# Integral of $\sin(x)\cdot x^n$ [duplicate]

The integral is as:

$$\int_0^\infty\sin\left(x\right)\times x^{n}\;\mathbb{d}x$$ Where $n\in\mathfrak{R}$.

I was able to find the convergence of this integral using Dirichlet's test, which implied $-2<n<0$.

But the hard part is to find the value of this integral for me. Wolfram alpha gives the answer as:
http://www.wolframalpha.com/input/?i=integrate+sin%28t%29*t^c+from+t%3D0+to+t%3Dinfinity

Which is very close to gamma function. So i tried to assume integral of form $$\int_0^\infty e^{-ix}\times x^n\;\mathbb{d}x$$

So that i would take the $-\mathfrak{Im}$ part of this integral. But I still have no idea how to evaluate this.