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calculus

# calculus - du dx dx 8 Z sin xdx =-cos x 9 Z cos xdx = sin x...

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CSC2110 Discrete Mathematics Topic: Calculus Reference Last Updated: October 7, 2009 Differentiation 1. d ( cu ) dx = c du dx , 2. d ( u + v ) dx = du dx + dv dx , 3. d ( uv ) dx = u dv dx + v du dx , 4. d ( u n ) dx = nu n - 1 du dx , 5. d ( u/v ) dx = v ( du dx ) - u ( dv dx ) v 2 , 6. d ( e cu ) dx = ce cu du dx , 7. d ( c u ) dx = (ln c ) c u du dx , 8. d (ln u ) dx = 1 u du dx , 9. d (sin u ) dx = cos u · du dx , 10. d (cos u ) dx = - sin u · du dx , 11. d (tan u ) dx = sec 2 u · du dx , 12. d (cot u ) dx = csc 2 u · du dx , 13. d (sec u ) dx = tan u sec u · du dx , 14. d (csc u ) dx = - cot u csc u · du dx , 15. d (arcsin u ) dx = 1 1 - u 2 du dx , 16. d (arccos u ) dx = - 1 1 - u 2 du dx , 17. d (arctan u ) dx = 1 1 + u 2 du dx , 18. d (arccot u ) dx = - 1 1 + u 2 du dx , 19. d (arcsec u ) dx = 1 u 1 - u 2 du dx , 20. d (arccsc u ) dx = - 1 u 1 - u 2 du dx , 1 arcsin, arccos, arctan, arcsec, arccsc and arccot are the inverse trigonometric functions of sin, cos, tan, sec, csc and cot respectively. For example, if arcsin y = θ , then sin θ = y . Here θ is in radian. 1

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Integration 1. Z cu dx = c Z u dx, 2. Z ( u + v ) dx = Z u dx + Z v dx, 3. Z x n dx = 1 n + 1 x n +1 , n 6 = - 1 , 4. Z 1 x dx = ln x, 5. Z e x dx = e x , 6. Z dx 1 + x 2 = arctan x, 7. Z u dv dx
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Unformatted text preview: du dx dx, 8. Z sin xdx =-cos x, 9. Z cos xdx = sin x, 10. Z tan xdx =-ln | cos x | , 11. Z cot xdx = ln | cos x | , 12. Z sec xdx = ln | sec x + tan x | , 13. Z csc xdx = ln | csc x + cot x | , 14. Z arcsin x a dx = arcsin x a + p a 2-x 2 , a > , 15. Z arccos x a dx = arccos x a-p a 2-x 2 , a > , 16. Z arctan x a dx = x arctan x a-a 2 ln( a 2 + x 2 ) , a > , 17. Z sin 2 ( ax ) dx = 1 2 a ( ax-sin( ax ) cos( ax ) ) , 18. Z cos 2 ( ax ) dx = 1 2 a ( ax + sin( ax ) cos( ax ) ) , 19. Z sec 2 xdx = tan x, 20. Z csc 2 xdx =-cot x, 2...
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