I would like to ask whether there exists a closed form formula for computing an integral of the modified Bessel function of the first kind zero order. In more detail, an integral including something close to the following: $$ \int_0^\infty x^a e^{-bx^c} I_0(dx) x \,dx $$
$a , b , c , d > 0$
In general, I get the idea that any integral including a modified Bessel function of the first order and simple power or exponential expressions can be expressed in closed form. Is this true?
Thanks in advance for both your time and patience :)