To integrate a product of functions, in which one of the functions is a composite radical function, like \(\sqrt{ax+b}\) or \(\sqrt[3]{ax+b}\), and the other is a polynomial function, like \(x^2+x\) or \(x^3-x^2+1\), we quickly see that U-Substitution won't work.
The method of substitution we learn in this section will allow us to integrate such proucts of functions.
Given an integral looking like: \[\int \begin{pmatrix} x^2-x\end{pmatrix} \sqrt{ax+b}.dx\]
In the following tutorial we learn how to use the three equations to find the formula for the \(n^{\text{th}}\) term of a quadratic sequence.
Using the substitution of your choice, find each of the following integrals: