This document provides formulas and properties related to calculus and trigonometry. It includes: 1) Derivative formulas for common functions like polynomials, logarithms, trigonometric functions, and hyperbolic functions. 2) Integral formulas for polynomials, logarithms, trigonometric functions, and the exponential function. 3) Trigonometric identity formulas like sum and difference formulas. 4) Limit formulas for important limits like sin(x)/x and (1+1/x)^x. The document is a reference sheet of calculus and trigonometry formulas for students to use. It covers derivatives, integrals, identities, and limits of common functions.

1. √ 1
√
”Mas h´ uma outra raz˜o que explica a elevada rep-
a a 12. 1 − x2 dx = 2 arcsin x + 1 x 1 − x2 + C
2
uta¸ao das matem´ticas, ´ que ela leva as ciˆncias nat-
c˜ a e e
13. √ 1 dx = arcsin x + C
urais exatas uma certa propor¸ao de seguran¸a que,
c˜ c 1−x2
sem ela, essas ciˆncias n˜o poderiam obter” .
e a 14. √ 1 dx = arccoshx + C
x2 −1
. Albert Einstein 1
15. √ 1 dx = arcsinhx + C
1+x2
1 Tabela de derivadas 16. 1
1+x2 dx = arctan x + C
d n
√
1. dx x = nxn−1 , n = 0 17. arcsin xdx = 1 − x2 + x arcsin x + C
√
2. d x
= ax ln a, (a > 0) 18. arccos xdx = x arccos x − 1 − x2 + C
dx a
d 1 19. arctan xdx = x arctan x − 1 ln x2 + 1 + C
3. dx ln x = x
2
√ √ √
d 20. x2 − 1dx = 1 x x2 − 1 − 1 ln x + x2 − 1 +
2 2
4. sin x = cos x
dx C
d √ √ √
5. dx cos x = − sin x 21. 1 + x2 dx = 1
ln x + 1
x2 + 1 + 2 x x2 + 1 +
2
d C
6. dx tan x = sec2 x
22. ex sin xdx = 1 ex (sin x − cos x) + C
2
d
7. dx cot x = − sec2 x 1
23. ex cos xdx = 2 ex (cos x + sin x) + C
d
8. dx sinh x = cosh x
9. d
dx cosh x = sinh x 3 F´rmulas trigonom´tricas
o e
10. d
arcsin x = √ 1 1.
dx 1−x2
sin (a + b) = cos a sin b + cos b sin a,
d 1
11. dx arccos x = − √1−x2
cos (a + b) = cos a cos b − sin a sin b
d 1
12. dx arctan x = x2 +1 2.
a 1 − cos a a 1 + cos a
sin2 = , cos2 =
2 2 2 2
2 Tabela de integrais
3.
xn+1
1. xn dx = n+1 + C, se n = 1 sin (2a) = 2 sin a cos a, cos 2a = cos2 a−sin2 a
2. ln x = x ln x − x + C 4.
3. 1
= ln |x| + C a+b a−b
x dx sin a + sin b = cos
2 sin
2 2
1
4. sin axdx = − a cos ax + C, a = 0
a+b a−b
cos a + cos b = cos cos
5. cos ax = 1
a sin ax + C 2 2
a+b a−b
6. tan xdx = − ln (cos x) + C cos b − cos a = 2 sin sin
2 2
7. sinh xdx = cosh x + C
8. cosh xdx = sinh x + C
4 Limites fundamentais
1
9. eax dx = a eax + C, a = 0
lim xx = 1
10. sec xdx = ln |sec x + tan x| + C x→0+
sin x
11. 1
= 1
ln x+1
+C lim = 1
1−x2 dx 2 x−1 x→0 x
x
1
lim 1+ = e
1 H.C. http://math-ime-hc.blogspot.com.br/ x→+∞ x
https://www.slideshare.net/leinaddd88/
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