# Thread: Finding the antiderivative of ∫t^3*e^6t dt

1. ## Finding the antiderivative of ∫t^3*e^6t dt

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

2. ## Re: Finding the antiderivative of ∫t^3*e^6t dt

Originally Posted by choph
Consider finding the antiderivative of ∫t^3*e^6t dt.
a)Find β
??? There is no " $\beta$" in your formula.

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