Question

How do you integrate `(5x)/ (x-2)^(1/2) dx`?

Answer 1

`f(x)=5intx/(x-2)^(1/2)dx`

Let's `u = x-2`

`du = 1`

`x = u +2`

Now we have : `=5int(u+2)/u^(1/2) du`

`=5intsqrt(u)du+10int1/sqrt(u)du`

`=[10/3sqrt(u^3)]+20[sqrt(u)]+C`

Substitute back

`10/3(x-2)^(3/2)+20(x-2)^(1/2)+C`