Tecnica De Integracion Por Completacion.docx

Tecnica de integracion por completacion F´ormulas de Integraci´on Inmediata 1. Z dx = x + c , 2. Z kdx = k Z dx , 3. Z kf(x)dx = k Z f(x)dx , 4. Z [f1(x) + f2(x) + ... + fn(x)] = Z f1(x)dx + Z f2(x)dx + ... + Z fn(x)dx , 5. Z x n dx = x n+1 n + 1 + c; n 6= −1; nQ , 6. Z dx x dx = ln |x| + c; x 6= 0 , 7. Z e x dx = e x + c , 8. Z a x dx = a x ln a + c; a > 0 , 9. Z sin(x)dx = −cos(x) + c , 10. Z cos(x)dx = sin(x) + c , 11. Z sec2 (x)dx = tg(x) + c; x 6= (2n + 1)π 2 ; nZ , 12. Z csc2 (x)dx = −ctg(x) + c; x 6= nπ; nZ , 13. Z sec(x).tg(x)dx = sec(x) + c; x 6= (2n + 1)π 2 ; nZ , 14. Z csc(x).ctg(x)dx = −csc(x) + c; x 6= nπ; nZ , 15. Z tg(x)dx = − ln |cos(x)| + c; x 6= (2n + 1)π 2 ; nZ , 16. Z ctg(x)dx = ln |sin(x)| + c; x 6= nπ , 17. Z sec(x)dx = ln |sec(x) + tan(x)| + c; x 6= (2n + 1)π 2 ; nZ , 18. Z csc(x)dx = ln |csc(x) − ctg(x)| + c; x 6= nπ; nZ , 1 19. Z dx x 2 + a 2 = 1 a arctg x a + c , 20. Z dx x 2 − a 2 = 1 2a ln

x−a x+a

+ c; |x| > a; a > 0 , 21. Z dx a 2 − x 2 = 1 2a ln

x+a x−a

+ c; |x| < a; a > 0 , 22. Z dx √ x 2 + a 2 = ln|x + p x 2 + a 2| + c , 23. Z dx √ x 2 − a 2 = ln|x + p x 2 − a 2| + c , 24. Z dx √ a 2 − x 2 = arcsen x a + c , 25. Z p x 2 + a 2.dx = x 2 p x 2 + a 2 + a 2 2 ln|x + p x 2 + a 2| + c , 26. Z p x 2 − a 2.dx = x 2 p x 2 − a 2 − a 2 2 ln|x + p x 2 − a 2| + c , 27. Z p a 2 − x 2.dx = x 2 p a 2 − x 2 + a 2 2 arcsen x a + c ,