1
I. F´
ORMULAS DE DERIVACI ´
ON
1. d
dx [c]=0
2. d
dx [x]=1
3. d
dx [kx] = k
4. d
dx [xn] = nxn−1, n 6=−1
5. d
dx sin x= cos x
6. d
dx cos x=−sin x
7. d
dx tan x= sec2x
8. d
dx cot x=−csc2x
9. d
dx sec x= sec xtan x
10. d
dx csc x=−csc xcot x
11. d
dxex=ex
12. d
dxax=axln a
13. d
dx ln |x|=1
x
14. d
dx ln |g(x)|=g0(x)
g(x)
15. d
dx sin−1x=1
√1−x2
16. d
dx cos−1x=−1
√1−x2
17. d
dx tan−1x=1
1 + x2
18. d
dx cot−1x=−1
1 + x2
19. d
dx sec−1x=1
|x|√x2−1
20. d
dx csc−1x=−1
|x|√x2−1
II. F´
ORMULAS DE INTEGRACI ´
ON
1. Z0dx =C
2. Z1dx =Zdx =x+C
3. Zk dx =kZdx =kx +C
4. Zxndx =xn+1
n+ 1 +C, n 6=−1
5. Zcos x dx = sin x+C
6. Zsin x dx =−cos x+C
7. Zsec2x dx = tan x+C
8. Zcsc2x dx =−cot x+C
9. Zsec xtan x dx = sec x+C
10. Zcsc xcot x dx =−csc x+C
11. Zexdx =ex+C
12. Zaxdx =1
ln aax+C
13. Z1
xdx = ln |x|+C
14. Zg0(x)
g(x)dx = ln |g(x)|+C
15. Z1
√1−x2dx = sin−1(x) + C
16. Z−1
√1−x2dx = cos−1(x) + C
17. Z1
1 + x2dx = tan−1(x) + C
18. Z−1
1 + x2dx = cot−1(x) + C
19. Z1
√x2−1dx = sec−1(x) + C
20. Z−1
x√x2−1dx = csc−1(x) + C