let be the function
$$ e^{-a|x|^{b}} $$
with $ a,b $ positive numbers bigger than zero
then how could i evaluate this 2 integrals ?
$$ \int_{-\infty}^{\infty}dxe^{-a|x|^{b}}e^{cx}$$
here 'c' can be either positive or negative or even pure complex (Fourier transform)
also how i would evaluate the Fourier cosine trasnform
$$ \int_{0}^{\infty}dxe^{-a|x|^{b}}cos(cx)$$
thanks in advance if possible give a hinto of course i know tht i could expand the function in powers of $ |x| $ but if possible i would like a closed answer thanks.