Dpto. Matematica Aplicada. E.T.S. Arquitectura. U.P.M. [email protected]

CALCULO.Hoja 6. Integrales inmediatas.

1.∫adx = ax+ C

2.∫xndx = xn+1

n+1+ C

3.∫

1xdx = log |x|+ C

4.∫

1√xdx = 2

√x+ C

5.∫exdx = ex + C

6.∫pxdx = px

log p+ C

7.∫sinxdx = − cosx+ C

8.∫cosxdx = sin x+ C

9.∫tanxdx = − log | cos x|+ C

10.∫sec x · tanxdx = sec x+ C

11.∫sec2 xdx = tanx+ C

12.∫cosec2 xdx = −cotanx+ C

13.∫

11+x2dx =

{arctanx+ C−arcotanx+ C

14.∫

1√1−x2dx =

{arcsin x+ C− arccosx+ C

15.∫f(x)n · f ′(x)dx = f(x)n+1

n+1+ C

16.∫ f ′(x)

f(x)dx = log |f(x)|+ C

17.∫ f ′(x)√

f(x)dx = 2

√f(x) + C

18.∫ef(x) · f ′(x)dx = ef(x) + C

19.∫f ′(x) · sin f(x)dx = − cos f(x) + C

20.∫f ′(x) · cos f(x)dx = sin f(x) + C

21.∫f ′(x) · tan f(x)dx = − log | cos f(x)|+ C

22.∫ f ′(x)

1+f(x)2dx =

{arctan f(x) + C−arcotan f(x) + C

23.∫ f ′(x)√

1−f(x)2dx =

{arcsin f(x) + C− arccos f(x) + C