Do the integrals below have solutions? $$\int_{0}^{\infty}\cos(Qt)J_{0}\left(A\sin\left(\frac{t}{2}\right)\right)dt$$ $$\int_{0}^{\infty}\cos(Qt)J_{2}\left(A\sin\left(\frac{t}{2}\right)\right)dt$$ $$\int_{-1}^{1}\cos(Qt)J_{0}\left(A\sqrt{1-t^2}\right)dt$$ $$\int_{-1}^{1}\sin(Qt)J_{0}\left(A\sqrt{1-t^2}\right)dt$$ $$\int_{-1}^{1}\cos(Qt)J_{2}\left(A\sqrt{1-t^2}\right)dt$$ $$\int_{-1}^{1}\sin(Qt)J_{2}\left(A\sqrt{1-t^2}\right)dt$$
where, $A$ and $Q$ are constants; $J_{0}$ and $J_{2}$ are the zetoth and second order Bessel functions of first kind respectively.
Any help would be highly appreciated.