Calc 9.3 - opposite add and divide. = xdx e x sin -xdx e x...

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9.3 “Table” Integration by Parts Table integration is an efficient way of integration by parts when multiple steps of integration by parts are required. The first example on pg 440 shows the process to be much easier when following these simple step by step rules.
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1. Pick u and dv. U DV x 2 cos4x 2. Differentiate u until 0 2x 3. Integrate dv until the 0 in the u column x 4 sin 4 1 2 x 4 cos 16 1 - 0 x 4 sin 64 1 - 4. Multiply answer diagonally alternating signs + -
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= xdx x sin 2 3 U DV 2x 3 sinx 6x 2 12x 12 -cosx -sinx cosx sinx 0 Solution: -2x 3 cosx + 6x 2 sinx+ 12xcosx – 12sinx + C
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= xdx e x sin U DV e x sinx Solution : e x -cosx -e x cosx e x -sinx + e x sinx When the integral becomes the
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Unformatted text preview: opposite add and divide. = xdx e x sin -xdx e x sin x e x e xdx e x x x sin cos sin 2 +-= = xdx 2 cos = xdx x cos cos U DV cosx cosx-sinx sinx Solution : --= xdx x x xdx 2 2 sin sin cos cos + = xdx x x xdx 2 2 sin sin cos cos -+ = xdx dx x x xdx 2 2 cos 1 sin cos cos -+ = xdx dx x x xdx 2 2 cos 1 sin cos cos -+ + = xdx c x x x xdx 2 2 cos sin cos cos c x x x xdx + + = sin cos cos 2 2 2 sin cos cos 2 c x x x xdx + + = Homework Pg 443; All Q, 1 9 odd...
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Calc 9.3 - opposite add and divide. = xdx e x sin -xdx e x...

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