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Kha hc Luyn thi THPT Quc Gia 2016 Thy NG VIT HNG Facebook: LyHung95
Chng trnh Luy n thi PROS v PROE: Gii php ti u nht cho k thi THPT Quc Gia 2016!
VIDEO BI GI NG v LI GII CHI TI T CC BI T P ch c ti website MOON.VN
DNG 3. PP TNG PHN
Cng thc tch phn tng phn ( )= = b b
b
aa a
I udv uv vdu
Th t u tin khi t u : Hm loga, ln Hm a thc Hm lng gic = Hm m.
V d 1: [VH]. Tnh cc tch phn sau:
a) 1
1
0
sinxI e xdx= b) 2 21
ln
( 1)
e
e
xI dx
x=
+ c) 23
1
lne
I x xdx=
d) 1
24
0
ln(1 )I x x dx= + e) 1
25
0
xI x e dx=
Li gii:
a) t ( ) ( )1 1
1 1
10 0
0 0
sin cos cos . cossin cos
x xx x x xe u e dx du I e xdx e x x e dx e x J
xdx dv x v
= = = = + = +
= =
t ( )1 1
110 1' 0
0 0
cos sinxcos sin sin sinx x x x
x x
xdx dv vJ xe dx e x xe dx e x I
u e du e dx
= = = = =
= =
( ) ( )1 11 10 0
1 (sin1 cos1)2 sin cos 1 (sin1 cos1)
2x x eI e x e x e I
= = =
b) t 2 2 11 12
lnln ln
1 ( 1) 1 ( 1)( 1)
1
ee e
ee e
dxx u dux x dxx I dxdx
dv x x x xvx
x
= = = = + = + + + = + +
11 1
1 1
ln lnln 1 1 0.
1 ( 1) 1 1
e ee ee
ee e
e e
x dx dx x x
x x x x x= + = + = + =
+ + + +
c) t 2 2 2
2 2 2 232
1 1 11 1
2lnln
ln ln ln ln ln2 2
2
e ee e e
dxdu x
x u x dx xxI x xdx x x x x x xdx
xxdx dv xv
= = = = = = =
Xt 1
ln .e
J x xdx= t 2 2 2
211 1
ln 1ln ln
2 2 2 4
2
e ee
dxdu
u x x x xxJ x xdx x
xdx dv xv
== = = = =
2 2 2 22
3
1
1ln ln .
2 2 4 4
e
x x x eI x x
= + =
d) t 2 2
2
2ln(1 ) 1
2
xdxdu
x u x
xdx dv xv
= + = +
= =
12. CC PP TNH TCH PHN P3 Thy ng Vit Hng [VH]
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Kha hc Luyn thi THPT Quc Gia 2016 Thy NG VIT HNG Facebook: LyHung95
Chng trnh Luy n thi PROS v PROE: Gii php ti u nht cho k thi THPT Quc Gia 2016!
( )
1 11 1 12 3 22 2 2
4 2 20 0 00 0
1 1 1 1 112 2 2 22 2 2
20 00 0 0 0
ln(1 ) ln(1 ) ln(1 )2 1 2 1
1 1ln(1 ) ln(1 ) ln 1 ln 2
2 2 1 2 2 2 2
x x dx x xI x x dx x x x dx
x x
x x xdx x xx x x
x
= + = + = + = + +
= + + = + + + = +
e) t ( ) ( )2 1 1
1 12 2 2
50 0
0 0
22 2x x x x
xx
du xdxx uI x e dx x e xe dx x e J
v ee dx dv
= = = = =
==
Xt 1
0
.xJ xe dx= t ( ) ( )1 1
1 1
0 00 0
x x x x x
x x
x u du dxxe dx xe e dx xe e
e dx dv v e
= = = =
= =
Vy ( ) ( ) ( )1 1 12 250 0 0
2 2 1.x x x xI x e J x e xe e e= = =
BI TP LUYN TP:
Bi 1: [VH]. Tnh cc tch phn sau:
a) 2
1
1
( 1) ln= I x xdx b) 2 21
ln= e x
I dxx
c) 2
3 21
ln= e x
I dxx
Bi 2: [VH]. Tnh cc tch phn sau:
a) 2
1 21
ln( 1)
(2 1)
+=
xI dx
x b)
12
2
0
(2 1)= xI x e dx c)
24
3
0
2 cos
1 sin 2
+=+
x xI dx
x
Bi 3: [VH]. Tnh cc tch phn sau:
a) 2
21
1
ln( )= +I x x x dx b) 3
2 20
sin
cos
= x x
I dxx
c) 6
2 23
0
2 cos .sin
= I x x xdx
Bi 4: [VH]. Tnh cc tch phn sau:
a) 1
1 20 ( 1)
=+
xxeI dx
x HD: t = xu xe
b) 2 2
2 20 ( 2)
=+
xx eI dx
x HD: t 2= xu x e
c) 4
3
0
sin ( 1)cos
sin cos
+ +=+
x x x xI dx
x x x HD: o hm biu thc ca mu s tm mi quan h vi t s.
d) 1 2 2
3
0
2
1 2
+ +=+x x
x
x e x eI dx
e
Bi 5: [VH]. Tnh cc tch phn sau:
a) 4
1 2 20
tan
cos (tan 1)
+=+
x xI dx
x x b)
6
2 20
tan tan 2
cos 2
+= x x x
I dxx
c) 30 1 sin
=+
xI dx
x
Bi 6: [VH]. Tnh cc tch phn sau:
a) 2
1 2
1 1
ln ln = e
e
I dxx x
b) 4
2 2
3
sin 2 ln(sin )
cos
+= x x x
I dxx
c)
2
4
3
4
sin
= I xdx
Bi 7: [VH]. Tnh cc tch phn sau:
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Kha hc Luyn thi THPT Quc Gia 2016 Thy NG VIT HNG Facebook: LyHung95
Chng trnh Luy n thi PROS v PROE: Gii php ti u nht cho k thi THPT Quc Gia 2016!
a) 2
1 2
2 ln
2ln
= e
e
x x xI dx
x b)
4
2 20
ln(sin cos )
cos
+= x x
I dxx
c) 2
3
1
1 ln
2ln
+=+
e x xI dx
x x