Tabela de Integrais

Prévia do material em texto

EMB5001 - Cálculo I - Prof. Victor Simões Barbosa - Tabela de Integrais
(1)
∫
dx = x+ c (2)
∫
xα =
xα+1
α + 1
+ c (α 6= −1)
(3)
∫
dx
x
= ln |x|+ c (4)
∫
ax =
ax
ln a
+ c
(5)
∫
exdx = ex + c (6)
∫
senx dx = − cosx+ c
(7)
∫
cosx dx = senx+ c (8)
∫
tanx dx = ln | secx|+ c
(9)
∫
cotgx dx = ln |senx|+ c (10)
∫
cosecx dx = ln |cosecx− cotgx|+ c
(11)
∫
secx dx = ln | secx+ tanx|+ c (12)
∫
sec2 x dx = tanx+ c
(13)
∫
cosec2 x dx = −cotgx+ c (14)
∫
secx · tanx dx = secx+ c
(15)
∫
cosecx · cotx dx = −cosecx+ c (16)
∫
dx√
a2 − x2
= arcsen
x
a
+ c
(17)
∫
dx
a2 + x2
=
1
a
arctan
x
a
+ c (18)
∫
dx
x
√
x2 − a2
=
1
a
arcsec
∣∣∣x
a
∣∣∣+ c
(19)
∫
senhx dx = coshx+ c (20)
∫
coshx dx = senhx+ c
(21)
∫
sech2 x dx = tanhx+ c (22)
∫
cosech2 x dx = −cotghx+ c
(23)
∫
sechx · tanhx dx = −sechx+ c (24)
∫
cosechx · cotghx dx = −cosech x+ c
(25)
∫
dx√
x2 ± a2
= ln
∣∣∣x+√x2 ± a2∣∣∣+ c (26) ∫ dx
a2 − x2
=
1
2a
ln
∣∣∣∣x+ ax− a
∣∣∣∣+ c
(27)
∫
dx
x
√
a2 ± x2
= −1
a
ln
∣∣∣∣a+√a± x2x
∣∣∣∣+ c
1