Calculate integral sin(x)/x^0.1dx from pi to infinity

[tub08918]

Homework Statement

So I have a problem with the integral

∫ sin(x)/x^0.1dx from pi to infinity

My teacher said this wouldn't require any maths beyond calc 3, but for some reason I cannot come up with a solution.

Homework Equations

The Attempt at a Solution

I have attempted a maclaurin series to replace the sin(x) term but the series does not converge so that doesn't work.
I tried integration by parts which just keeps reppeating the sin and cos terms with x^.1 in the denominator

I attempted substitution but that clearly doesn't work.
I even attempted contour integration but I don't think that could be the solution as we have not done that yet and that is not at the calc 3 level.

Is there anything I'm mising!?

 

[andrewkirk]

If it's any consolation, Wolfram Alpha gives the indefinite integral of this function as a complicated function involving imaginary numbers and the Incomplete Gamma Function, neither of which would typically be covered in introductory calculus courses.

 

[tub08918]

That's literally the first thing I did was to plug it into wolfram alpha! THats how I knew this wasn't going to be a picnic. The professor says that there is something in calc 3 I would've learned that makes solving this possible but I have no idea what (the professor is Russian btw) and he refuses to give out more info than that. The only thing I can maybe see is that sin(x) can be replaced by 1 and we can find the limit like that and see that it converges but that doesn't help me solve this problem