MATH 181 Study Guide - Final Guide: Methamphetamine, Farad, Horse Length
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Z x x2 + 5x + 4 dx x x2 + 4x + 5 dx. Solution: (a) we will evaluate the integral using partial fraction decomposition. Next, we multiply the above equation by (x 3)(x + 3) to get: (x 3)(x + 3) x 3 x2 3. 1 = a(x + 3) + b(x . We select x = 3 and x = 3 for simplicity. 3) = 1 b = x = 3 : a( 3 + 3) + b( 3 . 1 x2 3 dx =z (cid:18) a x 3. B x + 3(cid:19) dx x + 3! dx. 2 3 ln|x + 3| + c (b) we will evaluate this integral using the u-substitution method. 3 dx 3 du = dx and x = 3 u and we get: x. 3u2 + 3 ( 3 u)2 + 3 (cid:16) 3 du(cid:17) dx =z.
