Integral of cos2x x 1/x^2 sin2x 2x

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Integral of cos2x x 1/x^2 sin2x 2x

1+4x1+x+2x2dx C1IO9-S-

sin()

. dt

21-

(lnx)2 x dx 31-

1xlnx

dx

7 :.

f(x) =

1 5 (x2 + 3)5 +

C,11.

cnicas f(x) = 2 1

'o +

xn+ec2exs2a+ riCas,

19. f(x)

A =

resoluc 'of - 1

t+

Ca C,

2 lc1u.lfo(xI)II=13.(lnx)3

exerc + C, 31.

ifc(xio) s='olnd|elnCx|a+pC it.u0los 57

J. -53 :

Sti,Ca lculo ,5,1aEdic fito

'o. 2 -7 : sec2(t/4) dt 59-

pi 3

0 sen

clif.c5o9s2533d11.2519;149.5131:7:412 .

- 5.5 Sec. 7.1-

x ,

(x2 + 3)2 dx 11pap?. 476: 5, 9,

13, 27, 33 5 : .35 - re r 2 dr 2 9- ln(2x+ 1) dx 13- (lnx)2 dx 27- cox ln(sinx) dx 5 :. f(r) = 2(r - 2)e r2 + C, 9. f(x) = 1 2 (2x+ 1) ln (2x+ 1)- x+ C, 13. f(x) = x(lnx)2 - 2x ln +2x+ C, 27. f(x) = sinx(ln(sinx)- 1) + C. 33 - x dx 35- pi pi 2

2 5vacle

) dvacle 3

3

)) dvacle 33 : . f(x) =

:.f(x) = 2(sin - 11 384, 7. f(x) = pi

x-x cosx) 4, 9. f(x) = pi

+ C, 35.- 1 2 4, 15. f(x) = (

- 2

pi 7

4 . 7.2 . cos3 x-

- Trignome 2 3 cosx ) cosx+

tCric, a1s7.f(x) =1 g2.

484: 3, 7, 9, 15, 17, 19, 23, 41 3 -3 .43 pi cos2 x- ln | cosx|+ C, 19. f(x) = ln(1 + sinx) +

4 pi 2 C, 23.

sin5 x cos3 f(x) = tanx-

x dx 7- 0 2 cos2 x+ C, 41. f(x) = 1 6 sin

2 3x- 1 14 sin

d9 7x+ C,

- pi 0 sin4(3T) dt 15- 43. f(x) = 1 4 sin 2vam + 1

sin3 x 24 sin

cosx dx 17- 12vaj + C. Sec

cos2 x fiea 'o

tan3 x dx 19- 1- 7.3- Sustituc fietu

sinx cosx dx 23- tan2 'o Trignome trica, pa g.

x dx 490:

41- 5, 7,

sin 5x 9, 17,

sin 19,

2x 23

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1 2 2 -5 t3 t2 - 1 dt 7- 1 x2 25- x2 dx 9- 1 x2 + 16 dx 17- x x2 - 7 dx 19- 1 + x2 x dx 23- 5 + 4x- x2 dx 27- 1 (x2 + 2x+ 2)2 dx 5 :. f(x) = pi 24 + 3 8 - 1 4, 7. f(x) = - 25- x2 25x + C, 9. f(x) = ln ( x2 + 16 + x) + C, 17. f(x) = x2 - 7 + C, 19. f(x) = ln ( 1 + x2 - 1) x +1 + x2 + C, 23. f(x) = 9 2 sin-1 ( x- 2 3 ) + 1 2 (x- 2) 5 + 4x- x2 + C, 27.

f(x) = 1 2 [ tan-1(x+ 1) + 1 x(x2 + 1)2 dx 7 :.

(x+ 1) (x2 x+ 6 ln |x-

+ 2x+ 2) ] + 6|+ C, . r

C. Sec fia 2 2 - 4r +

'o 7.4- 16 ln |r + 4|+

Fracc C, 9.

'es, 2 ln

|pxa+

g. 5|

500: 7, - ln |x-

8, 9, 15, 21, 2|+ C, 15. 2

22, ln 2

23, + 1

25, 27, 38, 2, 21. 2 ln

39 7 : |x|+ 3 ln |x+ 2|+

1

x C, 22.

. 43 2 ln

| s|

-

x x2 ln

6 |

dx 8- s- 1| -

r2 r + 4 dr 9- x- 9 (x+ 1 s - 1 1 1) + C, 23. ln

5)(x- 2) dx 4 15- 0 2x+ 3 (x+ 1)2 dx 21- |x+ 1|+ 2 x+ 1 - 1 [2(x+ 1)2] + C, 25. ln |x-

5x2 1| -

+ 1

3x2 x3 2 ln(x2

+ +

2x2 dx 9)- 1 3

22- 1 s2(s- 1- (x 3) +

1)2 ds 23 C, 27. 1 2

- x2 ln(x2

(x+ 1)3 + 1) + (

dx 1

252 )

10 (x- 1)(x2 + 9) dx 1- ( x 2 ) + C, 38.

27- x3 ln |x|+ 1

+ x2 + 2x+ 1 (x2 + 1) + C.

(x2

+ 1) a

(x2 un

+ 2) dx 'o para

38- x4 + expressar

o

intretureando como uma func a 'o ricional e enta 'o avalei a 1 -39 : x x+ 1 dx 43- x3 3 x2 + 1 dx 39 :. ln x+ 1- 1x+ 1 + 1 + C, 43. 310(x2 + 1) 53 - 34(x2 + 1) 23 + C. Sec a 'o de Visea 'o- Exerc'icios, pa'g. 536: 1, 7, 9, 13, 15, 21, 29, 31 e 37. Avalei a 5 0 -1 : x+ 10 dx 7- sin(ln t) t dt 5 9- 4 1 x 3 2 lnx dx 13- dx x3 + x dx 15- sin2 vacle cos5

5 dvale 2 dx x2 - 4x dx 29- 1 -1 x5 secx dx 31- ln 10 0 ex ex - 1 ex + 8 dx 37- (cosx+ sinx)2 cos 2x dx Respostas : 1. 5 + 10 ln 2 3, 7. - cos(ln t) + C, 9. 64 5 ln 4- 124 25, 13. ln |x| - 1 2 ln (x2 + 1) + C, 15. 1 3 sin3 5 2 - sin5 7 1 + sin7 + C, 21. ln |x- 2 +x2 - 4x|+ C, 29. 0, 31. 6- 32 1 .37 2 sin 2x- 1 8 cos 4x+ C$ $int_0^\infuse\frac{\cos

2\,x-1}{x^2}\,dx=\frac12\,\int_{-\infra {\\cos 2\,x-1}{x^2}\,dx=\frac12\,\int_{-\inftify}^\infuse\frac{\Re(e^{2ix}-1)}{x^2}\,dx. $$ $$f(z)=\frac{e^{2iz}-1}{z^2}=\frac{2\ ,i}{z}-2-\frac{4\,i}{3}\,z+\cdtos $$ $z=0$ 2$ \,i$ . $R>$ $\epsilon>0$ . $R$

($C_R$) $[-R,-\epsilon]$ ($C_\epsilon$) $\epsilon$ $[\epsilon,R]$ $R\ \infuse$ $\epsilon\to0$. $lim_{R\to\infte}\int_{C_R}f(z)\,dz=0$, $lim_{R\to\infuse}\int_{C_\epsilon}f(z)\,dz=?$. $\lim_{R\to\infuse}\int_{C_\epsilon}f(z)\,dz=?$.

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