formulario

UNIVERSITARIO INSUCO

sin a + b = sin a cos b + cos a sin b
2
π
− a 2
cos a + b = cos a cos b − sin a sin b
cos = sin (a)
sin 2 1−cos (2a)
a =
2
cos 2 1+cos (2a)
(a) =
2
sin −a = −sin (a)
45º
cos −a = cos (a)
tan −a = −tan (a)
sin 2a = 2 sin a cos (a)
cos 2a = cos 2 a − sin 2 (a)
sin 2 a + cos 2 a = 1
1 + tan 2 a = sec 2 (a)
2
1 + cot 2 a = csc 2 (a)
sin π − a
2
= cos (a)
60º
1
1
30º
3
1

d dx f x + g(x) = f′ x + g x
d dx
cf(x) = cf′(x)
d dx f x g(x) = f x g′ x + g x f′(x)
d dx f(x)/g(x) = g x f′ x −f x g′(x)
g x 2
d dx xn = nx n−1
d dx
d dx
sin (u) = cos u u′
cos u = − sin u u′
d dx tan (u) = sec2 u u′

d dx cot (u) = − csc2 u u′
d dx
d dx
sec (u) = sec u tan u u′
csc (u) = − csc u cot u u′
d dx eu = e u u′
d dx au = a u ln a u′
d dx
ln (u) =
u′
u
d dx log a(u) = log a e u′
u

f x
cf x
+ g(x) dx = f x dx + g x dx
= c f x dx
x n dx = xn+1
+ c , n ≠ −1
n+1
sin (x) dx = − cos x + c
cos (x) dx = sin (x) + c
sec 2 (x) dx = tan(x) + c
csc 2 (x) dx = − cot(x) + c
sec (x) tan(x) dx = sec(x) + c
csc (x) cot(x) dx = −csc(x) + c

tan (x) dx = −ln |cos (x)| + c
cot (x) dx = ln |sin (x)| + c
sec (x) dx = ln | sec x + tan (x)| + c
csc (x) dx = ln | csc x − cot (x)| + c
e u du = e u + c
a u du = au
ln a + c
udv = uv − vdu + c
ln u du = u ln u − u + c

sinh u du = cosh u
cosh u du = sinh u
+ c
+ c
tanh u du = ln |cosh (u)| + c
coth u du = ln |sinh (u)| + c
sech u du = 2tan −1 e u + c
csch u du = ln tanh u + c
2
sech 2 u du = tanh u + c
csch 2 u du = − coth u + c
sech u tanh u du = − sech u + c
csch u coth u du = − csch u + c

ln u du = u ln u − u + c
u ln u = u2 ln u
2
− u2
4 + c
u n ln u du = un+1 ln u
− un+1
+ c
n+1 n+1 2
u e u du = ue u − e 2 + c
u 2 e u du = u 2 e u − 2ue u + 2e u + c
u 3 e u du = u 3 e u − 3u 2 e u + 6ue u − 6e u + c
ue au du = u eau
a
u 2 e au du = u 2 eau
a
−
eau
a 2
− 2u
+ c
eau
a 2
+ 2 eau
a 3
+ c

du
a 2 −u 2 = sin−1 u a + c
du
= 1
a 2 +u 2 a tan−1 u + c a
du
= 1
u u 2 −a 2 a sec−1 u + c a
u cos u du = cos u + u sin u + c
u sin u du = sin u − u cos u + c
e au cos bu =
e au
a 2 +b
2
a cos bu + b sin bu + c