Phương pháp tính tích phân và số phức phần 2

292 Tin

h I =

• 7

X sin

X + (

x + 1)

(7

X

sin

x + (x + 1) co

4 _

71

~ 4 0

xcos

- In

1 = I

J o

X sin

X + co

s x 4

h I =

x u = X

) + (x2+ xnx2V77377T )

i + x '

h I =

2tdt = 2xdx

dx

= In -

E sie l Tin

h I =

rl

(1 ^

-1 u >

^ Tinh

1 =

j "

^e'^ Idx

-Gidi

Dat t

= V e"

Vi t

^ +

1 = e" =

> d

x = 2tdt t^

1 =

1

t = V e"

u =

> d

t = (tan^u +

u + 1)

0 tan^

u +

1 du =

V e"

- Id

x =

•4 du

= 2- 2.

^ = 2

-^

[299I Tinh

(2" 9)73

"

2 =

^ t'=

3.2

-2

5

Gidi

Da

t t = 1

- X

=

>d

t = -

- tf

-

3(

1 t)^

- (1

- t) +

1

= -2t^

£

^2x^

- Sx

^

x + Idx = ^ ^-(

2t

^ St^

- t +

Su

y ra : 2

1 =

0 =

> I = 0 <=

> I =

^2t^

- St

^

t + Idt = 0

Jo

soil Ti nh

Ta

CO :

I =

Gidi

0 dx

fO

1 + V-x(l + x) "'-

^

dx

1 + 1

V4

4 1-

2 +

cos u

du

2p

n — =>

d

u = '^^^

1 +

e

Do

i ca

-2 + ^

305| Tin

-> d

x = -

=costd

td

t

fO l + cos2

t

V3 J td

t =

• ^

2 V

3 J (1 + co

s 2t)d

t

2 (

h I = ''Vx^

2x

-^ +xdx

- D^d

x = f

^Vx{

x)dx+ fVxC

l-

x-Dd

X2 dx - rl

2

x^dx +

4

2 i = -x

= 8

CO

: I =

Gidi

f3

3 + lnx

dx

l2 =

f3

I

nx , I

3 ,3

-d

x = + I

310 Tin

h I = In

x

Jl x(

2 + Inx

f -d

x

DHKhd'i B -2010

Gidi

Dat u = In

x =

> d

u = —

X

• 1

* 2 + (2 +

3

- (In

2 + 1) =

In

1

3

ill] Tin

h I = fe^

In

^x

'I xV ln

x +

1

dx

1

fx =

X = e

Gidi

t^ = Inx +

a t

^ - 1 = In

dt

t2

.4 -1

t

2dt

= 2t

2

315| Tinh

I = j

j x^Va

^ x^

-dx (a > 0)

£>// Su phqm Ha

Ngi +

CD Hdi quan -

1999

Gidi

Dat X = asin

t vd

i t

e

dx acostdt

^d -s in

l-^ r , sin4

" +

1 « = e

" +

1 ^ 2 td te Mx =>

I 317 I

Tinh va bi^n luan theo tham

so difdn

g a , b : I = f

- 1980

De h a m f(x) k h a tich t r e n [-a; a] t h i f(x) phai lien tuc t r e n [-a; a]

x = - a

Do do : I =

t =

dx , b |

Vay I =

I = -t°.t

" ^

0 Tinh

1

= > 2ud

u = e^d

x

x =

l n2

x =

0

• I n

^

I =

2 .V3

(u^ l)du =

CD Giao thong Van

tdi -2000

Gidi

Ta

CO :

^x^Vl + 3x^

> =

1 + 3x* =

> 2td

t = 2 4x

xi

«V iT 37

-dx

(a > 0)

u = 1

u = 0

I = fe V

2 +

nx ^ 1 f

i

dx = -

1 2

x 2 V2

+ ud

u = —

2

(2 + u)

2 3

= -(

3V3

-2 V2

I

/•In 10

p^d

x

Cho so thuc

b >

ln2

Ti nh

J = , v

2

DH Quoc gia TP.HCM

- 1999

Dat u =:

e"

- 2

Doi ca

n X = I

x

u = e

^"

i°

-2 = 1 0-

2 =

u = e"

-2

Va

y J = (•In 10 e^dx

•8 du

3

-K — =

i 2 e''-2

4

(e''

2)3

Suy r

a li

m J = li

m —

b^

.l n2 b ->

ln

2 2 4- (e '' -2 )3

= -.

4 = 6

i

25 T in

h I = tan

X

Jo (

4 co

s X- si

n x ) co

s X

•dx

Gidi

Ta CO : I tan

X -dx

= tan

x

(4 cos X

- si

n x ) co

s x Jo

(4

- ta

n x ) cos

^ x

X =

0

Dat u = tan

x

= >

du =

dx

CO S^

X Doi ca

n

7 1

=>

X = —

nx

• 3 (4 cos X

- si

n x ) co

s x -dx =

• 1 udu -1 f- 1-

- 4 = -

u

J o

J o u

- 4 -4

1n (u -4 )

= -1 -4

h I =

rr si n X + co

s x

J o 3 + si

n 2

x

-x

l + 2cos3

a cos4

x + cos2x = 2cos3xcosx

Suy r

a : cos5x - cos4x =

(cos2x cosx) +

2cos3x(cos2x cosx)

-= (cos2

x cosx)(l +

2cos3x)

J,

cos5x-cos4x (cos2x -

Vay

I2 =

W

dx = »

TT

- T

17

x + cos5x - cos4x ,

-J2 r ]=

Vay 1

= 8

dx =

V2 -V

rz xco

s X

+

cos8x cos7x

Gidi

(4

X C OS

X + C OS

8x cos 7

-x

1 +

2 C OS

5x

dx

X CO S

-x

l +

dx

Suy r a : cos8x - cos7x = (cos3x - cos2x) + 2cos5x(cos3x - cos2x)

= (cos3x - cos2x)(l + 2cos5x)

1 = '1 udu

• 1 udu ( •]

Jo

4 -u

0

u -4

u

4

= 4 1n

331 Tin

h I =

1-3 Vl

t t

hi -1 < x < 1 nhimg

d da

y 0 < x < 3 V

e 3 = sin

t

Do d

o tin

t khon

g ducfc

332I

Tin

h I =

- cos

dx

CD Hdi quan -

1999

7 1

Jo cos x :dx =

V8 -2 si n2

x V 2

x =

> d

u = cosxdx

Dat u =

h I =

1 ^ sin2x

° Vcos^

x + 4sin^x

1

(-x^ + l)dx +

1

—+

2x2-3x

Vay I =

Gidi

Dat f(x ) =

- 2

x +

m c

6 A ' =

1

m

Khi m > 1 <=>

A' = 1- m < 0 =>

I(m)

=

x ^ 2x +

m

X 2 X

-= m

- —

Isssj Tin

h tic

h pha

n I = £

I339I

Tinh

|d

x

DH Quo'c gia TP.HCM

- 1991 + DH

Y duac TP.HCM -

1996

Gidi

* Kh

i a < 0 t

hi x

- a > 0 Vx

e [0

; 1]

Vay

1(a

) = x

|x-a

|dx+

xlx-ald

+ (x

^ ax)dx

i a > 1

hi x

- a < 0 Vx

e [0

; 1]

3

a _

1

2 3

fix) - g(x)

+ 0 0

0 Vay 1 = |f(x)-g(x)|dx = | f ( x ) - g ( x ) | d x + f ^ | f ( x ) - g ( x ) l d x

(X S OD - ) + XS OO :

2

11

+ Xp (X U TS - ) "

f = xp |X U TS

^aisgyNg =

I

^p

^S OD /

-

;p

i S OO J = :^

K-U

= X UB D log

11-Do do I = - ^ |sin t| dt = - J ^ |sin t| dt + - ^ jgin t| dt

I =

A /1 + cos 2xd

x

DH Thuy Igi -

1997

Ta

C O

: I =

Gidi

Vl + COS2xd

x =

f V2cos

^ xd

x = ("'A /2 cosx

-x = V2 si

n x

2 V2 si

cosx 0 Vsin

xdx

DH Bach khoa Ha

: I =

|cosx| Vsi

n xd

x + „ |co

•

Vi ha

m s

o f(x) = x"

-x

^ -1

2

Gidi

la ha

m so' chSn, lie

f 1

dx

-1 x

^ x^ -

12

1 xd

x

0 x^ - x^ -

12

Da

t t = x

^ =

> d

t =

2xdx

- cos

^ x dx = 2

p

cos x-y/co

s x (l - cos^

= cos

x

= :>

2tdt = - si nx

2t dt ) =

0

5

350| Tin

h I =

f2

co sx

dx

0 V

2 + cos 2

x

DHYHaNoi -1996

Gidi

Taco: 1=

f i_

t vdt

i

t e 0;

^

2 V2

cosxdx = A

°'

^^

^' V 5

r«

co st

dt V2

* Va

a-si n^

t) 2

\35l\h I =

• o C OS X

+ s in

t 2x in + s Va 4 7

D/

/ Tdi chinh Ke

todn

1999

a) Ne

u m, n

1 - co

s 2x

2

1 + cos 2

X

= , cos

t t = sin

a am, da

t t = tan

x hoa

c t = cotx

53 Tin

h I =

2 cos* xd

x

DH Sa phqm TP.HCM

s 4

dx

- x + — sin 2

x + — si

n 4

2

_ 37

DH Quoc gia TP.HCM

4 2

(l-cos2x )Mx= - 4 J 0

— 2 cos 2

x + — co

2

2 (1 + COS 4x)dx =

m

271 4 U

7 1

4

356| Cho I = 2 cos^ X cos^ 2 x d x ; J = 2 sin^ X cos^ 2xdx

358 Tin

h I = 2

sin^ X CDs'* xd

x ,

DH Ngoai nga Ha

= - (

1 - co

s 2x)(

l + 2 cos 2

x

1 r

1 1 ^ — co s 4x x - co cos 2 1 + -

V4y I

= 1

+ - CO S

2x cos 4

-x — cos 6

dx

— x + — sin 2

s 4xd

x =

- M (cos 4

^ ° x

- cos

* x sin

* x)dx

DH Sa pham Hd

Ngi - 2000

168

Gidi

I = 2 (cos^° X + sin^° X - cos"* x sin^ x)dx

2 [cos^° X + sin'" X - CDs'* x sin'* x(sin^ x + cos^ x)]dx

2 [cos^ x(cos^ x - sin'' x) + sin^ x(sin'' x - cos'' x)]dx

2 [cos® x(cos'' X - sin^ x) - sin® x(cos^ x - sin^ x)]dx

2 (cos* x - sin* xXcos® x - sin® x)dx

36ll Tinh I = 2 cos 2x(sin'' x + cos* x)dx

DH Bach khoa Hd Noi - 1998 Gidi

Ta CO : fix) = cos2x(sin''x + cos'^x) = cos2x(l - 2sin^xcos^x)

= cos2x l - - s i n 2 2x

f(x) =

C OS

x + — co

i

62 Tin

h I =

2 sin^

xdx,

Ta

CO

: I =

2 sin^

xdx =

Gidi

2

(1-

2 _ 2

~ 3

laesl

Tin

h I =

sin* x sin xdx =

(l

-t 2) 2d t=

f

\l-2t2+t'')d

+ -

- — ~ 1 3 5

5 •

Tin

h I=

= f " sin^

° x si

n xd

x =

f "

(1 cos^

x)^

sin

Dat t = cosx => dt = -sinxdx

Gidi

Dat u = sin

x =

> d

u = cosxdx

2

sin^ x cos^ xd

x = ^ sj^

3 5

1 1 _2_

3 5 " 1

5

Tin

h I =

2

sin'* x cos^ xd

x

Gidi

I =

2 sin"* X cos^ X = 2

sin"* x(l - sin^ x)

l-t2 )2 dt =

(t"

-2t^

+t^

h I=

dt =

dx

cos^ x Doi ca

h I =

g (1

- si

n x) co

d(sin x

)

ln|sin X 1-

2

374 Tin

h I =

-l

n

3 2

= I

n 3 + -

3

37 5I

Tinh I =

X

dx

=>

du = sin xd

x cos^ x

cos^ x

V

= tan

X

2 Cho cac so thirc ai, 3.2, a„ thoa :

aiCosx + a2Cos2x + a3Cos3x + + anCosnx = 0, Vx € [0; 2n]

Hay siir dung ket qua tren T i n h ai, 32, &„

DH Qudc gla TP.HCM -A/1999

t T(x) = aicosx

+

a 2C os 2x +

+ a nC os nx = 0

o coskx

(aiCOSx + a2 Co s2

x + + a

jx cos jxdx

= T

Vay tCr (*

7t

377 Chufn

g min

h L =

2 cos

" X cos(

n + 2)xdx =

0 , Vn

- sin(

n + l)

x si

n x] d

x

2 cGs

(n + l)

x si

n x cos" xd

x

Da

t

u = sin(n + l)x => d

u = (n + 1) cos(

n + l)xdx

dv = sin

x cos

" xd

x =

> v = -

•

co s"

^ X

2 +

2 cos(

n + Dxcos"""^

0

+ I

i

Vay In

= I

i I2

= 0

,V

n e N

Tin

h I =

2 si

n 2x(l + sin

l + cos x)

^ d

DH Ngoai thuong -

1999

Da

t t = 1 + sin^

Dat t = 1 + cosx ^ dt = -sinxdx Doi can

Ta CO : cos2x = cos^x - sin^x = (cosx - sinxXcosx + sinx)

Dat t = sinx + cosx + 2 => dt = (cosx - sinx)dx

Ill

Tinh

I =

•- sin

dx

HV Ngan hang -

D/2000

Ta

CO

: I =

^ 2 sin 2x(2cos'^

x 1)

x =

> d

t = -sin2x

I =

|[

2(

l)-l](

t d

t) r2

(2t-3)

•dt ^ (2t-31nt)

h I =

dx

6 sm X s

in

X + —

6

DHLudt Hd Ndi -2000

m X si

n X COS

—

+ co

s X

= — sin

x(V3

sin

x + cos x

2 I

n

r

v3 + cot

x V3 +

n 2V3

= ln

|383 Chutn

g min

u

cos mx cos nxd

x = sin

Ta CO cos nix cos nxdx = —

Vay \ cos^ x cos 7xdx =

2 :

I = R(sin

x, cosx)d

x vd

i R l

a ham hufu t

ti chiJ

a sinx, cos

R

(sinx, cosx) t

hi da

t t = cos

x

2 Ne

u R

(sinx, -cosx) =

R

(sinx, cosx) t

hi da

t t = sin

x

3 Ne

u R

(-sinx, -cosx) =

R

(sinx, cosx) t

hi da

t t = tan

2

Luc d

o sin

x 2t

-t^

l-' 1 + t

-1 d

x

385| Tin

h I =

~ 4 sin^ xd

x

0 1 +

cos x

DH SiC pham TP.HCM

- 1994

Giai

Nhan

xet R

(-sinx, cosx) =

R

(sinx, cosx)

Da

t t = cos

x

= :>

d

t = -sinxd

x Do

C OS

38

^ Tin

h I =

ma

1999

Giai

Nh an

xet :

R

(sinx, -cosx) =

R

(sinx, cosx)

Dat t = sinx => dt = cosxdx Ddi can

Gidi

Dat t =

Ddi ca

n

tan —

1 2dt

-I =

1 +

0 (

l + t^)

h I _ f

B -2000

Gidi

Ta

CO :

sin xd

x sin

CO S^

X

•| d(cosx)

3

- CO

3

390| Tin

h I

JO sin^

X

— d

DH Quoc gia Ha

Ngi -1997

Dat t = cos

x

Gidi

dt = -sinxd

x Doi ca

n

X = —

q -cos

^ x) si

n xd

x _

f » (1 - t^

)(-dt)

0

•of

1 1-1

+ CO S^

X

2 ^

1 + t^

t^

+1

dt =

1

391 Tin

h I = r2

C OS

xd

x

- ~ (1 C0 SX )'

X

\D + ; r

(^P-)

;3 uis + X

5

,soD + ; —

= x

p Xg

U TS +

X

X

, UI

S +

X

0 = %

X

0-X

, UT

X z

- = ;p <

^ -"

- X7 U TS

XZSOD

+ X

X

+ X S OD

OD

= Xp

(X +

X SO

O

X j,SO0 ) g

X

+ X

S OD

- X j SO D)

[I

(T +

X gS OD )]

£ XPX „ SO

D

-= I

:

03

Suy ra : 21 = I + I = 1 X + Sin X H X + cos X

J

-J o 2t +

l

,2Vt2 +t 2Vt^

Tt, (it = V2 - ln(>,/

2 + 1)

Vay I cos2x

+ co

s X + 2

2 :dx =

- +l

- V

2 + ln(V

i 4£

l^

iiLl

£^

dx

3 + sin 2x

Gidi

Ta

CO

: I =

~ si

n X + cos

Dat u = sin

x cosx =

-> d

u = (cosx + sinx)dx

fO

du -0

du

-14-u'

-1

u^

-4

-

In

u -2

1

=

[ '"

-J :^

4t 4(

t + 1) 2(

t + 1)^

ln

398| Tin

h I =

dx

1 X

(x2012 ,

1)

400| Tin

h I =

« In

Ta

CO

: I =

• « In

X

1

1 x^

-In^

X

dx =

Gidi

re In

X

dx

Dat u =

In

X

(1-lnx

^ du

h I =

• e In

X

+ In

X

1 (In

X +

X +

if

dx

• e In

X

+ In

X

•1 (In

In

X +

1

dt = In

X

(ln

x + 1)^

ri

_dt_

8 (e

+ 2f

402I Tin

h I = 1 x^ + tan^ x

-i l + x

^ dx

Ta

CO :

* Tin

h I,

-U + x

^ -dx = -1 x^

-x

^+

^

l-1 + x

404 Tin

h I =

• s

-m X ,

•^9 +

4 cos

X

Gidi

Dat u = cos

x d

u = -sinxdx

Doi ca

n

K

X = —

a = —

t +

1 2 (•"

4 3-

dt =

- t 6 0

I = — vo

i ta

n a = -

405 Tin

h I = cos xd

Da

t t = sin

dt

X = —

-I = (ln

|t

-3

ln

|-|t

-2

|) r

h I 'i^^-'Sxd

x

Jo cos

X +

1

DH Quoc gia TP.HCM

sinmx.cosnx = — [sin(m + n)x + sin(m - n)x]

2 sinmxcosnx = — sin2nx

2n

neu m ?^ n

neu m = n

x = —

x =

0 Vm, n

x

-7 1

h I =

'2 cosxd

x

" V

l + cos^x

DH Da Ndng -

t u = sin

x =

> d

u = cosxdx

=

fi

du

V 2

^

du = costd

t

2 = 2

- 2si

n t = 2(

1 sin

-^) = 2cosn

4

t =

0

Vay 1 = V2 costd

'0

4sinxd

DH Thuang mai -

4

Nn3

o

sin xdx

sm

X + -

4J

Doi bien, da

t t=

4

X:

=t -^

4

h I =

2é'"''cosxdx +

^cos^xdx

2e

"'"''d(sinx) +

- 2(i + cos2x)dx =

h I =

2 ế" "

si

n x cos'^ xd

x

DH Kien true Ha

n

I = -

h I

-i

- 3 sin

X +

4 cos x ,

5

DH Thuy Igi -AI2000

Gidi

I =

f- 3sin

x + 4cosx

Ii = I2 =

0 3sin'^

x -dx

dx =

0 3sin^

X +

4 cos^ x

0 dt

0 3 + cos

^

X

-13 + 1^

eVs

2 d(sinx)

- sin

X , , ,

^ d

x =

- I

n cos

-l

71 ,

V 2I — In 4 2 — +

dx

0

2 cos^

4 0 X =

u =

a vd

=-

sU

1996

Dat t = cos

x

Gidi

dt = -sintd

4 -(

co

1-s x) si

n xd

x _ ^

^ 1 + cos'

* X l

(l-t

^)

dt

1

1+t

^

Lai dat u = - + t => du =

t Doi can

dt

t = 1

u = 2 3V2

422 Tin

h I =

1 + sin 2x + co

s 2

x ,

sin X + co s

X

BH Nong nghiep 1

Ha Nqi

- 1998

Ta c6 :

Gidi

1 + sin 2x + co

s 2

x sin

^ x + cos

^ x + cos

^ x

- sin

^ x + 2

sin

x co

s x

sin X + co s

X sin

X + co s

X

2cos x + 2 si nx co sx 2cos x(co

s x + si

n x )

= 2cos

Vay 1

^ Ti nh l=

f

i '^

"^

^^

^ ,

•'0 ll -7 si nx -c os

^ x

CD Hdi quan -

1998

Gidi

Ta CO : I = cos xd

x cos xd

x

0 1

1 7 si nx

x d

u = cosxdx

0 sin

X

7 si n

n 3 u-

2 so ' a , b sao cho : 1-

x

a b

x • • +

(x + l)(x^

+1)

X +

1 +

1 Vx

*

-1

b) Tin

h I = 2 (1 - sin x) co

s xd

x

0 (1 + sin x)(2 - cos^ x )

BHAn ninh -1999

a)

Gidi

Ta CO :

1

x = a(x^ + 1) + bx(x + 1 )

1

x = (a + b)x

^ + bx + a

Suyra j!h(x)dx

• + •

(2 + sin x)^ (2 + sin x)^ (2 + sin x)

DH Bach khoa Ha Noi - 1999

|426| Ti

m A , B , C sao cho

si nx

- cos

x +

1 = A (s in

x + 2cosx + 3 ) + B(cosx

- 2s in

x) +

C

DL TB

v ao d

o, ti nh

I =

r::

s in

-co sx + 1

Gidi

Ta

C O

: s in

x cosx + 1 = A (s in

-x + 2cosx + 3 ) + B(cosx

- 2B )s in

x + ( 2A + B)cos

x + 3

A +

C

A 2

-B =

1

2A + B = -

1

3A + C = 1

A = -

B = -

1 B

(c os

X

2 si

n x)

= A + + + 3 s x 2 co X + sin

Va

y 1=

, 5

J

^d x-

^ 5 0sin

X +

2 co

s x + 3 s in

x + 2 co sx + 3

X

5

2

3 ,.

„ s In — m

0

o

1=

_ JL _3 _3 (i n4 _i n5 )^

8

10

5 5

5 (*)

Ti nh

I =

dx

Da

t t = ta

n

-2

0

s in

X +

2cosx + 3 1/

dt = -

2

ta n2 -

+ l

dx dx

= 2d

n

71

X = —

t^

1-) „

• 'o t2

^

1 + t

^

La

i da

t t + 1 = 2t an

u

dt = 2 (t an

^u + l )d

u

4 sin X + 3 cos x + 5 4 sin x + 3 cos x + 5 dx

1 d

t

1 + t^

+ 5

0 2t

^ + 8t +

^ t + 2

XT- T

1

,9

1

Vay 1=

- + ln- +

428 Tin

h I =

dx

0

(sin

x + 2cosx)^

DH Su pham TP.HCM

-D/2001

Gidi

Kh

ai trie

n mau, chi

a t

u T mi

x =

> d

t = (tan^x +

l)dx Doi ca

n

I =

fi d

x -1

h I = ("

sin 4xdx

0 sin

^ X + cos

^ X

DH Ngoai thuang -

A/2001

Ta

CO

: f(x) =

Gidi

sin4x s

in4x

sin

«x + cos

«x i

_3 si n2

f lie

n tu

c tre

n doa

n hay I

ton t

ai

x + cosx =i d

t = (cosx - sinx)dx

t =

1 + sin2x

1

t =

1

t = ^

Vay I = -

3 + 4sinx - cos2x

sin2x

Gidi

3 + 4sinx - cos2x *

sin^ x + 2sin

x =

> d

t = cosxdx Do

i ca

n

Nen I =

• 1 tdt _

fH + 1 -1

sin2x ,

433| T i n h I =

Gidi CACH i : Ta CO : - ^ l ^ ^ ^ d x = -

Va , - X

tan

X tan

xdx + -

* 2 cos^

X -dx = -

2 J

o 3 tan^

xdx = -

2 3(tan

^ x + l )d

x-

pd

x) 3

1 0 ^

2

I

3

2

Suy r

a : I = Ij + I2 = -

-I n

x 6

2

7 1

43 5I Ti nh

I =

cos 2

x

sin 2x + cos 2

x

•dx

DH Thily sdn Nha

Trang

2001

Gidi

Ta da

t J=

[

8 sin 2x

0 sin 2x + cos 2

x -dx

Ta

CO

I

J = f- (c

os 2

x sin 2x)dx 1 r -d (s in 2x + cos 2x

-)

0 sin 2x + cos 2

x 2

J 0 sin 2x + cos 2

2

ln

Ta la i CO

I +

J = ' d

x = x|

8 = -

Vay 1

= i[

(I -J ) + (I + J)] =

Z Lli

436| Tinh

I =

f ^

1 + sin

X

0

1 + cos

X eMx

DH Y duac Hd

Noi

2000

Gidi

Ta CO : I = eMx

0 1 + CO

X

Phiiatng phdp : Ta phan tich h a m dudi dau tich phan t h a n h tich,

trong do c6 bleu thufc (tan^x + l)dx = d(tanx) hoac (cot^x + l)dx - d(cot),

hoac ddi bien so' dat t - tanx

Sau day la cac v i du :

DH Y Ha N6i - 2000 Gidi