This document contains lists of basic power series, integrals, and trigonometric formulas. The power series section lists common power series expansions such as 1/(1-x), ln(1+x), arctan(x), e^x, sin(x), and cos(x). The integrals section provides formulas for integrals of functions such as x^n, ln(x), sin(ax), e^ax, sec(x), and elliptic integrals. The trigonometric formulas section lists trigonometric identities for sums and differences of angles.

1. LISTA BÁSICA DE INTEGRAIS, SÉRIES DE POTÊNCIAS
E FÓRMULAS TRIGONOMÉTRICAS.1
SERIES DE POTÊNCIAS BÁSICAS
1. 1
1x =
P
1n
=0 xn, 8x 2 (1; 1).
2. ln (1 + x) =
P
1n
=0
(1)nxn+1
n+1 , x 2 (1; 1].
3. arctan x =
P
n0 (1)n x2n+1
2n+1 , x 2 [1; 1].
4. ex =
P
1k
=0
xk
k! , x 2 R
5. sin x =
P
=0 (1)k x2k+1
1k
(2k+1)! , x 2 R
6. cos x =
P
=0 (1)k x2k
1k
(2k)! , x 2 R
TABELA DE INTEGRAIS
1.
R
xndx = xn+1
n+1 + C, se n6= 1
2.
R
ln x = x ln x x + C
3.
R 1
xdx = ln jxj + C
4.
R
sin axdx = 1
a cos ax + C, a6= 0
5.
R
cos ax = 1
a sin ax + C
6.
R
tan xdx = ln (cos x) + C
7.
R
sinh xdx = cosh x + C
8.
R
cosh xdx = sinh x + C
9.
R
eaxdx = 1
a eax + C, a6= 0
10.
R
sec xdx = ln jsec x + tan xj + C
11.
R 1
1x2 dx = 1
2 ln