LISTA DE EXERCÍCIOS DE CÁLCULO II
Calcule as integrais Indefinidas pelo método da substituição.
a )∫(3 x−2)3 dx
b )∫ √3 x−2dx
c )∫13 x−2
dx
d )∫1(3 x−2 )2
dx
e )∫ x sen x2dxf )∫ xex
2
dx
g )∫ x2 ex3
dx
h )∫ sen 5 x dxi)∫ x3 cos x4dxj )∫cos 6 x dxl)∫ cos3 x sen x dxm)∫sen5 x cos x dxn )∫2x+3 dx
o )∫ 54 x+3
dx
p )∫ x1+4 x2
dx
q )∫ 3x5+6 x2
dx
r )∫ x(1+4 x2)2
dx
s )∫ x √1+3 x2dxt )∫ ex √1+ex dxu )∫1
(x−1)3dx
v )∫ senxcos2 x
dx
x )∫ xe−x2dx
Respontas:
a )(3 x−2)4
12+C
b )29
√(3 x−2)3+C
c )13ℓn |3 x−2|+C
d )−13(3 x−2 )
+C
e )−12cos x2+C
f )12ex
2
+C
g )13.ex
3
+C
h )−15. cos 5 x+C
i)14. sen x
4+C
j )16. sen 6 x+C
l)−14. cos4 x+C
m)16. sen6 x+C
n )2 . ℓn |x+3|+C
o )54. ℓn |4 x+3|+C
p )18. ℓn |1+4 x2|+C
q )14. ℓn |5+6 x2|+C
r )−18(1+4 x2)
+C
s )19.√(1+3 x2)3+C
t )23.√(1+ex )3+C
u )−12( x−1 )2
+C
v )1cos x
+C
x )−12.e− x
2
+C
Calcule as Integrais indefinidas pelo método de integração por partes
h )∫ x .exdxi)∫ x . sec2 x dxj )∫ x .e2 xdxl)∫ x3cos x2dxm)∫ x2sen x dxn )∫ x . sen 5 x dxo )∫ cos3 x dxp )∫√ x . ℓ nx dx
Re spostas :
a )x2
2. ℓn x−1
4x2+C
b )−x .cos x+sen x+Cc ) x .cos x+sen x+Cd )−e− x .( x+1)+Ce ) e x .( x2−2x+2 )+C
f )x3
3.(ℓn x−13 )+C
g )−12. sen x . cos x+x
2+C
h )∫ x .exdxi)∫ x . sec2 x dxj )∫ x .e2 xdxl)∫ x3cos x2dxm)∫ x2sen x dxn )∫ x . sen 5 x dxo )∫ cos3 x dxp )∫√ x . ℓ nx dx
h )( x−1) .ex+Ci) x . tg x+ℓn |cos x|+C
j )12e2X .( x−12 )+C
l)12
( x2 . sen x2+cos x2)+C
m)−x2cos x+2x . senx+2 . cos x+C
n )−x5
. cos5 x+125. sen 5 x+C
o )cos2 x . sen x+2 . sen3 x3
+C
p )23x .√ x . ℓ nx−4
9x .√x+C
Calcule as seguintes integrais por frações parciais
1) ∫ x4−10 x2+3 x+1x2−4
dx 2) ∫ (x+1 )x3−x2−2x
dx
3 ) ∫ x3−1x2 ( x−2 )3
dx 4 )∫1x2−4
dx
5 ) ∫5 x−2x2−4
dx 6 ) ∫ 4 x−112 x2+7 x−4
dx
7 ) ∫6 x2−2x−1
4 x3−xdx 8 ) ∫1
x3+3x2dx
9 ) ∫1x2 ( x+1 )2
dx 10)∫ x2−3x−7
(2 x+3 ) . ( x+1 )2dx
11 ) ∫3 x+1( x2−4 )2
dx 12) ∫ x4+3x3−5 x2−4 x+17x3+x2−5x+3
dx
13 ) ∫2 x4−2x+1
2 x5−x4dx 14 ) ∫ 1
( x+2)2 (x+1 )dx
15 ) ∫5 x2−11 x+5
x3−4 x2+5 x−2dx 16 )∫ x
4−10 x2+3 x+1x2−4
dx
2) Calcule
1) ∫ 0
4 1
√ xdx 2) ∫ 0
2 1
( x−1)2dx 3 )∫0
1x . ln x dx
4 )∫ 0
1 x
√1−xdx 5 )∫ 0
4 1
√16−x2dx 6 )∫−5
−3 x
√ x2−9dx
7 ) ∫ 2
4 1
√16−x2dx 8 ) ∫ 0
16 1
x34
dx 9 )∫−4
1 1( x+3)3
dx
10 ) ∫ 0
4 1x2−2x−3
dx 11)∫−2
0 1
√4−x2dx 12 )∫−2
2 1x3dx
13 ) ∫ 1
2 1
x√ x2−1dx 14 ) ∫ 1
3 13√x−2
dx 15 )∫−1
1 1
x2dx
16 ) ∫ 0
3 1x−1
dx 17 ) ∫ 0
1ln x dx 18 )∫ 0
1 3x5dx
19 ) ∫ 2
3 1
√3−xdx 20 ) ∫ 6
8 4
( x−6 )3dx 21)∫ 0
1 14 x−1
dx
22) ∫ 0
3 1
x2−6 x+5dx 23) ∫ 0
1 12 x−1
dx 24 )∫ 1
2ln ( x−1 ) dx
25 ) ∫−2
14 14√x+2
dx 26) ∫ 0
1 1
√1−x2dx 27)∫ 0
33( x−1)
−15 dx
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