Anexo D

Tabla de Integrales
(PUEDE SUMARSE UNA CONSTANTE ARBITRARIA A CADA INTEGRAL)

1. 2. 3. 4. 5. 6. 7. 8. 9.

xn dx =

1 xn+1 n+1

(n = −1)

1 dx = log | x | x ex dx = ex ax dx = ax log a

sen x dx = − cos x cos x dx = sen x tan x dx = − log |cos x| cot x dx = log |sen x| sec x dx = log |sec x + tan x| = log tan 227 1 1 x+ π 2 4

228 1 x 2 (a > 0) (a > 0) (a > 0)

Tabla de Integrales

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

csc x dx = log |csc x − cot x| = log tan arcsen arccos arctan x x √ 2 dx = x arcsen + a − x2 a a x x √ dx = x arccos − a2 − x2 a a

x x a dx = x arctan − log a2 + x2 a a 2 1 (mx − sen mx cos mx) 2m 1 (mx + sen mx cos mx) 2m

sen2 mx dx = cos2 mx dx =

sec2 x dx …ver más…

47. 48.

√

3

49.

√ 50. 51. 52. 53. 54. 55.

√ a2 − x2 a+ dx = a2 − x2 − a log x
3 2

√

a2 − x2 x

√ 1 x a2 − x2 dx = − a2 − x2 3

√ √ x a4 x x2 a2 − x2 dx = 2x2 − a2 a2 − x2 + arcsen 8 8 a √ a + a 2 − x2 1 1 √ dx = − log a x x a2 − x2 √ √ √ x dx = − a2 − x2 a2 − x2

(a > 0)

56.

x2 x√ 2 x a2 dx = − (a > 0) a − x2 + arcsen 2 − x2 2 2 a a √ √ √ a + x2 + a2 x2 + a2 dx = x2 + a2 − a log x x

231 √ 57. 58. 59. 60. 61. 62. √ √ x2 − a 2 a x dx = x2 − a2 − a arccos = x2 − a2 − arcsec x |x| a
3 2

(a > 0)

√ 1 2 x x2 ± a2 dx = x ± a2 3 x √ √ 1 x2 1 + a2 dx =

x 1 √ log a a + x2 + a2 (a > 0)

1 a dx = arccos a |x| x x2 − a 2 √ x2 ± a2 1 √ dx = ± a2 x x2 x2 ± a2 √ √ x dx = x2 ± a2 x2 ± a 2

63.

1 dx = 2 + bx + c ax

√ 2ax+b− 2 √ 1 log 2ax+b+√b2 −4ac b2 −4ac b −4ac 2ax+b √ 2 √ arctan 4ac−b2 4ac−b2

(b2 > 4ac) (b2 < 4ac)

64. 65.

x 1 b 1 dx = log ax2 + bx + c − dx 2 + bx + c + bx + c 2a 2a ax √ √ 1 √ log |2ax + b + 2 a ax2 + bx + c| (a > 0) 1 a √ dx = −2ax−b √1 arcsen √ (a < 0) ax2 + bx + c −a b2 −4ac ax2 √ 2ax + b √ 2 4ac − b2 1 √ ax + bx + c + dx 4a 8a ax2 + b +