I have a task to integrate the following integral: `
$$ \int \frac{x^3+1}{5x+\sqrt{6^2-x^2}}dx $$
and I tried to solve it, but do not know if my moves are correct.
1. $ u=\sqrt{6^2-x^2} $
$ u^2=6^2-x^2 $
$ u=6-x $
$ x=u-6 $
$ dx=(u-6)'du=du $
2. $ \int \frac{(u-6)^3 -1}{5(u-6)+u}du $
- Should I now substitute $t=u-6$ or what?