formulario
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UNIVERSITARIO INSUCO
sin a + b = sin a cos b + cos a sin b<br />
2<br />
π<br />
− a 2<br />
cos a + b = cos a cos b − sin a sin b<br />
cos = sin (a)<br />
sin 2 1−cos (2a)<br />
a =<br />
2<br />
cos 2 1+cos (2a)<br />
(a) =<br />
2<br />
sin −a = −sin (a)<br />
45º<br />
cos −a = cos (a)<br />
tan −a = −tan (a)<br />
sin 2a = 2 sin a cos (a)<br />
cos 2a = cos 2 a − sin 2 (a)<br />
sin 2 a + cos 2 a = 1<br />
1 + tan 2 a = sec 2 (a)<br />
2<br />
1 + cot 2 a = csc 2 (a)<br />
sin π − a<br />
2<br />
= cos (a)<br />
60º<br />
1<br />
1<br />
30º<br />
3<br />
1
d dx f x + g(x) = f′ x + g x<br />
d dx<br />
cf(x) = cf′(x)<br />
d dx f x g(x) = f x g′ x + g x f′(x)<br />
d dx f(x)/g(x) = g x f′ x −f x g′(x)<br />
g x 2<br />
d dx xn = nx n−1<br />
d dx<br />
d dx<br />
sin (u) = cos u u′<br />
cos u = − sin u u′<br />
d dx tan (u) = sec2 u u′
d dx cot (u) = − csc2 u u′<br />
d dx<br />
d dx<br />
sec (u) = sec u tan u u′<br />
csc (u) = − csc u cot u u′<br />
d dx eu = e u u′<br />
d dx au = a u ln a u′<br />
d dx<br />
ln (u) =<br />
u′<br />
u<br />
d dx log a(u) = log a e u′<br />
u
f x<br />
cf x<br />
+ g(x) dx = f x dx + g x dx<br />
= c f x dx<br />
x n dx = xn+1<br />
+ c , n ≠ −1<br />
n+1<br />
sin (x) dx = − cos x + c<br />
cos (x) dx = sin (x) + c<br />
sec 2 (x) dx = tan(x) + c<br />
csc 2 (x) dx = − cot(x) + c<br />
sec (x) tan(x) dx = sec(x) + c<br />
csc (x) cot(x) dx = −csc(x) + c
tan (x) dx = −ln |cos (x)| + c<br />
cot (x) dx = ln |sin (x)| + c<br />
sec (x) dx = ln | sec x + tan (x)| + c<br />
csc (x) dx = ln | csc x − cot (x)| + c<br />
e u du = e u + c<br />
a u du = au<br />
ln a + c<br />
udv = uv − vdu + c<br />
ln u du = u ln u − u + c
sinh u du = cosh u<br />
cosh u du = sinh u<br />
+ c<br />
+ c<br />
tanh u du = ln |cosh (u)| + c<br />
coth u du = ln |sinh (u)| + c<br />
sech u du = 2tan −1 e u + c<br />
csch u du = ln tanh u + c<br />
2<br />
sech 2 u du = tanh u + c<br />
csch 2 u du = − coth u + c<br />
sech u tanh u du = − sech u + c<br />
csch u coth u du = − csch u + c
ln u du = u ln u − u + c<br />
u ln u = u2 ln u<br />
2<br />
− u2<br />
4 + c<br />
u n ln u du = un+1 ln u<br />
− un+1<br />
+ c<br />
n+1 n+1 2<br />
u e u du = ue u − e 2 + c<br />
u 2 e u du = u 2 e u − 2ue u + 2e u + c<br />
u 3 e u du = u 3 e u − 3u 2 e u + 6ue u − 6e u + c<br />
ue au du = u eau<br />
a<br />
u 2 e au du = u 2 eau<br />
a<br />
−<br />
eau<br />
a 2<br />
− 2u<br />
+ c<br />
eau<br />
a 2<br />
+ 2 eau<br />
a 3<br />
+ c
du<br />
a 2 −u 2 = sin−1 u a + c<br />
du<br />
= 1<br />
a 2 +u 2 a tan−1 u + c a<br />
du<br />
= 1<br />
u u 2 −a 2 a sec−1 u + c a<br />
u cos u du = cos u + u sin u + c<br />
u sin u du = sin u − u cos u + c<br />
e au cos bu =<br />
e au<br />
a 2 +b<br />
2<br />
a cos bu + b sin bu + c