Now solved: Find the values of x, v, and z

MATH152 | Amy Austin | Week 1 Section 5.5 | Integration by Substitution • U-Substitution – Unwinding the Chain Rule • The Substitution Rule [in math terms, and then more simply explained]: o If u=g(x) is a differentiable function, then ∫ f(g(x))g’(x)dx = ∫ f(u)du o ∫ f(g(x))g’(x)dx ▪ u = g(x); where u is the differentiable expression ▪ du = g’(x)dx; where du is the derivative of ‘u’ ▪ Substitute ‘u’ and ‘du’ into the given integral to get ∫ f(u)du • Steps to Integrate using U-Substitution 1. Examine the integral a. Look for an expression and its derivative if possible b.