help with exponential integral and square root can somebody help me integrating this: !enter image description here where m, p and q are positive constants. I tired change of variables and searched for the solution but could not find it. Thanks Note: this is the result of mathematica (zeta==a and rho==p): !enter image description here but the Gamma(-0.25-0.5m) is illogical cuz this is infinity (gamma of a negative number) !!

$$\int_0^\infty\dfrac{x^{m-1}e^{-qx}}{(\sqrt{1+px})^{m-0.5}}dx$$

$$=\int_0^\infty x^{m-1}(1+px)^\frac{1-2m}{4}e^{-qx}~dx$$

$$=\int_0^\infty\left(\dfrac{x}{p}\right)^{m-1}(1+x)^\frac{1-2m}{4}~e^{-\frac{qx}{p}}~d\left(\dfrac{x}{p}\right)$$

$$=\int_0^\infty\dfrac{x^{m-1}(1+x)^\frac{1-2m}{4}~e^{-\frac{qx}{p}}}{p^m}dx$$

$$=\dfrac{\Gamma(m)U\left(m,\dfrac{2m+5}{4},\dfrac{q}{p}\right)}{p^m}$$