log(x^(7//2)+sqrt(1+x^(7)))+C`