Question

`int{sqrtx(ax^2+bx+c)}dx`

Answer 1

`int{sqrtx(ax^2+bx+c)}dx`

Treat `sqrtx = x^(1/2) "and integrate term-by-term (power rule" intx^ndx = (x^(n+1))/(n+1)`

`intsqrtx(ax^2+bx+c)dx=a intx^(5/2)dx +b intx^(3/2)dx+c intx^(1/2)dx`

`= a . 2/7 x^(7/2)+ b . 2/5x^(5/2) + c . 2/3 x^(3/2) + C`

`=(2a)/7 x^(7/2) + (2b)/5 x^(5/2) + (2c)/3 x^(3/2) + C`