Efficient Solution for Integrating cos(x)/(x^4) | Integration Homework Help

[kyrax]

Homework Statement

integral of cos(x)/(x^4)

Homework Equations

The Attempt at a Solution

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

 

[rock.freak667]

Homework Statement

integral of cos(x)/(x^4)

Homework Equations

The Attempt at a Solution

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

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

 

[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.

 

[NJunJie]

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

 

[zcd]

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

 

[Hootenanny]

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.

 

[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<br /> \left( x \right) }{{x}^{2}}}+\frac{1}{6}\,{\frac {\cos \left( x \right) }{x}}<br /> +\frac{1}{6}\,{\rm Si} \left( x \right) <br />