Question

integrate.
Given:
\[\LARGE \int {\frac{{9 - \sqrt x }}{{3 - \sqrt x }}dx} \]

following wolf.. Attempted: (I do understand everything till here.)

\[\LARGE \begin{array}{l}\int {\frac{{9 - \sqrt x }}{{3 - \sqrt x }}dx} = \left| {\begin{array}{*{20}{c}}{\sqrt x = u}\\{\frac{1}{{2\sqrt x }}dx = du}\\{dx = 2\sqrt x \,\, \cdot du}\end{array}} \right| = \\\\ = \int {\frac{{9 - u}}{{3 - u}} \cdot 2 \cdot u \cdot du = 2\int {\frac{{9u - {u^2}}}{{3 - u}}du} } \end{array}\]

Answer 1

but now what...

Answer 2

wow..are those matrices o.O in integrals :O

Answer 3

.. no , we just used to write like that (for explaining the process in my school) .. that's nothing. :)

Answer 4

\[\LARGE \begin{array}{l}\int {\frac{{9 - \sqrt x }}{{3 - \sqrt x }}dx} = \\\\ = \int {\frac{{9 - u}}{{3 - u}} \cdot 2 \cdot u \cdot du = 2\int {\frac{{9u - {u^2}}}{{3 - u}}du} } \end{array}\]

Answer 5

are you good up to that last line? split up the integrand...

Answer 6

I guess till here it's ok, but I'm just stuck now, I don't know what else to do...