how to prove an identity related to $\int_0^\infty\sin(x^{1-a})dx$?

how to prove an identity related to $\int_0^\infty\sin(x^{1-a})dx$?

i have made some experiments in maple evaluating the integral
$$\int_0^\infty\sin(x^{1+a})dx$$ and the computer give me the following
result
$$\int_0^\infty\sin(x^{1+a})dx=\frac{\sqrt{\pi}2^{\frac{2}{2+2a}}\Gamma(\frac{1}{2}+\frac{1}{2+2a})}{(2+2a)\Gamma(1-\frac{1}{2+2a})}$$
and i realy want to know how can i prove that. i hope some of you can help
me. An interesting thing is that de right side converges to $1$ when $a$
goes to $0$.