@Carl Love  I downloaded Maple2019 right now trail version ( for 15 days )  But it has an error in opening . the erorr is about (Load Library faild error 1114) .

@Carl Love Many thanks for your help , do you solved it by WolframAlpha ? or by Maple  ?

Unfortunitly I couldn't understand the meaning or the functions of LommelS1 , StruveH . I just studied the bessel function yet . I need the solution in terms of J1 and J0  , the lecturer want it in terms of J1 and J0 .

@acer The second one is the required {integral of   (ln(x) *BesselJ(1,x)dx ) / X } 

or as in the below photo :