Evaluate: (i) `int1/(sqrt(x))(1+1/x)\ dx` (ii) `int(x^6+1)/(x^2+1)\ dx`

Explanation

(i) `int1/(sqrt(x))(1+1/x)\ dx`


`=intx^(-1/2)dx+intx^(-3/2)dx`


`=2x^(1/2)-2x^(-1/2)+C`


(ii) `int(x^6+1)/(x^2+1)\ dx`


`=int((x^2+1)(x^4+1-x^2))/(x^2+1)dx`


`=int(x^4+1-x^2)dx`


`=(x^5)/(5)+x-(x^3)/(3)+C`