Question

what is integral of (cos x) / x ?

Answer 1

What integration techniques do you have right now?

Answer 2

techniques? like?

Answer 3

u-substitution
parts
trig substitution
etc.

Answer 4

i just wanna find out derivative of cosx/x between 3 pi/2 and pi/2

Answer 5

and then the integral of cos x/x

Answer 6

The derivative would be the slope of the tangent line, the integral is the area of the region. Two different (yet related) things.

Answer 7

i have tried finding out integral of cos x/x but it was an infinite loop!!! need an answer for this plz

Answer 8

i have tried finding out integral of cos x/x but it was an infinite loop!!! need an answer for this plz

Answer 9

ntegration by parts is a heuristic rather than a purely mechanical process for solving integrals; given a single function to integrate, the typical strategy is to carefully separate it into a product of two functions ƒ(x)g(x) such that the integral produced by the integration by parts formula is easier to evaluate than the original one.

Answer 10

So it sounds like you tried parts. Which is what I would do. The integral ends up being: \[[\ln(x)\cos(x)+\sin(x)/x]/2 + c\]

Answer 11

uh huh.

Answer 12

how did u get that answer? can u plz explain the steps..

Answer 13

I set u = cos(x) and dv = dx/x and solved for du and v.
Then I put in uv - ∫v du and had to use parts again using u = sin(x) and dv = ln(x)dx and solved for du and v again.
This time I ended up with ln(x)cos(x)+sin(x)/x - ∫cos(x)/x dx = ∫cos(x)/x dx (the original problem) then I added ∫cos(x)/x dx to both sides and divide by two.

Answer 14

hmm..so derv of cos x =-sinx and intg(dv) =1/x dx right?

Answer 15

du = -sin(x)dx and v = ln(x) for the first parts.

Answer 16

the formula is ,
u int (v)- int{d/dx(u) . int(v)}dx right?

Answer 17

∫u dv = u*v - ∫v du is what integration by parts states.

Answer 18

intr(u) dv or integral (uv)?

Answer 19

dont we ve any formula as "something / somethig" in intergral as we ve for derivatives?

Answer 20

This integral cannot be represented in terms of transcendental and algebraic functions. You can only represent it with series.

Answer 21

if we have lower limit as pi/2 and upper one as 3 pi/2 then?

Answer 22

as the sin terms become all zeroes with pi/2 's

Answer 23

It can't be done with any method other than series, even if you constrained the limits.

Answer 24

im sry the cos terms

Answer 25

ohh..isnt there any other way out?

Answer 26

Not from what I researched online. You may be able to use power series. However, u-substitution, backwards u-substitution, integration by parts, partial fractions, etc. will not solve this integral.

If I could remember power series from three years ago I could help, but I don't remember :(

Answer 27

ohh :(...anyways thanks

Answer 28

gotta findout frm somewhere else then

Answer 29

thanks Tbates and jshowa

Answer 30

hey can u just temme how do i join the group chat here??

Answer 31

i have got lot many questions to ask....!!!

Answer 32

anybody there?????

Answer 33

I'm not sure what you do, I tried typing something and it didn't work for me. You can just ask another question.

Answer 34

hmm...

Answer 35

so in such a case we get loops isnt it?

Answer 36

even if got the upper n lower limits for that

Answer 37

can anyone answer this?

Answer 38

I'm not sure, however, I intend on answering this question once I refresh myself with series. So, check back in a day or so.

The limits really don't matter because you still have to evaluate the integral before you use them. And with integration by parts, you will continually get integrals that must be done with parts and it will never end.

You must either construct a power series or Taylor series of cosx/x and estimate the integral.

Answer 39

yeah..that actually does go on n on..

Answer 40

n theres one more thing

Answer 41

n theres one more thing

Answer 42

tangent is a plane and normal is a line on that plane..is this staement correct?

Answer 43

anyone there?

Answer 44

integration by parts would do it

Answer 45

make 1/x your dv and and your u cos(x)

Answer 46

hmm...and how wud the final answer look like?