1. Integrations!

1. $\int xdx / \sqrt{4+5x}$.

2. Well there're lots of ways of doing this.

I keep the following: put $t=\sqrt{4+5x}.$

3. I tried plugin u=4+5 and dv=x but I got a mess. Can someone show me?

4. But you're integrating by parts, that's not necessary in this case.

We can write my substitution as $x=\frac{t^2-4}5,$ now $dx=\frac{2t}5\,dt.$ Substitute those in the integral now, what do you get?

5. $\int \frac{x}{\sqrt{4+5x}}~dx$

$t=\sqrt{4+5x} \implies x = \frac{t^2-4}{5}$

Now

$\int \frac{\frac{t^2-4}{5}}{t}~dx=\int \frac{t^2-4}{5t}\frac{2t}{5}~dt$