Consider finding the antiderivative of ∫t^3*e^6t dt.

a)Find β

b)Find the matrix [T]β for the differentiation operator T

c)Find [T]β^-1 and use it to find ∫t^3*e^6t dt. β

d)Use [T]β^-1 to find ∫(t^3-t^2+t-1)*e^6t dt

The problem is that i don't really understand how to get started with finding the basis of the antiderivative