This document provides a basic table of derivatives and integrals. It lists common functions and their derivatives on the left side and the corresponding integrals on the right side. For each function, it gives the derivative or integral formula in mathematical notation. There are formulas provided for numerous trigonometric, exponential, logarithmic and other common functions.

1. Departamento de Ciencias B´asicas
DEPARTAMENTO DE MATEM´ATICA
TABLA B´ASICA DE DERIVADAS E INTEGRALES
Derivadas Integrales
(xn
) = nxn−1
xn
dx =
xn+1
n + 1
+ c
( n
√
x) =
1
n
n
√
xn−1
ax
dx =
ax
ln a
+ c
(loga x) =
1
x ln a
1
x ln a
dx = loga |x| + c
(sin (x)) = cos (x) sin (x) dx = − cos (x) + c
(cos (x)) = − sin (x) cos (x) dx = sin x + c
(tan (x)) = sec2
(x) tan (x) dx = ln |sec (x)| + c
(cot (x)) = − csc2
(x) cot (x) dx = ln |sin (x)| + c
(sec (x)) = sec (x) tan (x) sec (x) dx = ln |sec (x) + tan (x)| + c
(csc (x)) = − csc (x) cot (x) csc (x) dx = ln |csc (x) − cot (x)| + c
(arcsin (x)) =
1
√
1 − x2
sin2
(x) dx =
(x − sin (x) cos (x))
2
+ c
(arc cos (x)) = −
1
√
1 − x2
cos2
(x) dx =
(x + sin (x) cos (x))
2
+ c
(arctan (x)) =
1
1 + x2
sec2
(x) dx = tan (x) + c
(arccot (x)) = −
1
1 + x2
csc2
(x) dx = − cot (x) + c
(arcsec (x)) =
1
x
√
x2 − 1
sec (x) tan (x) dx = sec (x) + c
(arccsc (x)) = −
1
x
√
x2 − 1
csc (x) cot (x) dx = − csc (x) + c
(ln (x)) =
1
x
1
x
dx = ln |x| + c
(loga x) =
1
x ln a
1
x ln a
dx = loga |x| + c
1 Ufidelitas