121616949-math.311 - x 2-1 24 C 8.4.1 cos x x sin x C 8.4.2...

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Appendix B Selected Answers 297 7.3.6. A = 18, B = 44 / 3, C = 10 / 3 8.1.1. - (1 - t ) 10 / 10 + C 8.1.2. x 5 / 5 + 2 x 3 / 3 + x + C 8.1.3. ( x 2 + 1) 101 / 202 + C 8.1.4. - 3(1 - 5 t ) 2 / 3 / 10 + C 8.1.5. (sin 4 x ) / 4 + C 8.1.6. - (100 - x 2 ) 3 / 2 / 3 + C 8.1.7. - 2 p 1 - x 3 / 3 + C 8.1.8. sin(sin πt ) + C 8.1.9. 1 / (2 cos 2 x ) = (1 / 2) sec 2 x + C 8.1.10. - ln | cos x | + C 8.1.11. 0 8.1.12. tan 2 ( x ) / 2 + C 8.1.13. 1 / 4 8.1.14. - cos(tan x ) + C 8.1.15. 1 / 10 8.1.16. 3 / 4 8.1.17. (27 / 8)( x 2 - 7) 8 / 9 8.1.18. - (3 7 + 1) / 14 8.1.19. 0 8.1.20. f ( x ) 2 / 2 8.2.1. x/ 2 - sin(2 x ) / 4 + C 8.2.2. - cos x + (cos 3 x ) / 3 + C 8.2.3. 3 x/ 8 - (sin 2 x ) / 4 + (sin 4 x ) / 32 + C 8.2.4. (cos 5 x ) / 5 - (cos 3 x ) / 3 + C 8.2.5. sin x - (sin 3 x ) / 3 + C 8.2.6. x/ 8 - (sin 4 x ) / 32 + C 8.2.7. (sin 3 x ) / 3 - (sin 5 x ) / 5 + C 8.2.8. - 2(cos x ) 5 / 2 / 5 + C 8.2.9. tan x - cot x + C 8.2.10. (sec 3 x ) / 3 - sec x + C 8.3.1. - ln | csc x + cot x | + C 8.3.2. - csc x cot x/ 2 - (1 / 2) ln | csc x + cot x | + C 8.3.3. x x 2 - 1 / 2 - ln | x + x 2 - 1 | / 2+ C 8.3.4. x 9 + 4 x 2 / 2 + (9 / 4) ln | 2 x + 9 + 4 x 2 | + C 8.3.5. - (1 - x 2 ) 3 / 2 / 3 + C 8.3.6. arcsin( x ) / 8 - sin(4 arcsin x ) / 32 + C 8.3.7. ln | x + 1 + x 2 | + C 8.3.8. ( x + 1) x 2 + 2 x/ 2 - ln | x + 1 + x 2 + 2 x | / 2 + C 8.3.9. - arctan x - 1 /x + C 8.3.10. 2 arcsin( x/ 2) - x 4 - x 2 / 2 + C 8.3.11. arcsin( x ) - x
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Unformatted text preview: x 2-1 / 24 + C 8.4.1. cos x + x sin x + C 8.4.2. x 2 sin x-2 sin x + 2 x cos x + C 8.4.3. ( x-1) e x + C 8.4.4. (1 / 2) e x 2 + C 8.4.5. ( x/ 2)-sin(2 x ) / 4 + C = ( x/ 2)-(sin x cos x ) / 2 + C 8.4.6. x ln x-x + C 8.4.7. ( x 2 arctan x + arctan x-x ) / 2 + C 8.4.8.-x 2 cos x + 2 x sin x + 2 cos x + C 8.4.9. x 2 / 4-(cos 2 x ) / 4-( x sin x cos x ) / 2+ C 8.4.10. x/ 4-( x cos 2 x ) / 2+(cos x sin x ) / 4+ C 8.4.11. x arctan( √ x )+arctan( √ x )-√ x + C 8.4.12. 2 sin( √ x )-2 √ x cos( √ x ) + C 8.4.13. sec x csc x-2 cot x + C 8.5.1.-ln | x-2 | / 4 + ln | x + 2 | / 4 + C...
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