Integrales

Matem´ticas (GADE) a

Tabla de derivadas

Funci´n constante o Funci´n identidad o Funci´n potencial o Funci´n radical o

f (x) = k (k ∈ R) f (x) = x f (x) = xn(n ∈ R) f (x) = √ n x (n ≥ 2)

f (x) = 0 f (x) = 1 f (x) = nxn−1 f (x) = √ n 1

n xn−1 1 ln(a)x 1 x

Funciones logar´ ıtmicas

f (x) = loga (x) f (x) = ln(x)f (x) = f (x) =

Funciones exponenciales

f (x) = ax f (x) = ex

f (x) = ln(a)ax f (x) = ex f (x) = cos(x) f (x) = − sen(x) f (x) = 1 = 1 + tg2 (x) cos2 (x)1 1 − x2 −1 1 − x2

Funciones trigonom´tricas e

f (x) = sen(x) f (x) = cos(x) f (x) = tg(x) f (x) = arcsen(x) f (x) = arccos(x) f (x) = arctg(x)

f (x) = √ f(x) = √ f (x) =

1 1 + x2

1

Tabla de integrales inmediatas

λdx = λx + C, para todo λ ∈ R xn dx = xn+1 + C, para todo n ∈ R, n = −1 n+1

1 dx = ln |x| +C x ex dx = ex + C ax dx = ax + C, para todo a ∈ R, con a > 0 ln(a)

sen(x)dx = − cos(x) + C

cos(x)dx = sen(x) + C 1 dx = cos2 (x) 1 dx = sen2 (x) √ 1 + tg2 (x)dx = tg(x) + C 1 + cotg2 (x) dx = − cotg(x) + C

1 dx = arcsen(x) + C 1 − x2

1 dx = arctg(x) + C 1 + x2

2

Tabla de integrales inmediatas generalizadast (x)dx = t(x) + C [t(x)]n t (x)dx = [t(x)]n+1 + C, para todo n ∈ R, n = −1 n+1

t (x) dx = ln |t(x)| + C t(x) et(x) t (x)dx = et(x) + C at(x) t (x)dx = at(x) + C,para todo a ∈ R, con a > 0 ln(a)

sen(t(x))t (x)dx = − cos(t(x)) + C

cos(t(x))t (x)dx = sen(t(x)) + C t (x) dx = cos2 (t(x)) t (x) dx = sen2 (t(x)) t (x) 1 −(t(x))2 1 + tg2 (t(x)) t (x)dx = tg(t(x)) + C 1 + cotg2 (t(x)) t (x)dx = − cotg(t(x)) + C

dx = arcsen(t(x)) + C

t (x) dx = arctg(t(x)) + C 1 + (t(x))2

3