If p(x) is a polynomial of degree n and G1, G2, .... Gn+1, are successive anti-derivatives of

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If p(x) is a polynomial of degree n and G1, G2, .... Gn+1, are successive anti-derivatives of a function g, then, by repeated integration by parts.
∫ p(x) g(x) dx = p(x) G1(x) - p' (x) G2(x) + p''(x) G3(x) - ... + (-1)n p(n) (x) Gn+1 (x) + C
Use this result to find each of the following:
(a) ∫(x3 - 2x)ex dx
(b) ∫ (x2 - 3x + 1) sin x dx
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Calculus

ISBN: 978-0131429246

9th edition

Authors: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon

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