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

1. Sep 23, 2015

tub08918

1. The problem statement, all variables and given/known data
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.
2. Relevant equations

3. 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 doesnt 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 dont 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!?

2. Sep 23, 2015

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.

3. Sep 23, 2015

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 doesnt help me solve this problem