Pre-Calc Homework Solutions 252

Pre-Calc Homework Solutions 252 - 252 Section 6.3 ln x 1 dx...

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Unformatted text preview: 252 Section 6.3 ln x 1 dx x 1 4 x ln x 4 1 4 x ln x 4 1 4 x ln x 4 9. Let u du dv v x 3 dx 1 4 x 4 12. Use tabular integration with f (x) f(x) and its derivatives x3 3x2 6x (+) () (+) () g(x) and its integrals e2x x 3 and g(x) e 2x . x 3 ln x dx 1 4 1 x dx 4 x 1 3 x dx 4 1 4 x C 16 10. Use tabular integration with f (x) f(x) and its derivatives x4 4x 3 12x 2 24x 24 0 (+) () (+) () (+) g(x) and its integrals ex ex ex ex ex ex x and g(x) 4 e . x 6 0 1 2x e 2 1 2x e 4 1 2x e 8 1 2x e 16 x 3e 2x dx 3 2x e 8 1 3 2x 3 2 2x 3 x e x e xe 2x 2 4 4 3 2 x 3x 3x 3 e 2x C 2 4 4 8 C 13. Let u du ey e y dy e y cos y dv v sin y dy cos y e y sin y dy Let u ey e dy y cos y e y dy dv v cos y dy sin y sin ye y dy x 4e x 4 dx x x e (x 4 11. Let u du (x 2 Let 4x e 4x 3 3 x 12x e 24x dv v 5x)e x dv v e 2 x 24xe 24)e e x dx x x 24e C x C du 12x 2 5x 5) dx (x 2 5 e y sin y dy 2 e y sin y dy e y sin y dy e y cos y e y cos y 1 y e (sin y 2 e y sin y e y sin y cos y) dv C x2 (2x ex e x(2x 5) dx 5x)e x dx u du 2x 2 dx 14. Let u e dx x x e y cos y dy sin y y du e y dy e ysin y dv v e ycos y dy Let u 2e x dx 2e x C e 2 e e y sin y e dy (x 2 (x 2 (x 2 (x 2 5x)e x 5x)e x 5x)e x 7x e x(2x (2x (2x 7)ex C 5) dx 5)e x 5)e x e y sin y dy cos y e ycos y e y du y e y dy e e y v sin y y cos y dy y e y cos y dy cos y dy sin y cos y C cos y dy 1 y e (sin y 2 cos y) ...
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