here are 2 sample questions i need help finding out how to solve:
1.) ∫ x(sin^-1(x))dx
2.) ∫ [(x+1)/√(4-(x^2))]dx
For the first one, use integration by parts, with $\displaystyle u=\sin^{-1}x$ and $\displaystyle \,dv=x\,dx$.
For the second one, note that
$\displaystyle \int\frac{x+1}{\sqrt{4-x^2}}\,dx=\int\frac{x\,dx}{\sqrt{4-x^2}}+\int\frac{\,dx}{\sqrt{4-x^2}}$.
The first of these two integrals requires a substitution, and the second integral should be a familiar one to you.
Can you take it from here? If you still need assistance, please post back.