tabela_de_integrais

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Prof.: Leandro/Andre´a
Produtos Notaveis
1. (a+ b)2 = a2 + 2ab+ b2
2. (a− b)2 = a2 − 2ab+ b2
3. (a+ b)(a− b) = a2 − b2
4. (a+ b)(a2 − ab+ b2) = a3 + b3
5. (a− b)(a2 + ab+ b2) = a3 − b3
6. (a+ b)3 = a3 + 3a2b+ 3ab2 + b3
7. (a− b)3 = a3 − 3a2b+ 3ab2 − b3
Identidades Trigonome´tricas
1. sen2 x+ cos2 x = 1
2. 1 + tg2 x = sec2 x
3. 1 + cotg2 x = cosec2 x
4. sen 2x = 2sen x cos x
5. cos 2x = cos2 x− sen2 x
6. cos2 x = 1
2
(1 + cos 2x)
7. sen2 x = 1
2
(1− cos 2x)
8. sen(x+ y) = sen x cos y + sen y cos x
9. cos(x+ y) = cos x cos y − cos x cos y
10. tg(x+ y) =
tg x+ tg y
1− tg x tg y
11. 2sen x cos y = sen(x+ y) + sen(x− y)
12. 2 cos x cos y = cos(x+ y) + cos(x− y)
13. 2sen xsen y = cos(x− y)− cos(x+ y)
Integrais Imediatas
1.
∫
dx = x+ C
2.
∫
xndx =
xn+1
n+ 1
+ C (n 6= −1)
3.
∫ 1
x
dx = ln |x|+ C
4.
∫
exdx = ex + C
5.
∫
axdx =
ax
ln a
(0 < a 6= 1)
6.
∫
senx dx = − cos x+ C
7.
∫
cos x dx = sen x+ C
8.
∫
sec x dx = ln | sec x+ tg x|+ C
9.
∫
tg x dx = − ln | cos x|+ C
10.
∫
cosec x dx = ln |cosec x− cotg x|+C
11.
∫
cotg x dx = ln |sen x|+ C
12.
∫
sec2 x dx = tg x+ C
13.
∫
cosec2x dx = −cotg x+ C
14.
∫
sec x tg x dx = sec x+ C
15.
∫
cosec x cotg x dx = −cosec x+ C
16.
∫
dx√
1− x2 = arc sen x+ C
17.
∫
dx
1 + x2
= arc tg x+ C
18.
∫
dx
x
√
x2 − 1 = arc sec |x|+ C
1