Reglas Basicas de derivaciòn y fòrmulas bàsicas de Integraciòn
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Reglas básicas de derivación 1. — [CH] = cu' dx dx vu — uv 7. —[x] = 1 dx 10. — [eu] = e"u' dx 2. —-[« ± v] = u' ± v ' dx 8. 4[|«|] = rr(«0, « * o dx \u\ 11. ^[iog a „] = -i^- aje (ln a)u 3. —[uv] = uv' + vu' dx [úh] = nun~xu' d_ dx —[ln u\ — dx u 12. —[a u ] = (ln a)attu' dx 13. —[sena] = ( COSM)M' 16. — [cot u] dx (esc 2 m d r i M ' 19. — aresenw = —¡ d r -, —«' 22. — larecotw = ~ <fx L J 1 + u 25. -7- [senh u] = (cosh w)w' dx 14. —[eos w] = — (sen u)u' dx 17. —[sec H] = (sec u tan M)M' dx d r -, —a' 20. —I arceos u\ —, dx1 JH^u1 ,, i M ' 23. —laresee w = ——. „ dx1 J IwlV^T 26. — [cosh u] = (senh W)M ' dx 15. —[tan M ] = (sec 2 u)u' dx 18. —[esc K] = — (esc w cot W)M' ox 21. — I arctan u\ « J 1 + M 2 ~ A d v -, — «' 24. — Larccsc HJ = , dx |M| V« - 1 27. — [tanh u] = (sech 2 u)u' dx 28. — [coth u] = - (csch 2 u)u' dx 31. -y-fsenh -1 u] = —, = dx1 J y^n 34. -^[coth" 1 u] = ~—; dx 1 - u¿ 29. — [sech u] = dx 32. -7- [cosh -1 w] dx 35. -7 -[sech~' u] dx - (sech 11 tanh w)«' 30. — [csch u] = - (csch u coth w)w 33. -—[tanh 1 u] = ~ dx 1 — u¿ Vu1 uJT í/r , _ , -, —U' 36. -— Icsch 1 u = ——, Fórmulas básicas de integración '•j 2. d« = W + C 4. e" dw = e" + C 6. '•J eos udu = sen « + C 8. '•J cot «fiu = ln 1 sen u | 4 C 10. "• J esc udu = — ln|csc M + cot M| f c 12. esc 2 udu = — cot M + C 14. 1S ' J esc M cot udu = — esc M + C 16. 17. di/ 1 w + c 18. 17. , , = arctan + c 18. J a¿ + u¿ a a 2. j[f(u) ± g(u)] du = T/(IÍ) ± jg(u) du 4. a"d« 1 ln a a" + C COS M + C •I: du aresen—h C 1 // —, = — aresee — uju2 - a2 a a C
Transcript of Reglas Basicas de derivaciòn y fòrmulas bàsicas de Integraciòn
Reglas básicas de derivación
1. — [CH] = cu' dx
dx vu — uv
7. —[x] = 1 dx 10. — [eu] = e"u' dx
2. —-[« ± v] = u' ± v ' dx
8. 4[|«|] = rr(«0, « * o dx \u\
11 . ^[ioga„] = - i ^ -aje (ln a)u
3 . —[uv] = uv' + vu' dx [úh] = nun~xu' d_ dx —[ln u\ — dx u
12. —[au] = (ln a)attu' dx
13. — [ s e n a ] = (COSM)M'
16. — [cot u]
dx (esc2
m d r i M ' 19. — aresenw = —¡ d r -, —«' 22. — larecotw = ~ <fxL J 1 + u
25. -7- [senh u] = (cosh w)w' dx
14. —[eos w] = — (sen u)u' dx 17. —[sec H] = (sec u tan M)M' dx
d r -, —a' 20. —I arceos u\ —, dx1 JH^u1
, , i M ' 23 . —laresee w = ——. „
dx1 J I w l V ^ T 26. — [cosh u] = (senh W)M '
dx
15. —[tan M] = (sec2 u)u' dx
18. —[esc K] = — (esc w cot W)M' ox
2 1 . — I arctan u\ « J 1 + M2
~ A d v -, — «' 24. — Larccsc HJ = , dx |M|V« - 1
27. — [tanh u] = (sech2 u)u' dx 28. — [coth u] = - (csch2 u)u' dx 3 1 . -y-fsenh - 1 u] = —, =
dx1 J y ^ n 34. - ^ [ c o t h " 1 u] = ~—; dx 1 - u¿
29. — [sech u] = dx 32. -7- [cosh - 1 w] dx 35. -7-[sech~' u] dx
- (sech 11 tanh w)«' 30. — [csch u] = - (csch u coth w)w'
33 . -—[tanh 1 u] = ~ dx 1 — u¿
Vu1
uJT
í / r , _ , -, —U'
36. -— Icsch 1 u = ——,
Fórmulas básicas de integración
' • j 2.
d« = W + C 4.
e" dw = e" + C 6.
' • J eos udu = sen « + C 8.
' • J cot «fiu = ln 1 sen u | 4 C 10.
" • J esc udu = — ln|csc M + cot M| f c 12.
esc2 udu = — cot M + C 14.
1 S ' J esc M cot udu = — esc M + C 16.
17. di/ 1 w + c 18. 17. , , = arctan + c 18. J a¿ + u¿ a a
2. j[f(u) ± g(u)] du = T/(IÍ) ± jg(u) du
4. a"d« 1 ln a
a" + C COS M + C
•I: du
aresen—h C 1 // — , = — aresee — uju2 - a2 a a C
