Let us evaluate the following integral using three different ways we have learned in class:f(x)=x3(x2-1)2dx1.f(x)=x3(x2-1)2dx=,+C2.u-substitution ofu=x2-1,we get dudx=, Rewriting our function in terms ofu,we state that our variable changedintegral is:f(u(x))=ddotscdots-duWe can expand this integral easily and integrate. Rewriting our final answer in terms ofx,we get:f(x)=,+D3.u=x2 and dvdx=x(x2-1)2.We can then rewrite our integral as:f(x)=,-dxNote: for the sake of the answer key, please integrate dvdx using u-substitution, otherwise your correct answer will be marked wrong.We can complete this lingering integration by expanding and getting a final answer of:f(x)=,-,+FWhile all of these expressions look different, they all equal the same f(x) Now suppose that we were told f(1)=0. This would implythat C=,D=, and F=