Integration
The first one asks you to compute $\displaystyle \int3x^2y^3\,dy,$ so $\displaystyle 3x^2$ behaves like a constant, you can take it apart of the integral, so it remains to integrate $\displaystyle y^3.$
It looks like the second one has to do with a differential equation, well, note that $\displaystyle v^2+2v+1=(v+1)^2.$ Define a simple substitution on the LHS and you're done (of course, the RHS is a known integral.)