[MATH 2Z03] - Final Exam Guide - Ultimate 122 pages long Study Guide!

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Order of by parts: log, inverse trig, algebraic function, trig, exponential y x. Remember this incredibly long integration by parts? xe cos x d x. 2 i by euler"s identity, so sub that in and you get: kx e i. 2 ix x e e ix d x. Or ax e cos bx d x ibx ax e e ibx e. Don"t confuse these with hyperbolic trig: kx kx kx kx. Integration by parts shortcut: tic tac toe method e. g. x. 3x : choose a u that can be derived, until it becomes 0 (e. g. put it into the following chart: Sign of u: always alternate and start positive. Derivatives of u: don"t stop, until you hit 0. Sinx: multiply each derivative of u, including u, by its sign and by the next integral of v and add the terms: cosx. This only works for linear factors (i. e. power of one).

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