Dpto. Matem´ atica Aplicada. E.T.S. Arquitectura. U.P.M. [email protected] C ´ ALCULO. Hoja 6. Integrales inmediatas. 1. R adx = ax + C 2. R x n dx = x n+1 n+1 + C 3. R 1 x dx = log |x| + C 4. R 1 √ x dx =2 √ x + C 5. R e x dx = e x + C 6. R p x dx = p x log p + C 7. R sin xdx = - cos x + C 8. R cos xdx = sin x + C 9. R tan xdx = - log | cos x| + C 10. R sec x · tan xdx = sec x + C 11. R sec 2 xdx = tan x + C 12. R cosec 2 xdx = -cotan x + C 13. R 1 1+x 2 dx = arctan x + C -arcotan x + C 14. R 1 √ 1-x 2 dx = arcsin x + C - arccos x + C 15. R f (x) n · f 0 (x)dx = f (x) n+1 n+1 + C 16. R f 0 (x) f (x) dx = log |f (x)| + C 17. R f 0 (x) √ f (x) dx =2 p f (x)+ C 18. R e f (x) · f 0 (x)dx = e f (x) + C 19. R f 0 (x) · sin f (x)dx = - cos f (x)+ C 20. R f 0 (x) · cos f (x)dx = sin f (x)+ C 21. R f 0 (x) · tan f (x)dx = - log | cos f (x)| + C 22. R f 0 (x) 1+f (x) 2 dx = arctan f (x)+ C -arcotan f (x)+ C 23. R f 0 (x) √ 1-f (x) 2 dx = arcsin f (x)+ C - arccos f (x)+ C