MTH 251 Study Guide - Midterm Guide: Product Rule, Partial Fraction Decomposition
Document Summary
To find u, look for a function who"s derivative is also in the function. Because -2sin(2x) is also in the function, without the -2. Plugging u back in: arctan () = tan 1. Factor out the lowest power in the denominator. We know from the product rule that [()()] = ()() + ()() Going to end up with a u, du, v, and dv. Look for something you can integrate for dv and something that can be made simpler by taking the derivative for u. Remember, you can always check your integrals using differentiation. This integral is one to know off hand: || must be u because it cannot be. Plug this back in to the original equation for : Integration by parts with the fundamental theorem of calculus. Also solve for new bounds, = 1 12 2 =34 , and = 1 02 = 1.
