Help in Integration?

Question

Hi, can anybody help me solving this integeration ?
Using this substitution:
x = p - t
Integerate
I = ∫(x.sin(x).dx)/(1+cos(x)^2)
From 0 to p.

Thank you guys for trying.
First, the integration is what I wrote, I mean that the fraction is right.
Second, I'm studying IT in Damascus University and yesterday my friend called me and asked me this question so I think that it may be (x = pi - t), so I'll check it from ymy friend, I put this question here when I had tried for about 3 hours.

ps: we can write the dx atop the fraction or on its right it doesn't matter but because I'm writing without an equation editor I put it with the x.sinx.

Thank you all again I'll check it and reply to you.

Sorry guys, it's pi not p.
It's not my fault, when we were in the fifth grade our teachers pronunced pi as we pronounce p, so we growed and we still pronounce it p, just a year ago I figuered how it's pronounced but not my all friends did.

But I solved it three times and I got :
I = (Pi^2)/4
Or
I = -(Pi^2)/4

not Pi/4!

Answer 1

This cannot be integrated in case it is indefinite integral

I think you want to integrate not from 0 to p but from 0 to pi

I = int x sin x/(1+cos^ 2x )

let f(x) = x sin x / (1+ cos^2 x)

now f(pi-x) = (pi -x) sin (x)/(1+ cos ^ 2x)
both are same as it is symteric about x = pi/2

add to get f(x) + f(pi-x) = pi sin x/(1 + cos ^2 x)

now u can integrate by putting cos x = t

f(x) + f(pi-x) = - lntegrate (1/(1+t^2) = - tan^-1(t)

2int f(x) = -tan^-1(cosx) = tan^-1(1) - tan ^-1(-1) = pi/4+pi/4
integral = pi/4

Answer 2

I am with the others on this. The substitution is of no help and only makes the integral more complicated.

I am not even sure that I = ∫(x.sin(x).dx)/(1+(cosx)^2) would be any easier as has been suggested.

I wonder if the question should be I = ∫(x.sin(x)^2.dx)/(1+cos(x)^2) and then I could do it for you.

Answer 3

its that annoying x^2 thats the trouble... if it was 1+(cosx)^2 then u cud use basic trig identity to change it into (sinx)^2 and solve the integral part using integration by parts, andthen dividing through by (sinx)^2.
although to be honest i cant see how the sustitution you have used will work as it has two new variables. thus when you try to substitute into the integral, substituting for "dx" will be a problem as there are two variables leading to problems defining dx in terms of those two variables, this is something i have not learnt.
good luck though, interesting question.
ps, one more thing, is the dx meant to be where it is or should it be right at the end of the integral

Answer 4

When I first saw a question on integration, I clicked on it just to tell you not to be lazy and try. When I saw the question however, It is not that easy after all. I am still working on it but I do not see how your substitution would work. I will get back to you if I get the answer (so check out later)
Nice question.
cheers to math_kp. well done.

Answer 5

Look buddy,I really think your integration is x.Sinx /(1+ Cos²x).
Unless you are the student of Pure Math or something.
Please add details if the fraction is typed correctly or my fraction explains better