Integrais Indefinidas
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Terceira Lista Exerc´ıcios de C´ alculo I - POLI - 2002I - Integrais Indefinidas
Calcule as integrais indefinidas abaixo. Para a verifica¸ca˜o da resposta lembre-se de que f (x)dx = F (x) + k (k constante ) ⇔ F (x) = f (x), ∀x ∈ Df . x7 + x 2 + 1 dx x2
4. tg 2 x dx sen3 x dx 7. √ cosx x dx 10.
1 + x2
√
13. x 1 − x2 dx
1.
√ x2 5 x3 + 1 dx dx √
(arcsenx) 1 − x2
2.
e2x dx
3.
cos7x dx
5.
7 x−2 6.
tg 3 x sec2 x dx
8.
tg x dx
dx
9. tg 3 x dx
x dx 1 + x4
14. secx dx
11.
12.
15.
x2 dx 1 + x2
1
√ dx x
√ 1 + ln x ln x dx x sen2x dx
1 +√ cos2 x sen x
√
dx x 22.
ex x2 dx
23.
4x + 8 dx 8x + 20 e dx
1 + ex
√
ex 3 1 + ex dx
25.
26.
2x(x + 1)2002 dx
27.
x senx dx
28.
earctg x dx 1 + x2 x e cosx dx
29.
x ln x dx
30.
ln x dx
31.
xe−x dx
32.
xarctg x dx
33.
arcsenx dx
34.
sec3 x dx
35.
36.
37.
sen2 x cos2 x dx
38.
cos2 x dx
1 − senx dx cosx
3x2 + 4x + 5 dx (x − 1)2 (x − 2)
√
x2 1 − x2 dx
sen2 x cos3 x dx
3x2 + 4x + 5 dx (x − 1)(x − 2)(x − 3) x5 + x + 1 dx x3 − 8
45.
e
√
48.
√ x ln x dx
16.
19.
40.
43.
46.
49.
52.
55.
3
1 dx 2x2 + 8x + 20 x2 √ dx 1 − x2
√
ln(x + 1 + x2 ) dx sen(ln x) dx
√
a2 + b2 x2 dx
√
3 − 2x − x2 dx
17.
20.
41.
44.
47.
50.
53.
56.
2x2x +
dx
5 − 2x + x2 x dx
2
x −4
1
√ dx 2 a + b 2 x2
1
√ dx (1 + x2 ) 1 − x2
1
18.
21.
24.
39.
42.
51.
54.
57.
√ x dx
3x2 + 5x + 4 dx x3 + x 2 + x − 3
√
x2 − 2x + 2 dx cos3 x dx
58.
61.
64.
67.
sen5 x dx
1
dx
5
sen x cos3 x sen2 x cos4 x dx
1
sen2 x cos4 x
62.
cos5 x dx sen3 x sen4 x dx
65.
cos6 (3x) dx
68.
1−x dx 1+x
59.
dx
sen3 ( x2 ) cos5 ( x2 ) dx
60.
sen2 x cos5 x dx cos2 x
66.
dx sen6 x
1
√
√ dx
69.
x− 3x √
(Dica: Fa¸ca u = 6 x)
63.
II - C´