# Can't figure out this integral

Hello,

I am having trouble with this integral, I don't know how to solve it.

integral(x * cos(x))dx
I tried it in the calculator and it gave me the integral back, and I don't know what method of integration to use to figure it out.
Well if anyone has a solution that would be great, thanks.

berkeman
Mentor
What do you get when you differentiate x * sin(x)?

Do these give you some ideas about what you could differentiate to get to x * cos(x)?

nrqed
Homework Helper
Gold Member
dark_omen said:
Hello,

I am having trouble with this integral, I don't know how to solve it.

integral(x * cos(x))dx
I tried it in the calculator and it gave me the integral back, and I don't know what method of integration to use to figure it out.
Well if anyone has a solution that would be great, thanks.
I would suggest integration by parts. There is on choice of "u" and "dv" that will lead to a very simple form after a single integration by part.s

Okay, I had to do integration by parts twice and I got:
((x^2 * cos(x))/6) + ((x^2 * cos(x))/3), I don't know if that is right though but it's what I came up with.

dark_omen, that answer is not correct.

Here's my solution:

u = x
dv = cos x dx

So:
du = dx
v = sin x

uv - I(v * du) = x sin x - I(sin x dx) = x sin x + cos x.

I've verified this answer in Mathematica as well.

Okay, so I guess I made the wrong choice in u and dv, and that's why my answer didn't come out right. Thanks.

VietDao29
Homework Helper
Guillochon said:
dark_omen, that answer is not correct.

Here's my solution:

u = x
dv = cos x dx

So:
du = dx
v = sin x

uv - I(v * du) = x sin x - I(sin x dx) = x sin x + cos x.

I've verified this answer in Mathematica as well.
:grumpy: :grumpy: :grumpy:
Why can't people just stop to give out COMPLETE solutions?!?!?!
???
Why?!?!?!   What's so tempting about posting complete solutions like that?
Noone bothered to read the rules, eh???
And also, where has the Constant of Integration gone? Vanished?

Last edited:
arildno
Homework Helper
Gold Member
Dearly Missed
Well, I find it excusable in that OP had shown quite a bit of work already.

VietDao29 said:
:grumpy: :grumpy: :grumpy:
Why can't people just stop to give out COMPLETE solutions?!?!?!
???
Why?!?!?!   What's so tempting about posting complete solutions like that?
Noone bothered to read the rules, eh???
And also, where has the Constant of Integration gone? Vanished?

First you chide me for giving out the complete solution. Then you lecture me about not giving the complete solution... :) I thought that since he knew how to take an indefinite integral in the first place, he'd be smart enough to remember the +C.

Anyhow, no, I guess I missed that sentence in the rules. My apologies. Though I don't quite understand why it isn't left to the discretion of the person helping as to how much they want to help.