# Homework Help: Help with this integration!

1. Sep 2, 2009

### kyrax

1. The problem statement, all variables and given/known data
integral of cos(x)/(x^4)

2. Relevant equations

3. The attempt at a solution

tried using integration by parts but lead to tons of work!. is there a simpler way?

2. Sep 2, 2009

### rock.freak667

Don't think there is a simpler way. u=cos(x); dv=1/x4 dx.

3. Sep 2, 2009

### Bohrok

You won't be able to find an integral in elementary functions, so I suggest you don't bother with it, unless you wrote the problem incorrectly.

4. Sep 2, 2009

### NJunJie

Cauchy Integral formula helps right? unless you are talking about Integral in complex plane.

5. Sep 3, 2009

### zcd

If it's an indefinite integral you could rewrite it as a taylor series.

6. Sep 3, 2009

### Hootenanny

Staff Emeritus
As Bohrok suggests, the integral has no anti-derivative in terms of elementary functions. However, if it is a definite integral, it may be possible to write a solution in terms of non-elementary functions.

7. Sep 3, 2009

### g_edgar

Integrate by parts 3 times, then recognize the "sine integral" function
$$-\frac{1}{3}\,{\frac {\cos \left( x \right) }{{x}^{3}}}+\frac{1}{6}\,{\frac {\sin \left( x \right) }{{x}^{2}}}+\frac{1}{6}\,{\frac {\cos \left( x \right) }{x}} +\frac{1}{6}\,{\rm Si} \left( x \right)$$